diff options
Diffstat (limited to 'vendor/golang.org/x/crypto')
| -rw-r--r-- | vendor/golang.org/x/crypto/acme/acme.go | 441 | ||||
| -rw-r--r-- | vendor/golang.org/x/crypto/acme/autocert/autocert.go | 126 | ||||
| -rw-r--r-- | vendor/golang.org/x/crypto/acme/autocert/renewal.go | 35 | ||||
| -rw-r--r-- | vendor/golang.org/x/crypto/acme/jws.go | 13 | ||||
| -rw-r--r-- | vendor/golang.org/x/crypto/acme/rfc8555.go | 2 | ||||
| -rw-r--r-- | vendor/golang.org/x/crypto/acme/types.go | 8 | ||||
| -rw-r--r-- | vendor/golang.org/x/crypto/ed25519/ed25519.go | 188 | ||||
| -rw-r--r-- | vendor/golang.org/x/crypto/ed25519/ed25519_go113.go | 74 | ||||
| -rw-r--r-- | vendor/golang.org/x/crypto/ed25519/internal/edwards25519/const.go | 1422 | ||||
| -rw-r--r-- | vendor/golang.org/x/crypto/ed25519/internal/edwards25519/edwards25519.go | 1793 | ||||
| -rw-r--r-- | vendor/golang.org/x/crypto/ssh/cipher.go | 8 | ||||
| -rw-r--r-- | vendor/golang.org/x/crypto/ssh/server.go | 24 |
12 files changed, 191 insertions, 3943 deletions
diff --git a/vendor/golang.org/x/crypto/acme/acme.go b/vendor/golang.org/x/crypto/acme/acme.go index 73b19ef3..f2d23f69 100644 --- a/vendor/golang.org/x/crypto/acme/acme.go +++ b/vendor/golang.org/x/crypto/acme/acme.go @@ -3,17 +3,20 @@ // license that can be found in the LICENSE file. // Package acme provides an implementation of the -// Automatic Certificate Management Environment (ACME) spec. -// The initial implementation was based on ACME draft-02 and -// is now being extended to comply with RFC 8555. -// See https://tools.ietf.org/html/draft-ietf-acme-acme-02 -// and https://tools.ietf.org/html/rfc8555 for details. +// Automatic Certificate Management Environment (ACME) spec, +// most famously used by Let's Encrypt. +// +// The initial implementation of this package was based on an early version +// of the spec. The current implementation supports only the modern +// RFC 8555 but some of the old API surface remains for compatibility. +// While code using the old API will still compile, it will return an error. +// Note the deprecation comments to update your code. +// +// See https://tools.ietf.org/html/rfc8555 for the spec. // // Most common scenarios will want to use autocert subdirectory instead, // which provides automatic access to certificates from Let's Encrypt // and any other ACME-based CA. -// -// This package is a work in progress and makes no API stability promises. package acme import ( @@ -33,8 +36,6 @@ import ( "encoding/pem" "errors" "fmt" - "io" - "io/ioutil" "math/big" "net/http" "strings" @@ -72,6 +73,7 @@ const ( ) // Client is an ACME client. +// // The only required field is Key. An example of creating a client with a new key // is as follows: // @@ -125,7 +127,9 @@ type Client struct { cacheMu sync.Mutex dir *Directory // cached result of Client's Discover method - kid keyID // cached Account.URI obtained from registerRFC or getAccountRFC + // KID is the key identifier provided by the CA. If not provided it will be + // retrieved from the CA by making a call to the registration endpoint. + KID KeyID noncesMu sync.Mutex nonces map[string]struct{} // nonces collected from previous responses @@ -140,23 +144,22 @@ type Client struct { // // When in pre-RFC mode or when c.getRegRFC responds with an error, accountKID // returns noKeyID. -func (c *Client) accountKID(ctx context.Context) keyID { +func (c *Client) accountKID(ctx context.Context) KeyID { c.cacheMu.Lock() defer c.cacheMu.Unlock() - if !c.dir.rfcCompliant() { - return noKeyID - } - if c.kid != noKeyID { - return c.kid + if c.KID != noKeyID { + return c.KID } a, err := c.getRegRFC(ctx) if err != nil { return noKeyID } - c.kid = keyID(a.URI) - return c.kid + c.KID = KeyID(a.URI) + return c.KID } +var errPreRFC = errors.New("acme: server does not support the RFC 8555 version of ACME") + // Discover performs ACME server discovery using c.DirectoryURL. // // It caches successful result. So, subsequent calls will not result in @@ -177,53 +180,36 @@ func (c *Client) Discover(ctx context.Context) (Directory, error) { c.addNonce(res.Header) var v struct { - Reg string `json:"new-reg"` - RegRFC string `json:"newAccount"` - Authz string `json:"new-authz"` - AuthzRFC string `json:"newAuthz"` - OrderRFC string `json:"newOrder"` - Cert string `json:"new-cert"` - Revoke string `json:"revoke-cert"` - RevokeRFC string `json:"revokeCert"` - NonceRFC string `json:"newNonce"` - KeyChangeRFC string `json:"keyChange"` - Meta struct { - Terms string `json:"terms-of-service"` - TermsRFC string `json:"termsOfService"` - WebsiteRFC string `json:"website"` - CAA []string `json:"caa-identities"` - CAARFC []string `json:"caaIdentities"` - ExternalAcctRFC bool `json:"externalAccountRequired"` + Reg string `json:"newAccount"` + Authz string `json:"newAuthz"` + Order string `json:"newOrder"` + Revoke string `json:"revokeCert"` + Nonce string `json:"newNonce"` + KeyChange string `json:"keyChange"` + Meta struct { + Terms string `json:"termsOfService"` + Website string `json:"website"` + CAA []string `json:"caaIdentities"` + ExternalAcct bool `json:"externalAccountRequired"` } } if err := json.NewDecoder(res.Body).Decode(&v); err != nil { return Directory{}, err } - if v.OrderRFC == "" { - // Non-RFC compliant ACME CA. - c.dir = &Directory{ - RegURL: v.Reg, - AuthzURL: v.Authz, - CertURL: v.Cert, - RevokeURL: v.Revoke, - Terms: v.Meta.Terms, - Website: v.Meta.WebsiteRFC, - CAA: v.Meta.CAA, - } - return *c.dir, nil + if v.Order == "" { + return Directory{}, errPreRFC } - // RFC compliant ACME CA. c.dir = &Directory{ - RegURL: v.RegRFC, - AuthzURL: v.AuthzRFC, - OrderURL: v.OrderRFC, - RevokeURL: v.RevokeRFC, - NonceURL: v.NonceRFC, - KeyChangeURL: v.KeyChangeRFC, - Terms: v.Meta.TermsRFC, - Website: v.Meta.WebsiteRFC, - CAA: v.Meta.CAARFC, - ExternalAccountRequired: v.Meta.ExternalAcctRFC, + RegURL: v.Reg, + AuthzURL: v.Authz, + OrderURL: v.Order, + RevokeURL: v.Revoke, + NonceURL: v.Nonce, + KeyChangeURL: v.KeyChange, + Terms: v.Meta.Terms, + Website: v.Meta.Website, + CAA: v.Meta.CAA, + ExternalAccountRequired: v.Meta.ExternalAcct, } return *c.dir, nil } @@ -235,55 +221,11 @@ func (c *Client) directoryURL() string { return LetsEncryptURL } -// CreateCert requests a new certificate using the Certificate Signing Request csr encoded in DER format. -// It is incompatible with RFC 8555. Callers should use CreateOrderCert when interfacing -// with an RFC-compliant CA. +// CreateCert was part of the old version of ACME. It is incompatible with RFC 8555. // -// The exp argument indicates the desired certificate validity duration. CA may issue a certificate -// with a different duration. -// If the bundle argument is true, the returned value will also contain the CA (issuer) certificate chain. -// -// In the case where CA server does not provide the issued certificate in the response, -// CreateCert will poll certURL using c.FetchCert, which will result in additional round-trips. -// In such a scenario, the caller can cancel the polling with ctx. -// -// CreateCert returns an error if the CA's response or chain was unreasonably large. -// Callers are encouraged to parse the returned value to ensure the certificate is valid and has the expected features. +// Deprecated: this was for the pre-RFC 8555 version of ACME. Callers should use CreateOrderCert. func (c *Client) CreateCert(ctx context.Context, csr []byte, exp time.Duration, bundle bool) (der [][]byte, certURL string, err error) { - if _, err := c.Discover(ctx); err != nil { - return nil, "", err - } - - req := struct { - Resource string `json:"resource"` - CSR string `json:"csr"` - NotBefore string `json:"notBefore,omitempty"` - NotAfter string `json:"notAfter,omitempty"` - }{ - Resource: "new-cert", - CSR: base64.RawURLEncoding.EncodeToString(csr), - } - now := timeNow() - req.NotBefore = now.Format(time.RFC3339) - if exp > 0 { - req.NotAfter = now.Add(exp).Format(time.RFC3339) - } - - res, err := c.post(ctx, nil, c.dir.CertURL, req, wantStatus(http.StatusCreated)) - if err != nil { - return nil, "", err - } - defer res.Body.Close() - - curl := res.Header.Get("Location") // cert permanent URL - if res.ContentLength == 0 { - // no cert in the body; poll until we get it - cert, err := c.FetchCert(ctx, curl, bundle) - return cert, curl, err - } - // slurp issued cert and CA chain, if requested - cert, err := c.responseCert(ctx, res, bundle) - return cert, curl, err + return nil, "", errPreRFC } // FetchCert retrieves already issued certificate from the given url, in DER format. @@ -297,20 +239,10 @@ func (c *Client) CreateCert(ctx context.Context, csr []byte, exp time.Duration, // Callers are encouraged to parse the returned value to ensure the certificate is valid // and has expected features. func (c *Client) FetchCert(ctx context.Context, url string, bundle bool) ([][]byte, error) { - dir, err := c.Discover(ctx) - if err != nil { - return nil, err - } - if dir.rfcCompliant() { - return c.fetchCertRFC(ctx, url, bundle) - } - - // Legacy non-authenticated GET request. - res, err := c.get(ctx, url, wantStatus(http.StatusOK)) - if err != nil { + if _, err := c.Discover(ctx); err != nil { return nil, err } - return c.responseCert(ctx, res, bundle) + return c.fetchCertRFC(ctx, url, bundle) } // RevokeCert revokes a previously issued certificate cert, provided in DER format. @@ -320,30 +252,10 @@ func (c *Client) FetchCert(ctx context.Context, url string, bundle bool) ([][]by // For instance, the key pair of the certificate may be authorized. // If the key is nil, c.Key is used instead. func (c *Client) RevokeCert(ctx context.Context, key crypto.Signer, cert []byte, reason CRLReasonCode) error { - dir, err := c.Discover(ctx) - if err != nil { - return err - } - if dir.rfcCompliant() { - return c.revokeCertRFC(ctx, key, cert, reason) - } - - // Legacy CA. - body := &struct { - Resource string `json:"resource"` - Cert string `json:"certificate"` - Reason int `json:"reason"` - }{ - Resource: "revoke-cert", - Cert: base64.RawURLEncoding.EncodeToString(cert), - Reason: int(reason), - } - res, err := c.post(ctx, key, dir.RevokeURL, body, wantStatus(http.StatusOK)) - if err != nil { + if _, err := c.Discover(ctx); err != nil { return err } - defer res.Body.Close() - return nil + return c.revokeCertRFC(ctx, key, cert, reason) } // AcceptTOS always returns true to indicate the acceptance of a CA's Terms of Service @@ -366,75 +278,33 @@ func (c *Client) Register(ctx context.Context, acct *Account, prompt func(tosURL if c.Key == nil { return nil, errors.New("acme: client.Key must be set to Register") } - - dir, err := c.Discover(ctx) - if err != nil { - return nil, err - } - if dir.rfcCompliant() { - return c.registerRFC(ctx, acct, prompt) - } - - // Legacy ACME draft registration flow. - a, err := c.doReg(ctx, dir.RegURL, "new-reg", acct) - if err != nil { + if _, err := c.Discover(ctx); err != nil { return nil, err } - var accept bool - if a.CurrentTerms != "" && a.CurrentTerms != a.AgreedTerms { - accept = prompt(a.CurrentTerms) - } - if accept { - a.AgreedTerms = a.CurrentTerms - a, err = c.UpdateReg(ctx, a) - } - return a, err + return c.registerRFC(ctx, acct, prompt) } // GetReg retrieves an existing account associated with c.Key. // -// The url argument is an Account URI used with pre-RFC 8555 CAs. -// It is ignored when interfacing with an RFC-compliant CA. +// The url argument is a legacy artifact of the pre-RFC 8555 API +// and is ignored. func (c *Client) GetReg(ctx context.Context, url string) (*Account, error) { - dir, err := c.Discover(ctx) - if err != nil { - return nil, err - } - if dir.rfcCompliant() { - return c.getRegRFC(ctx) - } - - // Legacy CA. - a, err := c.doReg(ctx, url, "reg", nil) - if err != nil { + if _, err := c.Discover(ctx); err != nil { return nil, err } - a.URI = url - return a, nil + return c.getRegRFC(ctx) } // UpdateReg updates an existing registration. // It returns an updated account copy. The provided account is not modified. // -// When interfacing with RFC-compliant CAs, a.URI is ignored and the account URL -// associated with c.Key is used instead. +// The account's URI is ignored and the account URL associated with +// c.Key is used instead. func (c *Client) UpdateReg(ctx context.Context, acct *Account) (*Account, error) { - dir, err := c.Discover(ctx) - if err != nil { - return nil, err - } - if dir.rfcCompliant() { - return c.updateRegRFC(ctx, acct) - } - - // Legacy CA. - uri := acct.URI - a, err := c.doReg(ctx, uri, "reg", acct) - if err != nil { + if _, err := c.Discover(ctx); err != nil { return nil, err } - a.URI = uri - return a, nil + return c.updateRegRFC(ctx, acct) } // Authorize performs the initial step in the pre-authorization flow, @@ -503,17 +373,11 @@ func (c *Client) authorize(ctx context.Context, typ, val string) (*Authorization // If a caller needs to poll an authorization until its status is final, // see the WaitAuthorization method. func (c *Client) GetAuthorization(ctx context.Context, url string) (*Authorization, error) { - dir, err := c.Discover(ctx) - if err != nil { + if _, err := c.Discover(ctx); err != nil { return nil, err } - var res *http.Response - if dir.rfcCompliant() { - res, err = c.postAsGet(ctx, url, wantStatus(http.StatusOK)) - } else { - res, err = c.get(ctx, url, wantStatus(http.StatusOK, http.StatusAccepted)) - } + res, err := c.postAsGet(ctx, url, wantStatus(http.StatusOK)) if err != nil { return nil, err } @@ -535,7 +399,6 @@ func (c *Client) GetAuthorization(ctx context.Context, url string) (*Authorizati // // It does not revoke existing certificates. func (c *Client) RevokeAuthorization(ctx context.Context, url string) error { - // Required for c.accountKID() when in RFC mode. if _, err := c.Discover(ctx); err != nil { return err } @@ -565,18 +428,11 @@ func (c *Client) RevokeAuthorization(ctx context.Context, url string) error { // In all other cases WaitAuthorization returns an error. // If the Status is StatusInvalid, the returned error is of type *AuthorizationError. func (c *Client) WaitAuthorization(ctx context.Context, url string) (*Authorization, error) { - // Required for c.accountKID() when in RFC mode. - dir, err := c.Discover(ctx) - if err != nil { + if _, err := c.Discover(ctx); err != nil { return nil, err } - getfn := c.postAsGet - if !dir.rfcCompliant() { - getfn = c.get - } - for { - res, err := getfn(ctx, url, wantStatus(http.StatusOK, http.StatusAccepted)) + res, err := c.postAsGet(ctx, url, wantStatus(http.StatusOK, http.StatusAccepted)) if err != nil { return nil, err } @@ -619,17 +475,11 @@ func (c *Client) WaitAuthorization(ctx context.Context, url string) (*Authorizat // // A client typically polls a challenge status using this method. func (c *Client) GetChallenge(ctx context.Context, url string) (*Challenge, error) { - // Required for c.accountKID() when in RFC mode. - dir, err := c.Discover(ctx) - if err != nil { + if _, err := c.Discover(ctx); err != nil { return nil, err } - getfn := c.postAsGet - if !dir.rfcCompliant() { - getfn = c.get - } - res, err := getfn(ctx, url, wantStatus(http.StatusOK, http.StatusAccepted)) + res, err := c.postAsGet(ctx, url, wantStatus(http.StatusOK, http.StatusAccepted)) if err != nil { return nil, err } @@ -647,29 +497,11 @@ func (c *Client) GetChallenge(ctx context.Context, url string) (*Challenge, erro // // The server will then perform the validation asynchronously. func (c *Client) Accept(ctx context.Context, chal *Challenge) (*Challenge, error) { - // Required for c.accountKID() when in RFC mode. - dir, err := c.Discover(ctx) - if err != nil { + if _, err := c.Discover(ctx); err != nil { return nil, err } - var req interface{} = json.RawMessage("{}") // RFC-compliant CA - if !dir.rfcCompliant() { - auth, err := keyAuth(c.Key.Public(), chal.Token) - if err != nil { - return nil, err - } - req = struct { - Resource string `json:"resource"` - Type string `json:"type"` - Auth string `json:"keyAuthorization"` - }{ - Resource: "challenge", - Type: chal.Type, - Auth: auth, - } - } - res, err := c.post(ctx, nil, chal.URI, req, wantStatus( + res, err := c.post(ctx, nil, chal.URI, json.RawMessage("{}"), wantStatus( http.StatusOK, // according to the spec http.StatusAccepted, // Let's Encrypt: see https://goo.gl/WsJ7VT (acme-divergences.md) )) @@ -720,7 +552,7 @@ func (c *Client) HTTP01ChallengePath(token string) string { // TLSSNI01ChallengeCert creates a certificate for TLS-SNI-01 challenge response. // -// Deprecated: This challenge type is unused in both draft-02 and RFC versions of ACME spec. +// Deprecated: This challenge type is unused in both draft-02 and RFC versions of the ACME spec. func (c *Client) TLSSNI01ChallengeCert(token string, opt ...CertOption) (cert tls.Certificate, name string, err error) { ka, err := keyAuth(c.Key.Public(), token) if err != nil { @@ -738,7 +570,7 @@ func (c *Client) TLSSNI01ChallengeCert(token string, opt ...CertOption) (cert tl // TLSSNI02ChallengeCert creates a certificate for TLS-SNI-02 challenge response. // -// Deprecated: This challenge type is unused in both draft-02 and RFC versions of ACME spec. +// Deprecated: This challenge type is unused in both draft-02 and RFC versions of the ACME spec. func (c *Client) TLSSNI02ChallengeCert(token string, opt ...CertOption) (cert tls.Certificate, name string, err error) { b := sha256.Sum256([]byte(token)) h := hex.EncodeToString(b[:]) @@ -805,63 +637,6 @@ func (c *Client) TLSALPN01ChallengeCert(token, domain string, opt ...CertOption) return tlsChallengeCert([]string{domain}, newOpt) } -// doReg sends all types of registration requests the old way (pre-RFC world). -// The type of request is identified by typ argument, which is a "resource" -// in the ACME spec terms. -// -// A non-nil acct argument indicates whether the intention is to mutate data -// of the Account. Only Contact and Agreement of its fields are used -// in such cases. -func (c *Client) doReg(ctx context.Context, url string, typ string, acct *Account) (*Account, error) { - req := struct { - Resource string `json:"resource"` - Contact []string `json:"contact,omitempty"` - Agreement string `json:"agreement,omitempty"` - }{ - Resource: typ, - } - if acct != nil { - req.Contact = acct.Contact - req.Agreement = acct.AgreedTerms - } - res, err := c.post(ctx, nil, url, req, wantStatus( - http.StatusOK, // updates and deletes - http.StatusCreated, // new account creation - http.StatusAccepted, // Let's Encrypt divergent implementation - )) - if err != nil { - return nil, err - } - defer res.Body.Close() - - var v struct { - Contact []string - Agreement string - Authorizations string - Certificates string - } - if err := json.NewDecoder(res.Body).Decode(&v); err != nil { - return nil, fmt.Errorf("acme: invalid response: %v", err) - } - var tos string - if v := linkHeader(res.Header, "terms-of-service"); len(v) > 0 { - tos = v[0] - } - var authz string - if v := linkHeader(res.Header, "next"); len(v) > 0 { - authz = v[0] - } - return &Account{ - URI: res.Header.Get("Location"), - Contact: v.Contact, - AgreedTerms: v.Agreement, - CurrentTerms: tos, - Authz: authz, - Authorizations: v.Authorizations, - Certificates: v.Certificates, - }, nil -} - // popNonce returns a nonce value previously stored with c.addNonce // or fetches a fresh one from c.dir.NonceURL. // If NonceURL is empty, it first tries c.directoryURL() and, failing that, @@ -936,78 +711,6 @@ func nonceFromHeader(h http.Header) string { return h.Get("Replay-Nonce") } -func (c *Client) responseCert(ctx context.Context, res *http.Response, bundle bool) ([][]byte, error) { - b, err := ioutil.ReadAll(io.LimitReader(res.Body, maxCertSize+1)) - if err != nil { - return nil, fmt.Errorf("acme: response stream: %v", err) - } - if len(b) > maxCertSize { - return nil, errors.New("acme: certificate is too big") - } - cert := [][]byte{b} - if !bundle { - return cert, nil - } - - // Append CA chain cert(s). - // At least one is required according to the spec: - // https://tools.ietf.org/html/draft-ietf-acme-acme-03#section-6.3.1 - up := linkHeader(res.Header, "up") - if len(up) == 0 { - return nil, errors.New("acme: rel=up link not found") - } - if len(up) > maxChainLen { - return nil, errors.New("acme: rel=up link is too large") - } - for _, url := range up { - cc, err := c.chainCert(ctx, url, 0) - if err != nil { - return nil, err - } - cert = append(cert, cc...) - } - return cert, nil -} - -// chainCert fetches CA certificate chain recursively by following "up" links. -// Each recursive call increments the depth by 1, resulting in an error -// if the recursion level reaches maxChainLen. -// -// First chainCert call starts with depth of 0. -func (c *Client) chainCert(ctx context.Context, url string, depth int) ([][]byte, error) { - if depth >= maxChainLen { - return nil, errors.New("acme: certificate chain is too deep") - } - - res, err := c.get(ctx, url, wantStatus(http.StatusOK)) - if err != nil { - return nil, err - } - defer res.Body.Close() - b, err := ioutil.ReadAll(io.LimitReader(res.Body, maxCertSize+1)) - if err != nil { - return nil, err - } - if len(b) > maxCertSize { - return nil, errors.New("acme: certificate is too big") - } - chain := [][]byte{b} - - uplink := linkHeader(res.Header, "up") - if len(uplink) > maxChainLen { - return nil, errors.New("acme: certificate chain is too large") - } - for _, up := range uplink { - cc, err := c.chainCert(ctx, up, depth+1) - if err != nil { - return nil, err - } - chain = append(chain, cc...) - } - - return chain, nil -} - // linkHeader returns URI-Reference values of all Link headers // with relation-type rel. // See https://tools.ietf.org/html/rfc5988#section-5 for details. @@ -1098,5 +801,5 @@ func encodePEM(typ string, b []byte) []byte { return pem.EncodeToMemory(pb) } -// timeNow is useful for testing for fixed current time. +// timeNow is time.Now, except in tests which can mess with it. var timeNow = time.Now diff --git a/vendor/golang.org/x/crypto/acme/autocert/autocert.go b/vendor/golang.org/x/crypto/acme/autocert/autocert.go index c7fbc54c..1858184e 100644 --- a/vendor/golang.org/x/crypto/acme/autocert/autocert.go +++ b/vendor/golang.org/x/crypto/acme/autocert/autocert.go @@ -47,6 +47,8 @@ var createCertRetryAfter = time.Minute // pseudoRand is safe for concurrent use. var pseudoRand *lockedMathRand +var errPreRFC = errors.New("autocert: ACME server doesn't support RFC 8555") + func init() { src := mathrand.NewSource(time.Now().UnixNano()) pseudoRand = &lockedMathRand{rnd: mathrand.New(src)} @@ -456,7 +458,7 @@ func (m *Manager) cert(ctx context.Context, ck certKey) (*tls.Certificate, error leaf: cert.Leaf, } m.state[ck] = s - go m.renew(ck, s.key, s.leaf.NotAfter) + go m.startRenew(ck, s.key, s.leaf.NotAfter) return cert, nil } @@ -582,8 +584,9 @@ func (m *Manager) createCert(ctx context.Context, ck certKey) (*tls.Certificate, if err != nil { // Remove the failed state after some time, // making the manager call createCert again on the following TLS hello. + didRemove := testDidRemoveState // The lifetime of this timer is untracked, so copy mutable local state to avoid races. time.AfterFunc(createCertRetryAfter, func() { - defer testDidRemoveState(ck) + defer didRemove(ck) m.stateMu.Lock() defer m.stateMu.Unlock() // Verify the state hasn't changed and it's still invalid @@ -601,7 +604,7 @@ func (m *Manager) createCert(ctx context.Context, ck certKey) (*tls.Certificate, } state.cert = der state.leaf = leaf - go m.renew(ck, state.key, state.leaf.NotAfter) + go m.startRenew(ck, state.key, state.leaf.NotAfter) return state.tlscert() } @@ -658,99 +661,24 @@ func (m *Manager) authorizedCert(ctx context.Context, key crypto.Signer, ck cert if err != nil { return nil, nil, err } + if dir.OrderURL == "" { + return nil, nil, errPreRFC + } - var chain [][]byte - switch { - // Pre-RFC legacy CA. - case dir.OrderURL == "": - if err := m.verify(ctx, client, ck.domain); err != nil { - return nil, nil, err - } - der, _, err := client.CreateCert(ctx, csr, 0, true) - if err != nil { - return nil, nil, err - } - chain = der - // RFC 8555 compliant CA. - default: - o, err := m.verifyRFC(ctx, client, ck.domain) - if err != nil { - return nil, nil, err - } - der, _, err := client.CreateOrderCert(ctx, o.FinalizeURL, csr, true) - if err != nil { - return nil, nil, err - } - chain = der + o, err := m.verifyRFC(ctx, client, ck.domain) + if err != nil { + return nil, nil, err } - leaf, err = validCert(ck, chain, key, m.now()) + chain, _, err := client.CreateOrderCert(ctx, o.FinalizeURL, csr, true) if err != nil { return nil, nil, err } - return chain, leaf, nil -} - -// verify runs the identifier (domain) pre-authorization flow for legacy CAs -// using each applicable ACME challenge type. -func (m *Manager) verify(ctx context.Context, client *acme.Client, domain string) error { - // Remove all hanging authorizations to reduce rate limit quotas - // after we're done. - var authzURLs []string - defer func() { - go m.deactivatePendingAuthz(authzURLs) - }() - - // errs accumulates challenge failure errors, printed if all fail - errs := make(map[*acme.Challenge]error) - challengeTypes := m.supportedChallengeTypes() - var nextTyp int // challengeType index of the next challenge type to try - for { - // Start domain authorization and get the challenge. - authz, err := client.Authorize(ctx, domain) - if err != nil { - return err - } - authzURLs = append(authzURLs, authz.URI) - // No point in accepting challenges if the authorization status - // is in a final state. - switch authz.Status { - case acme.StatusValid: - return nil // already authorized - case acme.StatusInvalid: - return fmt.Errorf("acme/autocert: invalid authorization %q", authz.URI) - } - - // Pick the next preferred challenge. - var chal *acme.Challenge - for chal == nil && nextTyp < len(challengeTypes) { - chal = pickChallenge(challengeTypes[nextTyp], authz.Challenges) - nextTyp++ - } - if chal == nil { - errorMsg := fmt.Sprintf("acme/autocert: unable to authorize %q", domain) - for chal, err := range errs { - errorMsg += fmt.Sprintf("; challenge %q failed with error: %v", chal.Type, err) - } - return errors.New(errorMsg) - } - cleanup, err := m.fulfill(ctx, client, chal, domain) - if err != nil { - errs[chal] = err - continue - } - defer cleanup() - if _, err := client.Accept(ctx, chal); err != nil { - errs[chal] = err - continue - } - // A challenge is fulfilled and accepted: wait for the CA to validate. - if _, err := client.WaitAuthorization(ctx, authz.URI); err != nil { - errs[chal] = err - continue - } - return nil + leaf, err = validCert(ck, chain, key, m.now()) + if err != nil { + return nil, nil, err } + return chain, leaf, nil } // verifyRFC runs the identifier (domain) order-based authorization flow for RFC compliant CAs @@ -966,7 +894,7 @@ func httpTokenCacheKey(tokenPath string) string { return path.Base(tokenPath) + "+http-01" } -// renew starts a cert renewal timer loop, one per domain. +// startRenew starts a cert renewal timer loop, one per domain. // // The loop is scheduled in two cases: // - a cert was fetched from cache for the first time (wasn't in m.state) @@ -974,7 +902,7 @@ func httpTokenCacheKey(tokenPath string) string { // // The key argument is a certificate private key. // The exp argument is the cert expiration time (NotAfter). -func (m *Manager) renew(ck certKey, key crypto.Signer, exp time.Time) { +func (m *Manager) startRenew(ck certKey, key crypto.Signer, exp time.Time) { m.renewalMu.Lock() defer m.renewalMu.Unlock() if m.renewal[ck] != nil { @@ -1200,6 +1128,10 @@ func validCert(ck certKey, der [][]byte, key crypto.Signer, now time.Time) (leaf if err := leaf.VerifyHostname(ck.domain); err != nil { return nil, err } + // renew certificates revoked by Let's Encrypt in January 2022 + if isRevokedLetsEncrypt(leaf) { + return nil, errors.New("acme/autocert: certificate was probably revoked by Let's Encrypt") + } // ensure the leaf corresponds to the private key and matches the certKey type switch pub := leaf.PublicKey.(type) { case *rsa.PublicKey: @@ -1230,6 +1162,18 @@ func validCert(ck certKey, der [][]byte, key crypto.Signer, now time.Time) (leaf return leaf, nil } +// https://community.letsencrypt.org/t/2022-01-25-issue-with-tls-alpn-01-validation-method/170450 +var letsEncryptFixDeployTime = time.Date(2022, time.January, 26, 00, 48, 0, 0, time.UTC) + +// isRevokedLetsEncrypt returns whether the certificate is likely to be part of +// a batch of certificates revoked by Let's Encrypt in January 2022. This check +// can be safely removed from May 2022. +func isRevokedLetsEncrypt(cert *x509.Certificate) bool { + O := cert.Issuer.Organization + return len(O) == 1 && O[0] == "Let's Encrypt" && + cert.NotBefore.Before(letsEncryptFixDeployTime) +} + type lockedMathRand struct { sync.Mutex rnd *mathrand.Rand diff --git a/vendor/golang.org/x/crypto/acme/autocert/renewal.go b/vendor/golang.org/x/crypto/acme/autocert/renewal.go index 665f870d..0df7da78 100644 --- a/vendor/golang.org/x/crypto/acme/autocert/renewal.go +++ b/vendor/golang.org/x/crypto/acme/autocert/renewal.go @@ -21,8 +21,9 @@ type domainRenewal struct { ck certKey key crypto.Signer - timerMu sync.Mutex - timer *time.Timer + timerMu sync.Mutex + timer *time.Timer + timerClose chan struct{} // if non-nil, renew closes this channel (and nils out the timer fields) instead of running } // start starts a cert renewal timer at the time @@ -38,16 +39,28 @@ func (dr *domainRenewal) start(exp time.Time) { dr.timer = time.AfterFunc(dr.next(exp), dr.renew) } -// stop stops the cert renewal timer. -// If the timer is already stopped, calling stop is a noop. +// stop stops the cert renewal timer and waits for any in-flight calls to renew +// to complete. If the timer is already stopped, calling stop is a noop. func (dr *domainRenewal) stop() { dr.timerMu.Lock() defer dr.timerMu.Unlock() - if dr.timer == nil { - return + for { + if dr.timer == nil { + return + } + if dr.timer.Stop() { + dr.timer = nil + return + } else { + // dr.timer fired, and we acquired dr.timerMu before the renew callback did. + // (We know this because otherwise the renew callback would have reset dr.timer!) + timerClose := make(chan struct{}) + dr.timerClose = timerClose + dr.timerMu.Unlock() + <-timerClose + dr.timerMu.Lock() + } } - dr.timer.Stop() - dr.timer = nil } // renew is called periodically by a timer. @@ -55,7 +68,9 @@ func (dr *domainRenewal) stop() { func (dr *domainRenewal) renew() { dr.timerMu.Lock() defer dr.timerMu.Unlock() - if dr.timer == nil { + if dr.timerClose != nil { + close(dr.timerClose) + dr.timer, dr.timerClose = nil, nil return } @@ -67,8 +82,8 @@ func (dr *domainRenewal) renew() { next = renewJitter / 2 next += time.Duration(pseudoRand.int63n(int64(next))) } - dr.timer = time.AfterFunc(next, dr.renew) testDidRenewLoop(next, err) + dr.timer = time.AfterFunc(next, dr.renew) } // updateState locks and replaces the relevant Manager.state item with the given diff --git a/vendor/golang.org/x/crypto/acme/jws.go b/vendor/golang.org/x/crypto/acme/jws.go index 8c3eccec..403e5b0c 100644 --- a/vendor/golang.org/x/crypto/acme/jws.go +++ b/vendor/golang.org/x/crypto/acme/jws.go @@ -20,12 +20,12 @@ import ( "math/big" ) -// keyID is the account identity provided by a CA during registration. -type keyID string +// KeyID is the account key identity provided by a CA during registration. +type KeyID string // noKeyID indicates that jwsEncodeJSON should compute and use JWK instead of a KID. // See jwsEncodeJSON for details. -const noKeyID = keyID("") +const noKeyID = KeyID("") // noPayload indicates jwsEncodeJSON will encode zero-length octet string // in a JWS request. This is called POST-as-GET in RFC 8555 and is used to make @@ -43,14 +43,17 @@ type jsonWebSignature struct { // jwsEncodeJSON signs claimset using provided key and a nonce. // The result is serialized in JSON format containing either kid or jwk -// fields based on the provided keyID value. +// fields based on the provided KeyID value. // // If kid is non-empty, its quoted value is inserted in the protected head // as "kid" field value. Otherwise, JWK is computed using jwkEncode and inserted // as "jwk" field value. The "jwk" and "kid" fields are mutually exclusive. // // See https://tools.ietf.org/html/rfc7515#section-7. -func jwsEncodeJSON(claimset interface{}, key crypto.Signer, kid keyID, nonce, url string) ([]byte, error) { +func jwsEncodeJSON(claimset interface{}, key crypto.Signer, kid KeyID, nonce, url string) ([]byte, error) { + if key == nil { + return nil, errors.New("nil key") + } alg, sha := jwsHasher(key.Public()) if alg == "" || !sha.Available() { return nil, ErrUnsupportedKey diff --git a/vendor/golang.org/x/crypto/acme/rfc8555.go b/vendor/golang.org/x/crypto/acme/rfc8555.go index f9d3011f..928a5aa0 100644 --- a/vendor/golang.org/x/crypto/acme/rfc8555.go +++ b/vendor/golang.org/x/crypto/acme/rfc8555.go @@ -78,7 +78,7 @@ func (c *Client) registerRFC(ctx context.Context, acct *Account, prompt func(tos } // Cache Account URL even if we return an error to the caller. // It is by all means a valid and usable "kid" value for future requests. - c.kid = keyID(a.URI) + c.KID = KeyID(a.URI) if res.StatusCode == http.StatusOK { return nil, ErrAccountAlreadyExists } diff --git a/vendor/golang.org/x/crypto/acme/types.go b/vendor/golang.org/x/crypto/acme/types.go index eaae4529..67b82520 100644 --- a/vendor/golang.org/x/crypto/acme/types.go +++ b/vendor/golang.org/x/crypto/acme/types.go @@ -305,14 +305,6 @@ type Directory struct { ExternalAccountRequired bool } -// rfcCompliant reports whether the ACME server implements RFC 8555. -// Note that some servers may have incomplete RFC implementation -// even if the returned value is true. -// If rfcCompliant reports false, the server most likely implements draft-02. -func (d *Directory) rfcCompliant() bool { - return d.OrderURL != "" -} - // Order represents a client's request for a certificate. // It tracks the request flow progress through to issuance. type Order struct { diff --git a/vendor/golang.org/x/crypto/ed25519/ed25519.go b/vendor/golang.org/x/crypto/ed25519/ed25519.go index 71ad917d..a7828345 100644 --- a/vendor/golang.org/x/crypto/ed25519/ed25519.go +++ b/vendor/golang.org/x/crypto/ed25519/ed25519.go @@ -1,13 +1,7 @@ -// Copyright 2016 The Go Authors. All rights reserved. +// Copyright 2019 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. -// In Go 1.13, the ed25519 package was promoted to the standard library as -// crypto/ed25519, and this package became a wrapper for the standard library one. -// -//go:build !go1.13 -// +build !go1.13 - // Package ed25519 implements the Ed25519 signature algorithm. See // https://ed25519.cr.yp.to/. // @@ -16,21 +10,15 @@ // representation includes a public key suffix to make multiple signing // operations with the same key more efficient. This package refers to the RFC // 8032 private key as the “seed”. +// +// Beginning with Go 1.13, the functionality of this package was moved to the +// standard library as crypto/ed25519. This package only acts as a compatibility +// wrapper. package ed25519 -// This code is a port of the public domain, “ref10” implementation of ed25519 -// from SUPERCOP. - import ( - "bytes" - "crypto" - cryptorand "crypto/rand" - "crypto/sha512" - "errors" + "crypto/ed25519" "io" - "strconv" - - "golang.org/x/crypto/ed25519/internal/edwards25519" ) const ( @@ -45,57 +33,21 @@ const ( ) // PublicKey is the type of Ed25519 public keys. -type PublicKey []byte +// +// This type is an alias for crypto/ed25519's PublicKey type. +// See the crypto/ed25519 package for the methods on this type. +type PublicKey = ed25519.PublicKey // PrivateKey is the type of Ed25519 private keys. It implements crypto.Signer. -type PrivateKey []byte - -// Public returns the PublicKey corresponding to priv. -func (priv PrivateKey) Public() crypto.PublicKey { - publicKey := make([]byte, PublicKeySize) - copy(publicKey, priv[32:]) - return PublicKey(publicKey) -} - -// Seed returns the private key seed corresponding to priv. It is provided for -// interoperability with RFC 8032. RFC 8032's private keys correspond to seeds -// in this package. -func (priv PrivateKey) Seed() []byte { - seed := make([]byte, SeedSize) - copy(seed, priv[:32]) - return seed -} - -// Sign signs the given message with priv. -// Ed25519 performs two passes over messages to be signed and therefore cannot -// handle pre-hashed messages. Thus opts.HashFunc() must return zero to -// indicate the message hasn't been hashed. This can be achieved by passing -// crypto.Hash(0) as the value for opts. -func (priv PrivateKey) Sign(rand io.Reader, message []byte, opts crypto.SignerOpts) (signature []byte, err error) { - if opts.HashFunc() != crypto.Hash(0) { - return nil, errors.New("ed25519: cannot sign hashed message") - } - - return Sign(priv, message), nil -} +// +// This type is an alias for crypto/ed25519's PrivateKey type. +// See the crypto/ed25519 package for the methods on this type. +type PrivateKey = ed25519.PrivateKey // GenerateKey generates a public/private key pair using entropy from rand. // If rand is nil, crypto/rand.Reader will be used. func GenerateKey(rand io.Reader) (PublicKey, PrivateKey, error) { - if rand == nil { - rand = cryptorand.Reader - } - - seed := make([]byte, SeedSize) - if _, err := io.ReadFull(rand, seed); err != nil { - return nil, nil, err - } - - privateKey := NewKeyFromSeed(seed) - publicKey := make([]byte, PublicKeySize) - copy(publicKey, privateKey[32:]) - - return publicKey, privateKey, nil + return ed25519.GenerateKey(rand) } // NewKeyFromSeed calculates a private key from a seed. It will panic if @@ -103,121 +55,17 @@ func GenerateKey(rand io.Reader) (PublicKey, PrivateKey, error) { // with RFC 8032. RFC 8032's private keys correspond to seeds in this // package. func NewKeyFromSeed(seed []byte) PrivateKey { - if l := len(seed); l != SeedSize { - panic("ed25519: bad seed length: " + strconv.Itoa(l)) - } - - digest := sha512.Sum512(seed) - digest[0] &= 248 - digest[31] &= 127 - digest[31] |= 64 - - var A edwards25519.ExtendedGroupElement - var hBytes [32]byte - copy(hBytes[:], digest[:]) - edwards25519.GeScalarMultBase(&A, &hBytes) - var publicKeyBytes [32]byte - A.ToBytes(&publicKeyBytes) - - privateKey := make([]byte, PrivateKeySize) - copy(privateKey, seed) - copy(privateKey[32:], publicKeyBytes[:]) - - return privateKey + return ed25519.NewKeyFromSeed(seed) } // Sign signs the message with privateKey and returns a signature. It will // panic if len(privateKey) is not PrivateKeySize. func Sign(privateKey PrivateKey, message []byte) []byte { - if l := len(privateKey); l != PrivateKeySize { - panic("ed25519: bad private key length: " + strconv.Itoa(l)) - } - - h := sha512.New() - h.Write(privateKey[:32]) - - var digest1, messageDigest, hramDigest [64]byte - var expandedSecretKey [32]byte - h.Sum(digest1[:0]) - copy(expandedSecretKey[:], digest1[:]) - expandedSecretKey[0] &= 248 - expandedSecretKey[31] &= 63 - expandedSecretKey[31] |= 64 - - h.Reset() - h.Write(digest1[32:]) - h.Write(message) - h.Sum(messageDigest[:0]) - - var messageDigestReduced [32]byte - edwards25519.ScReduce(&messageDigestReduced, &messageDigest) - var R edwards25519.ExtendedGroupElement - edwards25519.GeScalarMultBase(&R, &messageDigestReduced) - - var encodedR [32]byte - R.ToBytes(&encodedR) - - h.Reset() - h.Write(encodedR[:]) - h.Write(privateKey[32:]) - h.Write(message) - h.Sum(hramDigest[:0]) - var hramDigestReduced [32]byte - edwards25519.ScReduce(&hramDigestReduced, &hramDigest) - - var s [32]byte - edwards25519.ScMulAdd(&s, &hramDigestReduced, &expandedSecretKey, &messageDigestReduced) - - signature := make([]byte, SignatureSize) - copy(signature[:], encodedR[:]) - copy(signature[32:], s[:]) - - return signature + return ed25519.Sign(privateKey, message) } // Verify reports whether sig is a valid signature of message by publicKey. It // will panic if len(publicKey) is not PublicKeySize. func Verify(publicKey PublicKey, message, sig []byte) bool { - if l := len(publicKey); l != PublicKeySize { - panic("ed25519: bad public key length: " + strconv.Itoa(l)) - } - - if len(sig) != SignatureSize || sig[63]&224 != 0 { - return false - } - - var A edwards25519.ExtendedGroupElement - var publicKeyBytes [32]byte - copy(publicKeyBytes[:], publicKey) - if !A.FromBytes(&publicKeyBytes) { - return false - } - edwards25519.FeNeg(&A.X, &A.X) - edwards25519.FeNeg(&A.T, &A.T) - - h := sha512.New() - h.Write(sig[:32]) - h.Write(publicKey[:]) - h.Write(message) - var digest [64]byte - h.Sum(digest[:0]) - - var hReduced [32]byte - edwards25519.ScReduce(&hReduced, &digest) - - var R edwards25519.ProjectiveGroupElement - var s [32]byte - copy(s[:], sig[32:]) - - // https://tools.ietf.org/html/rfc8032#section-5.1.7 requires that s be in - // the range [0, order) in order to prevent signature malleability. - if !edwards25519.ScMinimal(&s) { - return false - } - - edwards25519.GeDoubleScalarMultVartime(&R, &hReduced, &A, &s) - - var checkR [32]byte - R.ToBytes(&checkR) - return bytes.Equal(sig[:32], checkR[:]) + return ed25519.Verify(publicKey, message, sig) } diff --git a/vendor/golang.org/x/crypto/ed25519/ed25519_go113.go b/vendor/golang.org/x/crypto/ed25519/ed25519_go113.go deleted file mode 100644 index b5974dc8..00000000 --- a/vendor/golang.org/x/crypto/ed25519/ed25519_go113.go +++ /dev/null @@ -1,74 +0,0 @@ -// Copyright 2019 The Go Authors. All rights reserved. -// Use of this source code is governed by a BSD-style -// license that can be found in the LICENSE file. - -//go:build go1.13 -// +build go1.13 - -// Package ed25519 implements the Ed25519 signature algorithm. See -// https://ed25519.cr.yp.to/. -// -// These functions are also compatible with the “Ed25519” function defined in -// RFC 8032. However, unlike RFC 8032's formulation, this package's private key -// representation includes a public key suffix to make multiple signing -// operations with the same key more efficient. This package refers to the RFC -// 8032 private key as the “seed”. -// -// Beginning with Go 1.13, the functionality of this package was moved to the -// standard library as crypto/ed25519. This package only acts as a compatibility -// wrapper. -package ed25519 - -import ( - "crypto/ed25519" - "io" -) - -const ( - // PublicKeySize is the size, in bytes, of public keys as used in this package. - PublicKeySize = 32 - // PrivateKeySize is the size, in bytes, of private keys as used in this package. - PrivateKeySize = 64 - // SignatureSize is the size, in bytes, of signatures generated and verified by this package. - SignatureSize = 64 - // SeedSize is the size, in bytes, of private key seeds. These are the private key representations used by RFC 8032. - SeedSize = 32 -) - -// PublicKey is the type of Ed25519 public keys. -// -// This type is an alias for crypto/ed25519's PublicKey type. -// See the crypto/ed25519 package for the methods on this type. -type PublicKey = ed25519.PublicKey - -// PrivateKey is the type of Ed25519 private keys. It implements crypto.Signer. -// -// This type is an alias for crypto/ed25519's PrivateKey type. -// See the crypto/ed25519 package for the methods on this type. -type PrivateKey = ed25519.PrivateKey - -// GenerateKey generates a public/private key pair using entropy from rand. -// If rand is nil, crypto/rand.Reader will be used. -func GenerateKey(rand io.Reader) (PublicKey, PrivateKey, error) { - return ed25519.GenerateKey(rand) -} - -// NewKeyFromSeed calculates a private key from a seed. It will panic if -// len(seed) is not SeedSize. This function is provided for interoperability -// with RFC 8032. RFC 8032's private keys correspond to seeds in this -// package. -func NewKeyFromSeed(seed []byte) PrivateKey { - return ed25519.NewKeyFromSeed(seed) -} - -// Sign signs the message with privateKey and returns a signature. It will -// panic if len(privateKey) is not PrivateKeySize. -func Sign(privateKey PrivateKey, message []byte) []byte { - return ed25519.Sign(privateKey, message) -} - -// Verify reports whether sig is a valid signature of message by publicKey. It -// will panic if len(publicKey) is not PublicKeySize. -func Verify(publicKey PublicKey, message, sig []byte) bool { - return ed25519.Verify(publicKey, message, sig) -} diff --git a/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/const.go b/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/const.go deleted file mode 100644 index e39f086c..00000000 --- a/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/const.go +++ /dev/null @@ -1,1422 +0,0 @@ -// Copyright 2016 The Go Authors. All rights reserved. -// Use of this source code is governed by a BSD-style -// license that can be found in the LICENSE file. - -package edwards25519 - -// These values are from the public domain, “ref10” implementation of ed25519 -// from SUPERCOP. - -// d is a constant in the Edwards curve equation. -var d = FieldElement{ - -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116, -} - -// d2 is 2*d. -var d2 = FieldElement{ - -21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199, -} - -// SqrtM1 is the square-root of -1 in the field. -var SqrtM1 = FieldElement{ - -32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482, -} - -// A is a constant in the Montgomery-form of curve25519. -var A = FieldElement{ - 486662, 0, 0, 0, 0, 0, 0, 0, 0, 0, -} - -// bi contains precomputed multiples of the base-point. See the Ed25519 paper -// for a discussion about how these values are used. -var bi = [8]PreComputedGroupElement{ - { - FieldElement{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605}, - FieldElement{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378}, - FieldElement{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546}, - }, - { - FieldElement{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024}, - FieldElement{16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574}, - FieldElement{30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357}, - }, - { - FieldElement{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380}, - FieldElement{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306}, - FieldElement{19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942}, - }, - { - FieldElement{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766}, - FieldElement{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701}, - FieldElement{28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300}, - }, - { - FieldElement{-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, -13062696, 13821877}, - FieldElement{-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, 18853322, -14220951}, - FieldElement{4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, 2207753, -3209784}, - }, - { - FieldElement{-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, -31111463, -16132436}, - FieldElement{25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, 6466918}, - FieldElement{23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, -30714912, 16193877}, - }, - { - FieldElement{-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, -18074513, 9256800}, - FieldElement{-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 9761698, -19827198, 630305}, - FieldElement{-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -15960994, -2449256, -14291300}, - }, - { - FieldElement{-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 15033784, 25105118, -7894876}, - FieldElement{-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892, -2625887, 2198790, -15804619}, - FieldElement{-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -16236442, -32461234, -12290683}, - }, -} - -// base contains precomputed multiples of the base-point. See the Ed25519 paper -// for a discussion about how these values are used. -var base = [32][8]PreComputedGroupElement{ - { - { - FieldElement{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605}, - FieldElement{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378}, - FieldElement{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546}, - }, - { - FieldElement{-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903, -3814571, -358445, -10211303}, - FieldElement{-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268, -26829678, -5319081}, - FieldElement{26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118, -15472047, -4166697}, - }, - { - FieldElement{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024}, - FieldElement{16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574}, - FieldElement{30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357}, - }, - { - FieldElement{-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023, 3284568, -6276540}, - FieldElement{23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445, 13059162, 10374397}, - FieldElement{7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045, -641708, -101325}, - }, - { - FieldElement{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380}, - FieldElement{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306}, - FieldElement{19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942}, - }, - { - FieldElement{-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627, -15224819, -9818940, -12085777}, - FieldElement{-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -15689887, 1762328, 14866737}, - FieldElement{-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412, 3959421, 27914454, 4383652}, - }, - { - FieldElement{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766}, - FieldElement{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701}, - FieldElement{28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300}, - }, - { - FieldElement{14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735, 10876454, -33154098, 2381726}, - FieldElement{-7195431, -2655363, -14730155, 462251, -27724326, 3941372, -6236617, 3696005, -32300832, 15351955}, - FieldElement{27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401, -2970515, 29551813, 10109425}, - }, - }, - { - { - FieldElement{-13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284, -1627556, 10092783, -4764171}, - FieldElement{27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754, 12005538, -17810127, 12803510}, - FieldElement{17228999, -15661624, -1233527, 300140, -1224870, -11714777, 30364213, -9038194, 18016357, 4397660}, - }, - { - FieldElement{-10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106, 14544525, -17477504, 982639}, - FieldElement{29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -4120128, -21047696, 9934963}, - FieldElement{5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930, 4559895, -30123922, -10897950}, - }, - { - FieldElement{-27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034, 4541697, -13338309, 5500568}, - FieldElement{12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592, 12264343, 10874051, 13524335}, - FieldElement{25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 5080568, -22528059, 5376628}, - }, - { - FieldElement{-26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305, -9447443, 4535768, 1569007}, - FieldElement{-2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562, 3044290, 31848280, 12543772}, - FieldElement{-22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195, -2062731, 7718482, 14474653}, - }, - { - FieldElement{2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665, 24316168, -5253567}, - FieldElement{13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651, -13424532, -20729456, 8321686}, - FieldElement{21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965, -11874838, -9984458, 608372}, - }, - { - FieldElement{-13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968, -6780577, 27229399, 23887}, - FieldElement{-23244140, -294205, -11744728, 14712571, -29465699, -2029617, 12797024, -6440308, -1633405, 16678954}, - FieldElement{-29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144, -4795045, -17169265, 4904953}, - }, - { - FieldElement{24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211, 16191880, 2128236, -4326833}, - FieldElement{-16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336, 916033, -6882542, -2986532}, - FieldElement{-22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 285431, 2763829, 15736322, 4143876}, - }, - { - FieldElement{2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -14594663, 23527084, -16458268}, - FieldElement{33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340, 4087881, -15188911, -14416214}, - FieldElement{1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 4357868, -4774191, -16323038}, - }, - }, - { - { - FieldElement{6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147, -3949732, 7390890, 2759800}, - FieldElement{4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -4264057, 1244380, -12919645}, - FieldElement{-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 9208236, 15886429, 16489664}, - }, - { - FieldElement{1996075, 10375649, 14346367, 13311202, -6874135, -16438411, -13693198, 398369, -30606455, -712933}, - FieldElement{-25307465, 9795880, -2777414, 14878809, -33531835, 14780363, 13348553, 12076947, -30836462, 5113182}, - FieldElement{-17770784, 11797796, 31950843, 13929123, -25888302, 12288344, -30341101, -7336386, 13847711, 5387222}, - }, - { - FieldElement{-18582163, -3416217, 17824843, -2340966, 22744343, -10442611, 8763061, 3617786, -19600662, 10370991}, - FieldElement{20246567, -14369378, 22358229, -543712, 18507283, -10413996, 14554437, -8746092, 32232924, 16763880}, - FieldElement{9648505, 10094563, 26416693, 14745928, -30374318, -6472621, 11094161, 15689506, 3140038, -16510092}, - }, - { - FieldElement{-16160072, 5472695, 31895588, 4744994, 8823515, 10365685, -27224800, 9448613, -28774454, 366295}, - FieldElement{19153450, 11523972, -11096490, -6503142, -24647631, 5420647, 28344573, 8041113, 719605, 11671788}, - FieldElement{8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, -15266516, 27000813, -10195553}, - }, - { - FieldElement{-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, 5336097, 6750977, -14521026}, - FieldElement{11836410, -3979488, 26297894, 16080799, 23455045, 15735944, 1695823, -8819122, 8169720, 16220347}, - FieldElement{-18115838, 8653647, 17578566, -6092619, -8025777, -16012763, -11144307, -2627664, -5990708, -14166033}, - }, - { - FieldElement{-23308498, -10968312, 15213228, -10081214, -30853605, -11050004, 27884329, 2847284, 2655861, 1738395}, - FieldElement{-27537433, -14253021, -25336301, -8002780, -9370762, 8129821, 21651608, -3239336, -19087449, -11005278}, - FieldElement{1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 5821408, 10478196, 8544890}, - }, - { - FieldElement{32173121, -16129311, 24896207, 3921497, 22579056, -3410854, 19270449, 12217473, 17789017, -3395995}, - FieldElement{-30552961, -2228401, -15578829, -10147201, 13243889, 517024, 15479401, -3853233, 30460520, 1052596}, - FieldElement{-11614875, 13323618, 32618793, 8175907, -15230173, 12596687, 27491595, -4612359, 3179268, -9478891}, - }, - { - FieldElement{31947069, -14366651, -4640583, -15339921, -15125977, -6039709, -14756777, -16411740, 19072640, -9511060}, - FieldElement{11685058, 11822410, 3158003, -13952594, 33402194, -4165066, 5977896, -5215017, 473099, 5040608}, - FieldElement{-20290863, 8198642, -27410132, 11602123, 1290375, -2799760, 28326862, 1721092, -19558642, -3131606}, - }, - }, - { - { - FieldElement{7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, 8076149, -27868496, 11538389}, - FieldElement{-19935666, 3899861, 18283497, -6801568, -15728660, -11249211, 8754525, 7446702, -5676054, 5797016}, - FieldElement{-11295600, -3793569, -15782110, -7964573, 12708869, -8456199, 2014099, -9050574, -2369172, -5877341}, - }, - { - FieldElement{-22472376, -11568741, -27682020, 1146375, 18956691, 16640559, 1192730, -3714199, 15123619, 10811505}, - FieldElement{14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, 15776356, -28886779, -11974553}, - FieldElement{-28241164, -8072475, -4978962, -5315317, 29416931, 1847569, -20654173, -16484855, 4714547, -9600655}, - }, - { - FieldElement{15200332, 8368572, 19679101, 15970074, -31872674, 1959451, 24611599, -4543832, -11745876, 12340220}, - FieldElement{12876937, -10480056, 33134381, 6590940, -6307776, 14872440, 9613953, 8241152, 15370987, 9608631}, - FieldElement{-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, 15866074, -28210621, -8814099}, - }, - { - FieldElement{26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, 858697, 20571223, 8420556}, - FieldElement{14620715, 13067227, -15447274, 8264467, 14106269, 15080814, 33531827, 12516406, -21574435, -12476749}, - FieldElement{236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, 7256740, 8791136, 15069930}, - }, - { - FieldElement{1276410, -9371918, 22949635, -16322807, -23493039, -5702186, 14711875, 4874229, -30663140, -2331391}, - FieldElement{5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, -7912378, -33069337, 9234253}, - FieldElement{20590503, -9018988, 31529744, -7352666, -2706834, 10650548, 31559055, -11609587, 18979186, 13396066}, - }, - { - FieldElement{24474287, 4968103, 22267082, 4407354, 24063882, -8325180, -18816887, 13594782, 33514650, 7021958}, - FieldElement{-11566906, -6565505, -21365085, 15928892, -26158305, 4315421, -25948728, -3916677, -21480480, 12868082}, - FieldElement{-28635013, 13504661, 19988037, -2132761, 21078225, 6443208, -21446107, 2244500, -12455797, -8089383}, - }, - { - FieldElement{-30595528, 13793479, -5852820, 319136, -25723172, -6263899, 33086546, 8957937, -15233648, 5540521}, - FieldElement{-11630176, -11503902, -8119500, -7643073, 2620056, 1022908, -23710744, -1568984, -16128528, -14962807}, - FieldElement{23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, 892185, -11513277, -15205948}, - }, - { - FieldElement{9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, 4763127, -19179614, 5867134}, - FieldElement{-32765025, 1927590, 31726409, -4753295, 23962434, -16019500, 27846559, 5931263, -29749703, -16108455}, - FieldElement{27461885, -2977536, 22380810, 1815854, -23033753, -3031938, 7283490, -15148073, -19526700, 7734629}, - }, - }, - { - { - FieldElement{-8010264, -9590817, -11120403, 6196038, 29344158, -13430885, 7585295, -3176626, 18549497, 15302069}, - FieldElement{-32658337, -6171222, -7672793, -11051681, 6258878, 13504381, 10458790, -6418461, -8872242, 8424746}, - 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FieldElement{-7171154, 3178080, 23970071, 6201893, -17195577, -4489192, -21876275, -13982627, 32208683, -1198248}, - }, - { - FieldElement{-16657702, 2817643, -10286362, 14811298, 6024667, 13349505, -27315504, -10497842, -27672585, -11539858}, - FieldElement{15941029, -9405932, -21367050, 8062055, 31876073, -238629, -15278393, -1444429, 15397331, -4130193}, - FieldElement{8934485, -13485467, -23286397, -13423241, -32446090, 14047986, 31170398, -1441021, -27505566, 15087184}, - }, - { - FieldElement{-18357243, -2156491, 24524913, -16677868, 15520427, -6360776, -15502406, 11461896, 16788528, -5868942}, - FieldElement{-1947386, 16013773, 21750665, 3714552, -17401782, -16055433, -3770287, -10323320, 31322514, -11615635}, - FieldElement{21426655, -5650218, -13648287, -5347537, -28812189, -4920970, -18275391, -14621414, 13040862, -12112948}, - }, - { - FieldElement{11293895, 12478086, -27136401, 15083750, -29307421, 14748872, 14555558, -13417103, 1613711, 4896935}, - FieldElement{-25894883, 15323294, -8489791, -8057900, 25967126, -13425460, 2825960, -4897045, -23971776, -11267415}, - FieldElement{-15924766, -5229880, -17443532, 6410664, 3622847, 10243618, 20615400, 12405433, -23753030, -8436416}, - }, - { - FieldElement{-7091295, 12556208, -20191352, 9025187, -17072479, 4333801, 4378436, 2432030, 23097949, -566018}, - FieldElement{4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264, 10103221, -18512313, 2424778}, - FieldElement{366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678, 1344109, -3642553, 12412659}, - }, - { - FieldElement{-24001791, 7690286, 14929416, -168257, -32210835, -13412986, 24162697, -15326504, -3141501, 11179385}, - FieldElement{18289522, -14724954, 8056945, 16430056, -21729724, 7842514, -6001441, -1486897, -18684645, -11443503}, - FieldElement{476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959, 13403813, 11052904, 5219329}, - }, - }, - { - { - FieldElement{20678546, -8375738, -32671898, 8849123, -5009758, 14574752, 31186971, -3973730, 9014762, -8579056}, - FieldElement{-13644050, -10350239, -15962508, 5075808, -1514661, -11534600, -33102500, 9160280, 8473550, -3256838}, - FieldElement{24900749, 14435722, 17209120, -15292541, -22592275, 9878983, -7689309, -16335821, -24568481, 11788948}, - }, - { - FieldElement{-3118155, -11395194, -13802089, 14797441, 9652448, -6845904, -20037437, 10410733, -24568470, -1458691}, - FieldElement{-15659161, 16736706, -22467150, 10215878, -9097177, 7563911, 11871841, -12505194, -18513325, 8464118}, - FieldElement{-23400612, 8348507, -14585951, -861714, -3950205, -6373419, 14325289, 8628612, 33313881, -8370517}, - }, - { - FieldElement{-20186973, -4967935, 22367356, 5271547, -1097117, -4788838, -24805667, -10236854, -8940735, -5818269}, - FieldElement{-6948785, -1795212, -32625683, -16021179, 32635414, -7374245, 15989197, -12838188, 28358192, -4253904}, - FieldElement{-23561781, -2799059, -32351682, -1661963, -9147719, 10429267, -16637684, 4072016, -5351664, 5596589}, - }, - { - FieldElement{-28236598, -3390048, 12312896, 6213178, 3117142, 16078565, 29266239, 2557221, 1768301, 15373193}, - FieldElement{-7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902, -4504991, -24660491, 3442910}, - FieldElement{-30210571, 5124043, 14181784, 8197961, 18964734, -11939093, 22597931, 7176455, -18585478, 13365930}, - }, - { - FieldElement{-7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107, -8570186, -9689599, -3031667}, - FieldElement{25008904, -10771599, -4305031, -9638010, 16265036, 15721635, 683793, -11823784, 15723479, -15163481}, - FieldElement{-9660625, 12374379, -27006999, -7026148, -7724114, -12314514, 11879682, 5400171, 519526, -1235876}, - }, - { - FieldElement{22258397, -16332233, -7869817, 14613016, -22520255, -2950923, -20353881, 7315967, 16648397, 7605640}, - FieldElement{-8081308, -8464597, -8223311, 9719710, 19259459, -15348212, 23994942, -5281555, -9468848, 4763278}, - FieldElement{-21699244, 9220969, -15730624, 1084137, -25476107, -2852390, 31088447, -7764523, -11356529, 728112}, - }, - { - FieldElement{26047220, -11751471, -6900323, -16521798, 24092068, 9158119, -4273545, -12555558, -29365436, -5498272}, - FieldElement{17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007, 12327945, 10750447, 10014012}, - FieldElement{-10312768, 3936952, 9156313, -8897683, 16498692, -994647, -27481051, -666732, 3424691, 7540221}, - }, - { - FieldElement{30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422, -16317219, -9244265, 15258046}, - FieldElement{13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406, 2711395, 1062915, -5136345}, - FieldElement{-19240248, -11254599, -29509029, -7499965, -5835763, 13005411, -6066489, 12194497, 32960380, 1459310}, - }, - }, - { - { - FieldElement{19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197, -6101885, 18638003, -11174937}, - FieldElement{31395534, 15098109, 26581030, 8030562, -16527914, -5007134, 9012486, -7584354, -6643087, -5442636}, - FieldElement{-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222, 9677543, -32294889, -6456008}, - }, - { - FieldElement{-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579, -7839692, -7852844, -8138429}, - FieldElement{-15236356, -15433509, 7766470, 746860, 26346930, -10221762, -27333451, 10754588, -9431476, 5203576}, - FieldElement{31834314, 14135496, -770007, 5159118, 20917671, -16768096, -7467973, -7337524, 31809243, 7347066}, - }, - { - FieldElement{-9606723, -11874240, 20414459, 13033986, 13716524, -11691881, 19797970, -12211255, 15192876, -2087490}, - FieldElement{-12663563, -2181719, 1168162, -3804809, 26747877, -14138091, 10609330, 12694420, 33473243, -13382104}, - FieldElement{33184999, 11180355, 15832085, -11385430, -1633671, 225884, 15089336, -11023903, -6135662, 14480053}, - }, - { - FieldElement{31308717, -5619998, 31030840, -1897099, 15674547, -6582883, 5496208, 13685227, 27595050, 8737275}, - FieldElement{-20318852, -15150239, 10933843, -16178022, 8335352, -7546022, -31008351, -12610604, 26498114, 66511}, - FieldElement{22644454, -8761729, -16671776, 4884562, -3105614, -13559366, 30540766, -4286747, -13327787, -7515095}, - }, - { - FieldElement{-28017847, 9834845, 18617207, -2681312, -3401956, -13307506, 8205540, 13585437, -17127465, 15115439}, - FieldElement{23711543, -672915, 31206561, -8362711, 6164647, -9709987, -33535882, -1426096, 8236921, 16492939}, - FieldElement{-23910559, -13515526, -26299483, -4503841, 25005590, -7687270, 19574902, 10071562, 6708380, -6222424}, - }, - { - FieldElement{2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, 9328700, 29955601, -11678310}, - FieldElement{3096359, 9271816, -21620864, -15521844, -14847996, -7592937, -25892142, -12635595, -9917575, 6216608}, - FieldElement{-32615849, 338663, -25195611, 2510422, -29213566, -13820213, 24822830, -6146567, -26767480, 7525079}, - }, - { - FieldElement{-23066649, -13985623, 16133487, -7896178, -3389565, 778788, -910336, -2782495, -19386633, 11994101}, - FieldElement{21691500, -13624626, -641331, -14367021, 3285881, -3483596, -25064666, 9718258, -7477437, 13381418}, - FieldElement{18445390, -4202236, 14979846, 11622458, -1727110, -3582980, 23111648, -6375247, 28535282, 15779576}, - }, - { - FieldElement{30098053, 3089662, -9234387, 16662135, -21306940, 11308411, -14068454, 12021730, 9955285, -16303356}, - FieldElement{9734894, -14576830, -7473633, -9138735, 2060392, 11313496, -18426029, 9924399, 20194861, 13380996}, - FieldElement{-26378102, -7965207, -22167821, 15789297, -18055342, -6168792, -1984914, 15707771, 26342023, 10146099}, - }, - }, - { - { - FieldElement{-26016874, -219943, 21339191, -41388, 19745256, -2878700, -29637280, 2227040, 21612326, -545728}, - FieldElement{-13077387, 1184228, 23562814, -5970442, -20351244, -6348714, 25764461, 12243797, -20856566, 11649658}, - FieldElement{-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, 6114064, 33514190, 2333242}, - }, - { - FieldElement{-21433588, -12421821, 8119782, 7219913, -21830522, -9016134, -6679750, -12670638, 24350578, -13450001}, - FieldElement{-4116307, -11271533, -23886186, 4843615, -30088339, 690623, -31536088, -10406836, 8317860, 12352766}, - FieldElement{18200138, -14475911, -33087759, -2696619, -23702521, -9102511, -23552096, -2287550, 20712163, 6719373}, - }, - { - FieldElement{26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, -3763210, 26224235, -3297458}, - FieldElement{-17168938, -14854097, -3395676, -16369877, -19954045, 14050420, 21728352, 9493610, 18620611, -16428628}, - FieldElement{-13323321, 13325349, 11432106, 5964811, 18609221, 6062965, -5269471, -9725556, -30701573, -16479657}, - }, - { - FieldElement{-23860538, -11233159, 26961357, 1640861, -32413112, -16737940, 12248509, -5240639, 13735342, 1934062}, - FieldElement{25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -15136294, -3765346, -21277997, 5473616}, - FieldElement{31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -7125085, 12469656, 29111212, -5451014}, - }, - { - FieldElement{24244947, -15050407, -26262976, 2791540, -14997599, 16666678, 24367466, 6388839, -10295587, 452383}, - FieldElement{-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -24236251, -5915248, 15766062, 8407814}, - FieldElement{-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -8917023, -4388953, -8067909, 2276718}, - }, - { - FieldElement{30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -23827587, 5096219, 22740376, -7303417}, - FieldElement{2041139, -14256350, 7783687, 13876377, -25946985, -13352459, 24051124, 13742383, -15637599, 13295222}, - FieldElement{33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -17720195, -4612972, -4451357, -14669444}, - }, - { - FieldElement{-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -2469266, -4141880, 7770569, 9620597}, - FieldElement{23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -1694323, -33502340, -14767970}, - FieldElement{1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 1220118, 30494170, -11440799}, - }, - { - FieldElement{-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -26739026, 926050, -1684339, -13333647}, - FieldElement{13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 9021034, 9078865, 3353509, 4033511}, - FieldElement{-29663431, -15113610, 32259991, -344482, 24295849, -12912123, 23161163, 8839127, 27485041, 7356032}, - }, - }, - { - { - FieldElement{9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 2625015, 28431036, -16771834}, - FieldElement{-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -22545972, 14150565, 15970762, 4099461}, - FieldElement{29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 13617293, -9937143, 11465739, 8317062}, - }, - { - FieldElement{-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 14898637, 3848455, 20969334, -5157516}, - FieldElement{-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -21610826, -3649888, 11177095, 14989547}, - FieldElement{-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 13515641, 2581286, -28487508, 9930240}, - }, - { - FieldElement{-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 18345767, -13403753, 16291481, -5314038}, - FieldElement{-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 6957617, 4368891, 9788741}, - FieldElement{16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -21722536, -8613148, 16250552, -11111103}, - }, - { - FieldElement{-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 10604807, -30190403, 4782747}, - FieldElement{-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -9981571, 4383045, 22546403, 437323}, - FieldElement{31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 27343084, 2786261, -30633590, -14097016}, - }, - { - FieldElement{-14467279, -683715, -33374107, 7448552, 19294360, 14334329, -19690631, 2355319, -19284671, -6114373}, - FieldElement{15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 18952177, 15496498, -29380133, 11754228}, - FieldElement{-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 7141596, 11724556, 22761615, -10134141}, - }, - { - FieldElement{16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -28741185, -12227393, 32851222, 11717399}, - FieldElement{11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 31474879, 3483633, -1193175, -4030831}, - FieldElement{-185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376}, - }, - { - FieldElement{-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313}, - FieldElement{-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958}, - FieldElement{-6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577}, - }, - { - FieldElement{-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743}, - FieldElement{29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684}, - FieldElement{-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476}, - }, - }, -} diff --git a/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/edwards25519.go b/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/edwards25519.go deleted file mode 100644 index fd03c252..00000000 --- a/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/edwards25519.go +++ /dev/null @@ -1,1793 +0,0 @@ -// Copyright 2016 The Go Authors. All rights reserved. -// Use of this source code is governed by a BSD-style -// license that can be found in the LICENSE file. - -package edwards25519 - -import "encoding/binary" - -// This code is a port of the public domain, “ref10” implementation of ed25519 -// from SUPERCOP. - -// FieldElement represents an element of the field GF(2^255 - 19). An element -// t, entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 -// t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on -// context. -type FieldElement [10]int32 - -var zero FieldElement - -func FeZero(fe *FieldElement) { - copy(fe[:], zero[:]) -} - -func FeOne(fe *FieldElement) { - FeZero(fe) - fe[0] = 1 -} - -func FeAdd(dst, a, b *FieldElement) { - dst[0] = a[0] + b[0] - dst[1] = a[1] + b[1] - dst[2] = a[2] + b[2] - dst[3] = a[3] + b[3] - dst[4] = a[4] + b[4] - dst[5] = a[5] + b[5] - dst[6] = a[6] + b[6] - dst[7] = a[7] + b[7] - dst[8] = a[8] + b[8] - dst[9] = a[9] + b[9] -} - -func FeSub(dst, a, b *FieldElement) { - dst[0] = a[0] - b[0] - dst[1] = a[1] - b[1] - dst[2] = a[2] - b[2] - dst[3] = a[3] - b[3] - dst[4] = a[4] - b[4] - dst[5] = a[5] - b[5] - dst[6] = a[6] - b[6] - dst[7] = a[7] - b[7] - dst[8] = a[8] - b[8] - dst[9] = a[9] - b[9] -} - -func FeCopy(dst, src *FieldElement) { - copy(dst[:], src[:]) -} - -// Replace (f,g) with (g,g) if b == 1; -// replace (f,g) with (f,g) if b == 0. -// -// Preconditions: b in {0,1}. -func FeCMove(f, g *FieldElement, b int32) { - b = -b - f[0] ^= b & (f[0] ^ g[0]) - f[1] ^= b & (f[1] ^ g[1]) - f[2] ^= b & (f[2] ^ g[2]) - f[3] ^= b & (f[3] ^ g[3]) - f[4] ^= b & (f[4] ^ g[4]) - f[5] ^= b & (f[5] ^ g[5]) - f[6] ^= b & (f[6] ^ g[6]) - f[7] ^= b & (f[7] ^ g[7]) - f[8] ^= b & (f[8] ^ g[8]) - f[9] ^= b & (f[9] ^ g[9]) -} - -func load3(in []byte) int64 { - var r int64 - r = int64(in[0]) - r |= int64(in[1]) << 8 - r |= int64(in[2]) << 16 - return r -} - -func load4(in []byte) int64 { - var r int64 - r = int64(in[0]) - r |= int64(in[1]) << 8 - r |= int64(in[2]) << 16 - r |= int64(in[3]) << 24 - return r -} - -func FeFromBytes(dst *FieldElement, src *[32]byte) { - h0 := load4(src[:]) - h1 := load3(src[4:]) << 6 - h2 := load3(src[7:]) << 5 - h3 := load3(src[10:]) << 3 - h4 := load3(src[13:]) << 2 - h5 := load4(src[16:]) - h6 := load3(src[20:]) << 7 - h7 := load3(src[23:]) << 5 - h8 := load3(src[26:]) << 4 - h9 := (load3(src[29:]) & 8388607) << 2 - - FeCombine(dst, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9) -} - -// FeToBytes marshals h to s. -// Preconditions: -// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. -// -// Write p=2^255-19; q=floor(h/p). -// Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). -// -// Proof: -// Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. -// Also have |h-2^230 h9|<2^230 so |19 2^(-255)(h-2^230 h9)|<1/4. -// -// Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). -// Then 0<y<1. -// -// Write r=h-pq. -// Have 0<=r<=p-1=2^255-20. -// Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. -// -// Write x=r+19(2^-255)r+y. -// Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. -// -// Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) -// so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. -func FeToBytes(s *[32]byte, h *FieldElement) { - var carry [10]int32 - - q := (19*h[9] + (1 << 24)) >> 25 - q = (h[0] + q) >> 26 - q = (h[1] + q) >> 25 - q = (h[2] + q) >> 26 - q = (h[3] + q) >> 25 - q = (h[4] + q) >> 26 - q = (h[5] + q) >> 25 - q = (h[6] + q) >> 26 - q = (h[7] + q) >> 25 - q = (h[8] + q) >> 26 - q = (h[9] + q) >> 25 - - // Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. - h[0] += 19 * q - // Goal: Output h-2^255 q, which is between 0 and 2^255-20. - - carry[0] = h[0] >> 26 - h[1] += carry[0] - h[0] -= carry[0] << 26 - carry[1] = h[1] >> 25 - h[2] += carry[1] - h[1] -= carry[1] << 25 - carry[2] = h[2] >> 26 - h[3] += carry[2] - h[2] -= carry[2] << 26 - carry[3] = h[3] >> 25 - h[4] += carry[3] - h[3] -= carry[3] << 25 - carry[4] = h[4] >> 26 - h[5] += carry[4] - h[4] -= carry[4] << 26 - carry[5] = h[5] >> 25 - h[6] += carry[5] - h[5] -= carry[5] << 25 - carry[6] = h[6] >> 26 - h[7] += carry[6] - h[6] -= carry[6] << 26 - carry[7] = h[7] >> 25 - h[8] += carry[7] - h[7] -= carry[7] << 25 - carry[8] = h[8] >> 26 - h[9] += carry[8] - h[8] -= carry[8] << 26 - carry[9] = h[9] >> 25 - h[9] -= carry[9] << 25 - // h10 = carry9 - - // Goal: Output h[0]+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. - // Have h[0]+...+2^230 h[9] between 0 and 2^255-1; - // evidently 2^255 h10-2^255 q = 0. - // Goal: Output h[0]+...+2^230 h[9]. - - s[0] = byte(h[0] >> 0) - s[1] = byte(h[0] >> 8) - s[2] = byte(h[0] >> 16) - s[3] = byte((h[0] >> 24) | (h[1] << 2)) - s[4] = byte(h[1] >> 6) - s[5] = byte(h[1] >> 14) - s[6] = byte((h[1] >> 22) | (h[2] << 3)) - s[7] = byte(h[2] >> 5) - s[8] = byte(h[2] >> 13) - s[9] = byte((h[2] >> 21) | (h[3] << 5)) - s[10] = byte(h[3] >> 3) - s[11] = byte(h[3] >> 11) - s[12] = byte((h[3] >> 19) | (h[4] << 6)) - s[13] = byte(h[4] >> 2) - s[14] = byte(h[4] >> 10) - s[15] = byte(h[4] >> 18) - s[16] = byte(h[5] >> 0) - s[17] = byte(h[5] >> 8) - s[18] = byte(h[5] >> 16) - s[19] = byte((h[5] >> 24) | (h[6] << 1)) - s[20] = byte(h[6] >> 7) - s[21] = byte(h[6] >> 15) - s[22] = byte((h[6] >> 23) | (h[7] << 3)) - s[23] = byte(h[7] >> 5) - s[24] = byte(h[7] >> 13) - s[25] = byte((h[7] >> 21) | (h[8] << 4)) - s[26] = byte(h[8] >> 4) - s[27] = byte(h[8] >> 12) - s[28] = byte((h[8] >> 20) | (h[9] << 6)) - s[29] = byte(h[9] >> 2) - s[30] = byte(h[9] >> 10) - s[31] = byte(h[9] >> 18) -} - -func FeIsNegative(f *FieldElement) byte { - var s [32]byte - FeToBytes(&s, f) - return s[0] & 1 -} - -func FeIsNonZero(f *FieldElement) int32 { - var s [32]byte - FeToBytes(&s, f) - var x uint8 - for _, b := range s { - x |= b - } - x |= x >> 4 - x |= x >> 2 - x |= x >> 1 - return int32(x & 1) -} - -// FeNeg sets h = -f -// -// Preconditions: -// |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. -// -// Postconditions: -// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. -func FeNeg(h, f *FieldElement) { - h[0] = -f[0] - h[1] = -f[1] - h[2] = -f[2] - h[3] = -f[3] - h[4] = -f[4] - h[5] = -f[5] - h[6] = -f[6] - h[7] = -f[7] - h[8] = -f[8] - h[9] = -f[9] -} - -func FeCombine(h *FieldElement, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 int64) { - var c0, c1, c2, c3, c4, c5, c6, c7, c8, c9 int64 - - /* - |h0| <= (1.1*1.1*2^52*(1+19+19+19+19)+1.1*1.1*2^50*(38+38+38+38+38)) - i.e. |h0| <= 1.2*2^59; narrower ranges for h2, h4, h6, h8 - |h1| <= (1.1*1.1*2^51*(1+1+19+19+19+19+19+19+19+19)) - i.e. |h1| <= 1.5*2^58; narrower ranges for h3, h5, h7, h9 - */ - - c0 = (h0 + (1 << 25)) >> 26 - h1 += c0 - h0 -= c0 << 26 - c4 = (h4 + (1 << 25)) >> 26 - h5 += c4 - h4 -= c4 << 26 - /* |h0| <= 2^25 */ - /* |h4| <= 2^25 */ - /* |h1| <= 1.51*2^58 */ - /* |h5| <= 1.51*2^58 */ - - c1 = (h1 + (1 << 24)) >> 25 - h2 += c1 - h1 -= c1 << 25 - c5 = (h5 + (1 << 24)) >> 25 - h6 += c5 - h5 -= c5 << 25 - /* |h1| <= 2^24; from now on fits into int32 */ - /* |h5| <= 2^24; from now on fits into int32 */ - /* |h2| <= 1.21*2^59 */ - /* |h6| <= 1.21*2^59 */ - - c2 = (h2 + (1 << 25)) >> 26 - h3 += c2 - h2 -= c2 << 26 - c6 = (h6 + (1 << 25)) >> 26 - h7 += c6 - h6 -= c6 << 26 - /* |h2| <= 2^25; from now on fits into int32 unchanged */ - /* |h6| <= 2^25; from now on fits into int32 unchanged */ - /* |h3| <= 1.51*2^58 */ - /* |h7| <= 1.51*2^58 */ - - c3 = (h3 + (1 << 24)) >> 25 - h4 += c3 - h3 -= c3 << 25 - c7 = (h7 + (1 << 24)) >> 25 - h8 += c7 - h7 -= c7 << 25 - /* |h3| <= 2^24; from now on fits into int32 unchanged */ - /* |h7| <= 2^24; from now on fits into int32 unchanged */ - /* |h4| <= 1.52*2^33 */ - /* |h8| <= 1.52*2^33 */ - - c4 = (h4 + (1 << 25)) >> 26 - h5 += c4 - h4 -= c4 << 26 - c8 = (h8 + (1 << 25)) >> 26 - h9 += c8 - h8 -= c8 << 26 - /* |h4| <= 2^25; from now on fits into int32 unchanged */ - /* |h8| <= 2^25; from now on fits into int32 unchanged */ - /* |h5| <= 1.01*2^24 */ - /* |h9| <= 1.51*2^58 */ - - c9 = (h9 + (1 << 24)) >> 25 - h0 += c9 * 19 - h9 -= c9 << 25 - /* |h9| <= 2^24; from now on fits into int32 unchanged */ - /* |h0| <= 1.8*2^37 */ - - c0 = (h0 + (1 << 25)) >> 26 - h1 += c0 - h0 -= c0 << 26 - /* |h0| <= 2^25; from now on fits into int32 unchanged */ - /* |h1| <= 1.01*2^24 */ - - h[0] = int32(h0) - h[1] = int32(h1) - h[2] = int32(h2) - h[3] = int32(h3) - h[4] = int32(h4) - h[5] = int32(h5) - h[6] = int32(h6) - h[7] = int32(h7) - h[8] = int32(h8) - h[9] = int32(h9) -} - -// FeMul calculates h = f * g -// Can overlap h with f or g. -// -// Preconditions: -// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. -// |g| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. -// -// Postconditions: -// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. -// -// Notes on implementation strategy: -// -// Using schoolbook multiplication. -// Karatsuba would save a little in some cost models. -// -// Most multiplications by 2 and 19 are 32-bit precomputations; -// cheaper than 64-bit postcomputations. -// -// There is one remaining multiplication by 19 in the carry chain; -// one *19 precomputation can be merged into this, -// but the resulting data flow is considerably less clean. -// -// There are 12 carries below. -// 10 of them are 2-way parallelizable and vectorizable. -// Can get away with 11 carries, but then data flow is much deeper. -// -// With tighter constraints on inputs, can squeeze carries into int32. -func FeMul(h, f, g *FieldElement) { - f0 := int64(f[0]) - f1 := int64(f[1]) - f2 := int64(f[2]) - f3 := int64(f[3]) - f4 := int64(f[4]) - f5 := int64(f[5]) - f6 := int64(f[6]) - f7 := int64(f[7]) - f8 := int64(f[8]) - f9 := int64(f[9]) - - f1_2 := int64(2 * f[1]) - f3_2 := int64(2 * f[3]) - f5_2 := int64(2 * f[5]) - f7_2 := int64(2 * f[7]) - f9_2 := int64(2 * f[9]) - - g0 := int64(g[0]) - g1 := int64(g[1]) - g2 := int64(g[2]) - g3 := int64(g[3]) - g4 := int64(g[4]) - g5 := int64(g[5]) - g6 := int64(g[6]) - g7 := int64(g[7]) - g8 := int64(g[8]) - g9 := int64(g[9]) - - g1_19 := int64(19 * g[1]) /* 1.4*2^29 */ - g2_19 := int64(19 * g[2]) /* 1.4*2^30; still ok */ - g3_19 := int64(19 * g[3]) - g4_19 := int64(19 * g[4]) - g5_19 := int64(19 * g[5]) - g6_19 := int64(19 * g[6]) - g7_19 := int64(19 * g[7]) - g8_19 := int64(19 * g[8]) - g9_19 := int64(19 * g[9]) - - h0 := f0*g0 + f1_2*g9_19 + f2*g8_19 + f3_2*g7_19 + f4*g6_19 + f5_2*g5_19 + f6*g4_19 + f7_2*g3_19 + f8*g2_19 + f9_2*g1_19 - h1 := f0*g1 + f1*g0 + f2*g9_19 + f3*g8_19 + f4*g7_19 + f5*g6_19 + f6*g5_19 + f7*g4_19 + f8*g3_19 + f9*g2_19 - h2 := f0*g2 + f1_2*g1 + f2*g0 + f3_2*g9_19 + f4*g8_19 + f5_2*g7_19 + f6*g6_19 + f7_2*g5_19 + f8*g4_19 + f9_2*g3_19 - h3 := f0*g3 + f1*g2 + f2*g1 + f3*g0 + f4*g9_19 + f5*g8_19 + f6*g7_19 + f7*g6_19 + f8*g5_19 + f9*g4_19 - h4 := f0*g4 + f1_2*g3 + f2*g2 + f3_2*g1 + f4*g0 + f5_2*g9_19 + f6*g8_19 + f7_2*g7_19 + f8*g6_19 + f9_2*g5_19 - h5 := f0*g5 + f1*g4 + f2*g3 + f3*g2 + f4*g1 + f5*g0 + f6*g9_19 + f7*g8_19 + f8*g7_19 + f9*g6_19 - h6 := f0*g6 + f1_2*g5 + f2*g4 + f3_2*g3 + f4*g2 + f5_2*g1 + f6*g0 + f7_2*g9_19 + f8*g8_19 + f9_2*g7_19 - h7 := f0*g7 + f1*g6 + f2*g5 + f3*g4 + f4*g3 + f5*g2 + f6*g1 + f7*g0 + f8*g9_19 + f9*g8_19 - h8 := f0*g8 + f1_2*g7 + f2*g6 + f3_2*g5 + f4*g4 + f5_2*g3 + f6*g2 + f7_2*g1 + f8*g0 + f9_2*g9_19 - h9 := f0*g9 + f1*g8 + f2*g7 + f3*g6 + f4*g5 + f5*g4 + f6*g3 + f7*g2 + f8*g1 + f9*g0 - - FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9) -} - -func feSquare(f *FieldElement) (h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 int64) { - f0 := int64(f[0]) - f1 := int64(f[1]) - f2 := int64(f[2]) - f3 := int64(f[3]) - f4 := int64(f[4]) - f5 := int64(f[5]) - f6 := int64(f[6]) - f7 := int64(f[7]) - f8 := int64(f[8]) - f9 := int64(f[9]) - f0_2 := int64(2 * f[0]) - f1_2 := int64(2 * f[1]) - f2_2 := int64(2 * f[2]) - f3_2 := int64(2 * f[3]) - f4_2 := int64(2 * f[4]) - f5_2 := int64(2 * f[5]) - f6_2 := int64(2 * f[6]) - f7_2 := int64(2 * f[7]) - f5_38 := 38 * f5 // 1.31*2^30 - f6_19 := 19 * f6 // 1.31*2^30 - f7_38 := 38 * f7 // 1.31*2^30 - f8_19 := 19 * f8 // 1.31*2^30 - f9_38 := 38 * f9 // 1.31*2^30 - - h0 = f0*f0 + f1_2*f9_38 + f2_2*f8_19 + f3_2*f7_38 + f4_2*f6_19 + f5*f5_38 - h1 = f0_2*f1 + f2*f9_38 + f3_2*f8_19 + f4*f7_38 + f5_2*f6_19 - h2 = f0_2*f2 + f1_2*f1 + f3_2*f9_38 + f4_2*f8_19 + f5_2*f7_38 + f6*f6_19 - h3 = f0_2*f3 + f1_2*f2 + f4*f9_38 + f5_2*f8_19 + f6*f7_38 - h4 = f0_2*f4 + f1_2*f3_2 + f2*f2 + f5_2*f9_38 + f6_2*f8_19 + f7*f7_38 - h5 = f0_2*f5 + f1_2*f4 + f2_2*f3 + f6*f9_38 + f7_2*f8_19 - h6 = f0_2*f6 + f1_2*f5_2 + f2_2*f4 + f3_2*f3 + f7_2*f9_38 + f8*f8_19 - h7 = f0_2*f7 + f1_2*f6 + f2_2*f5 + f3_2*f4 + f8*f9_38 - h8 = f0_2*f8 + f1_2*f7_2 + f2_2*f6 + f3_2*f5_2 + f4*f4 + f9*f9_38 - h9 = f0_2*f9 + f1_2*f8 + f2_2*f7 + f3_2*f6 + f4_2*f5 - - return -} - -// FeSquare calculates h = f*f. Can overlap h with f. -// -// Preconditions: -// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. -// -// Postconditions: -// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. -func FeSquare(h, f *FieldElement) { - h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 := feSquare(f) - FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9) -} - -// FeSquare2 sets h = 2 * f * f -// -// Can overlap h with f. -// -// Preconditions: -// |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. -// -// Postconditions: -// |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. -// See fe_mul.c for discussion of implementation strategy. -func FeSquare2(h, f *FieldElement) { - h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 := feSquare(f) - - h0 += h0 - h1 += h1 - h2 += h2 - h3 += h3 - h4 += h4 - h5 += h5 - h6 += h6 - h7 += h7 - h8 += h8 - h9 += h9 - - FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9) -} - -func FeInvert(out, z *FieldElement) { - var t0, t1, t2, t3 FieldElement - var i int - - FeSquare(&t0, z) // 2^1 - FeSquare(&t1, &t0) // 2^2 - for i = 1; i < 2; i++ { // 2^3 - FeSquare(&t1, &t1) - } - FeMul(&t1, z, &t1) // 2^3 + 2^0 - FeMul(&t0, &t0, &t1) // 2^3 + 2^1 + 2^0 - FeSquare(&t2, &t0) // 2^4 + 2^2 + 2^1 - FeMul(&t1, &t1, &t2) // 2^4 + 2^3 + 2^2 + 2^1 + 2^0 - FeSquare(&t2, &t1) // 5,4,3,2,1 - for i = 1; i < 5; i++ { // 9,8,7,6,5 - FeSquare(&t2, &t2) - } - FeMul(&t1, &t2, &t1) // 9,8,7,6,5,4,3,2,1,0 - FeSquare(&t2, &t1) // 10..1 - for i = 1; i < 10; i++ { // 19..10 - FeSquare(&t2, &t2) - } - FeMul(&t2, &t2, &t1) // 19..0 - FeSquare(&t3, &t2) // 20..1 - for i = 1; i < 20; i++ { // 39..20 - FeSquare(&t3, &t3) - } - FeMul(&t2, &t3, &t2) // 39..0 - FeSquare(&t2, &t2) // 40..1 - for i = 1; i < 10; i++ { // 49..10 - FeSquare(&t2, &t2) - } - FeMul(&t1, &t2, &t1) // 49..0 - FeSquare(&t2, &t1) // 50..1 - for i = 1; i < 50; i++ { // 99..50 - FeSquare(&t2, &t2) - } - FeMul(&t2, &t2, &t1) // 99..0 - FeSquare(&t3, &t2) // 100..1 - for i = 1; i < 100; i++ { // 199..100 - FeSquare(&t3, &t3) - } - FeMul(&t2, &t3, &t2) // 199..0 - FeSquare(&t2, &t2) // 200..1 - for i = 1; i < 50; i++ { // 249..50 - FeSquare(&t2, &t2) - } - FeMul(&t1, &t2, &t1) // 249..0 - FeSquare(&t1, &t1) // 250..1 - for i = 1; i < 5; i++ { // 254..5 - FeSquare(&t1, &t1) - } - FeMul(out, &t1, &t0) // 254..5,3,1,0 -} - -func fePow22523(out, z *FieldElement) { - var t0, t1, t2 FieldElement - var i int - - FeSquare(&t0, z) - for i = 1; i < 1; i++ { - FeSquare(&t0, &t0) - } - FeSquare(&t1, &t0) - for i = 1; i < 2; i++ { - FeSquare(&t1, &t1) - } - FeMul(&t1, z, &t1) - FeMul(&t0, &t0, &t1) - FeSquare(&t0, &t0) - for i = 1; i < 1; i++ { - FeSquare(&t0, &t0) - } - FeMul(&t0, &t1, &t0) - FeSquare(&t1, &t0) - for i = 1; i < 5; i++ { - FeSquare(&t1, &t1) - } - FeMul(&t0, &t1, &t0) - FeSquare(&t1, &t0) - for i = 1; i < 10; i++ { - FeSquare(&t1, &t1) - } - FeMul(&t1, &t1, &t0) - FeSquare(&t2, &t1) - for i = 1; i < 20; i++ { - FeSquare(&t2, &t2) - } - FeMul(&t1, &t2, &t1) - FeSquare(&t1, &t1) - for i = 1; i < 10; i++ { - FeSquare(&t1, &t1) - } - FeMul(&t0, &t1, &t0) - FeSquare(&t1, &t0) - for i = 1; i < 50; i++ { - FeSquare(&t1, &t1) - } - FeMul(&t1, &t1, &t0) - FeSquare(&t2, &t1) - for i = 1; i < 100; i++ { - FeSquare(&t2, &t2) - } - FeMul(&t1, &t2, &t1) - FeSquare(&t1, &t1) - for i = 1; i < 50; i++ { - FeSquare(&t1, &t1) - } - FeMul(&t0, &t1, &t0) - FeSquare(&t0, &t0) - for i = 1; i < 2; i++ { - FeSquare(&t0, &t0) - } - FeMul(out, &t0, z) -} - -// Group elements are members of the elliptic curve -x^2 + y^2 = 1 + d * x^2 * -// y^2 where d = -121665/121666. -// -// Several representations are used: -// ProjectiveGroupElement: (X:Y:Z) satisfying x=X/Z, y=Y/Z -// ExtendedGroupElement: (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT -// CompletedGroupElement: ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T -// PreComputedGroupElement: (y+x,y-x,2dxy) - -type ProjectiveGroupElement struct { - X, Y, Z FieldElement -} - -type ExtendedGroupElement struct { - X, Y, Z, T FieldElement -} - -type CompletedGroupElement struct { - X, Y, Z, T FieldElement -} - -type PreComputedGroupElement struct { - yPlusX, yMinusX, xy2d FieldElement -} - -type CachedGroupElement struct { - yPlusX, yMinusX, Z, T2d FieldElement -} - -func (p *ProjectiveGroupElement) Zero() { - FeZero(&p.X) - FeOne(&p.Y) - FeOne(&p.Z) -} - -func (p *ProjectiveGroupElement) Double(r *CompletedGroupElement) { - var t0 FieldElement - - FeSquare(&r.X, &p.X) - FeSquare(&r.Z, &p.Y) - FeSquare2(&r.T, &p.Z) - FeAdd(&r.Y, &p.X, &p.Y) - FeSquare(&t0, &r.Y) - FeAdd(&r.Y, &r.Z, &r.X) - FeSub(&r.Z, &r.Z, &r.X) - FeSub(&r.X, &t0, &r.Y) - FeSub(&r.T, &r.T, &r.Z) -} - -func (p *ProjectiveGroupElement) ToBytes(s *[32]byte) { - var recip, x, y FieldElement - - FeInvert(&recip, &p.Z) - FeMul(&x, &p.X, &recip) - FeMul(&y, &p.Y, &recip) - FeToBytes(s, &y) - s[31] ^= FeIsNegative(&x) << 7 -} - -func (p *ExtendedGroupElement) Zero() { - FeZero(&p.X) - FeOne(&p.Y) - FeOne(&p.Z) - FeZero(&p.T) -} - -func (p *ExtendedGroupElement) Double(r *CompletedGroupElement) { - var q ProjectiveGroupElement - p.ToProjective(&q) - q.Double(r) -} - -func (p *ExtendedGroupElement) ToCached(r *CachedGroupElement) { - FeAdd(&r.yPlusX, &p.Y, &p.X) - FeSub(&r.yMinusX, &p.Y, &p.X) - FeCopy(&r.Z, &p.Z) - FeMul(&r.T2d, &p.T, &d2) -} - -func (p *ExtendedGroupElement) ToProjective(r *ProjectiveGroupElement) { - FeCopy(&r.X, &p.X) - FeCopy(&r.Y, &p.Y) - FeCopy(&r.Z, &p.Z) -} - -func (p *ExtendedGroupElement) ToBytes(s *[32]byte) { - var recip, x, y FieldElement - - FeInvert(&recip, &p.Z) - FeMul(&x, &p.X, &recip) - FeMul(&y, &p.Y, &recip) - FeToBytes(s, &y) - s[31] ^= FeIsNegative(&x) << 7 -} - -func (p *ExtendedGroupElement) FromBytes(s *[32]byte) bool { - var u, v, v3, vxx, check FieldElement - - FeFromBytes(&p.Y, s) - FeOne(&p.Z) - FeSquare(&u, &p.Y) - FeMul(&v, &u, &d) - FeSub(&u, &u, &p.Z) // y = y^2-1 - FeAdd(&v, &v, &p.Z) // v = dy^2+1 - - FeSquare(&v3, &v) - FeMul(&v3, &v3, &v) // v3 = v^3 - FeSquare(&p.X, &v3) - FeMul(&p.X, &p.X, &v) - FeMul(&p.X, &p.X, &u) // x = uv^7 - - fePow22523(&p.X, &p.X) // x = (uv^7)^((q-5)/8) - FeMul(&p.X, &p.X, &v3) - FeMul(&p.X, &p.X, &u) // x = uv^3(uv^7)^((q-5)/8) - - var tmpX, tmp2 [32]byte - - FeSquare(&vxx, &p.X) - FeMul(&vxx, &vxx, &v) - FeSub(&check, &vxx, &u) // vx^2-u - if FeIsNonZero(&check) == 1 { - FeAdd(&check, &vxx, &u) // vx^2+u - if FeIsNonZero(&check) == 1 { - return false - } - FeMul(&p.X, &p.X, &SqrtM1) - - FeToBytes(&tmpX, &p.X) - for i, v := range tmpX { - tmp2[31-i] = v - } - } - - if FeIsNegative(&p.X) != (s[31] >> 7) { - FeNeg(&p.X, &p.X) - } - - FeMul(&p.T, &p.X, &p.Y) - return true -} - -func (p *CompletedGroupElement) ToProjective(r *ProjectiveGroupElement) { - FeMul(&r.X, &p.X, &p.T) - FeMul(&r.Y, &p.Y, &p.Z) - FeMul(&r.Z, &p.Z, &p.T) -} - -func (p *CompletedGroupElement) ToExtended(r *ExtendedGroupElement) { - FeMul(&r.X, &p.X, &p.T) - FeMul(&r.Y, &p.Y, &p.Z) - FeMul(&r.Z, &p.Z, &p.T) - FeMul(&r.T, &p.X, &p.Y) -} - -func (p *PreComputedGroupElement) Zero() { - FeOne(&p.yPlusX) - FeOne(&p.yMinusX) - FeZero(&p.xy2d) -} - -func geAdd(r *CompletedGroupElement, p *ExtendedGroupElement, q *CachedGroupElement) { - var t0 FieldElement - - FeAdd(&r.X, &p.Y, &p.X) - FeSub(&r.Y, &p.Y, &p.X) - FeMul(&r.Z, &r.X, &q.yPlusX) - FeMul(&r.Y, &r.Y, &q.yMinusX) - FeMul(&r.T, &q.T2d, &p.T) - FeMul(&r.X, &p.Z, &q.Z) - FeAdd(&t0, &r.X, &r.X) - FeSub(&r.X, &r.Z, &r.Y) - FeAdd(&r.Y, &r.Z, &r.Y) - FeAdd(&r.Z, &t0, &r.T) - FeSub(&r.T, &t0, &r.T) -} - -func geSub(r *CompletedGroupElement, p *ExtendedGroupElement, q *CachedGroupElement) { - var t0 FieldElement - - FeAdd(&r.X, &p.Y, &p.X) - FeSub(&r.Y, &p.Y, &p.X) - FeMul(&r.Z, &r.X, &q.yMinusX) - FeMul(&r.Y, &r.Y, &q.yPlusX) - FeMul(&r.T, &q.T2d, &p.T) - FeMul(&r.X, &p.Z, &q.Z) - FeAdd(&t0, &r.X, &r.X) - FeSub(&r.X, &r.Z, &r.Y) - FeAdd(&r.Y, &r.Z, &r.Y) - FeSub(&r.Z, &t0, &r.T) - FeAdd(&r.T, &t0, &r.T) -} - -func geMixedAdd(r *CompletedGroupElement, p *ExtendedGroupElement, q *PreComputedGroupElement) { - var t0 FieldElement - - FeAdd(&r.X, &p.Y, &p.X) - FeSub(&r.Y, &p.Y, &p.X) - FeMul(&r.Z, &r.X, &q.yPlusX) - FeMul(&r.Y, &r.Y, &q.yMinusX) - FeMul(&r.T, &q.xy2d, &p.T) - FeAdd(&t0, &p.Z, &p.Z) - FeSub(&r.X, &r.Z, &r.Y) - FeAdd(&r.Y, &r.Z, &r.Y) - FeAdd(&r.Z, &t0, &r.T) - FeSub(&r.T, &t0, &r.T) -} - -func geMixedSub(r *CompletedGroupElement, p *ExtendedGroupElement, q *PreComputedGroupElement) { - var t0 FieldElement - - FeAdd(&r.X, &p.Y, &p.X) - FeSub(&r.Y, &p.Y, &p.X) - FeMul(&r.Z, &r.X, &q.yMinusX) - FeMul(&r.Y, &r.Y, &q.yPlusX) - FeMul(&r.T, &q.xy2d, &p.T) - FeAdd(&t0, &p.Z, &p.Z) - FeSub(&r.X, &r.Z, &r.Y) - FeAdd(&r.Y, &r.Z, &r.Y) - FeSub(&r.Z, &t0, &r.T) - FeAdd(&r.T, &t0, &r.T) -} - -func slide(r *[256]int8, a *[32]byte) { - for i := range r { - r[i] = int8(1 & (a[i>>3] >> uint(i&7))) - } - - for i := range r { - if r[i] != 0 { - for b := 1; b <= 6 && i+b < 256; b++ { - if r[i+b] != 0 { - if r[i]+(r[i+b]<<uint(b)) <= 15 { - r[i] += r[i+b] << uint(b) - r[i+b] = 0 - } else if r[i]-(r[i+b]<<uint(b)) >= -15 { - r[i] -= r[i+b] << uint(b) - for k := i + b; k < 256; k++ { - if r[k] == 0 { - r[k] = 1 - break - } - r[k] = 0 - } - } else { - break - } - } - } - } - } -} - -// GeDoubleScalarMultVartime sets r = a*A + b*B -// where a = a[0]+256*a[1]+...+256^31 a[31]. -// and b = b[0]+256*b[1]+...+256^31 b[31]. -// B is the Ed25519 base point (x,4/5) with x positive. -func GeDoubleScalarMultVartime(r *ProjectiveGroupElement, a *[32]byte, A *ExtendedGroupElement, b *[32]byte) { - var aSlide, bSlide [256]int8 - var Ai [8]CachedGroupElement // A,3A,5A,7A,9A,11A,13A,15A - var t CompletedGroupElement - var u, A2 ExtendedGroupElement - var i int - - slide(&aSlide, a) - slide(&bSlide, b) - - A.ToCached(&Ai[0]) - A.Double(&t) - t.ToExtended(&A2) - - for i := 0; i < 7; i++ { - geAdd(&t, &A2, &Ai[i]) - t.ToExtended(&u) - u.ToCached(&Ai[i+1]) - } - - r.Zero() - - for i = 255; i >= 0; i-- { - if aSlide[i] != 0 || bSlide[i] != 0 { - break - } - } - - for ; i >= 0; i-- { - r.Double(&t) - - if aSlide[i] > 0 { - t.ToExtended(&u) - geAdd(&t, &u, &Ai[aSlide[i]/2]) - } else if aSlide[i] < 0 { - t.ToExtended(&u) - geSub(&t, &u, &Ai[(-aSlide[i])/2]) - } - - if bSlide[i] > 0 { - t.ToExtended(&u) - geMixedAdd(&t, &u, &bi[bSlide[i]/2]) - } else if bSlide[i] < 0 { - t.ToExtended(&u) - geMixedSub(&t, &u, &bi[(-bSlide[i])/2]) - } - - t.ToProjective(r) - } -} - -// equal returns 1 if b == c and 0 otherwise, assuming that b and c are -// non-negative. -func equal(b, c int32) int32 { - x := uint32(b ^ c) - x-- - return int32(x >> 31) -} - -// negative returns 1 if b < 0 and 0 otherwise. -func negative(b int32) int32 { - return (b >> 31) & 1 -} - -func PreComputedGroupElementCMove(t, u *PreComputedGroupElement, b int32) { - FeCMove(&t.yPlusX, &u.yPlusX, b) - FeCMove(&t.yMinusX, &u.yMinusX, b) - FeCMove(&t.xy2d, &u.xy2d, b) -} - -func selectPoint(t *PreComputedGroupElement, pos int32, b int32) { - var minusT PreComputedGroupElement - bNegative := negative(b) - bAbs := b - (((-bNegative) & b) << 1) - - t.Zero() - for i := int32(0); i < 8; i++ { - PreComputedGroupElementCMove(t, &base[pos][i], equal(bAbs, i+1)) - } - FeCopy(&minusT.yPlusX, &t.yMinusX) - FeCopy(&minusT.yMinusX, &t.yPlusX) - FeNeg(&minusT.xy2d, &t.xy2d) - PreComputedGroupElementCMove(t, &minusT, bNegative) -} - -// GeScalarMultBase computes h = a*B, where -// a = a[0]+256*a[1]+...+256^31 a[31] -// B is the Ed25519 base point (x,4/5) with x positive. -// -// Preconditions: -// a[31] <= 127 -func GeScalarMultBase(h *ExtendedGroupElement, a *[32]byte) { - var e [64]int8 - - for i, v := range a { - e[2*i] = int8(v & 15) - e[2*i+1] = int8((v >> 4) & 15) - } - - // each e[i] is between 0 and 15 and e[63] is between 0 and 7. - - carry := int8(0) - for i := 0; i < 63; i++ { - e[i] += carry - carry = (e[i] + 8) >> 4 - e[i] -= carry << 4 - } - e[63] += carry - // each e[i] is between -8 and 8. - - h.Zero() - var t PreComputedGroupElement - var r CompletedGroupElement - for i := int32(1); i < 64; i += 2 { - selectPoint(&t, i/2, int32(e[i])) - geMixedAdd(&r, h, &t) - r.ToExtended(h) - } - - var s ProjectiveGroupElement - - h.Double(&r) - r.ToProjective(&s) - s.Double(&r) - r.ToProjective(&s) - s.Double(&r) - r.ToProjective(&s) - s.Double(&r) - r.ToExtended(h) - - for i := int32(0); i < 64; i += 2 { - selectPoint(&t, i/2, int32(e[i])) - geMixedAdd(&r, h, &t) - r.ToExtended(h) - } -} - -// The scalars are GF(2^252 + 27742317777372353535851937790883648493). - -// Input: -// a[0]+256*a[1]+...+256^31*a[31] = a -// b[0]+256*b[1]+...+256^31*b[31] = b -// c[0]+256*c[1]+...+256^31*c[31] = c -// -// Output: -// s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l -// where l = 2^252 + 27742317777372353535851937790883648493. -func ScMulAdd(s, a, b, c *[32]byte) { - a0 := 2097151 & load3(a[:]) - a1 := 2097151 & (load4(a[2:]) >> 5) - a2 := 2097151 & (load3(a[5:]) >> 2) - a3 := 2097151 & (load4(a[7:]) >> 7) - a4 := 2097151 & (load4(a[10:]) >> 4) - a5 := 2097151 & (load3(a[13:]) >> 1) - a6 := 2097151 & (load4(a[15:]) >> 6) - a7 := 2097151 & (load3(a[18:]) >> 3) - a8 := 2097151 & load3(a[21:]) - a9 := 2097151 & (load4(a[23:]) >> 5) - a10 := 2097151 & (load3(a[26:]) >> 2) - a11 := (load4(a[28:]) >> 7) - b0 := 2097151 & load3(b[:]) - b1 := 2097151 & (load4(b[2:]) >> 5) - b2 := 2097151 & (load3(b[5:]) >> 2) - b3 := 2097151 & (load4(b[7:]) >> 7) - b4 := 2097151 & (load4(b[10:]) >> 4) - b5 := 2097151 & (load3(b[13:]) >> 1) - b6 := 2097151 & (load4(b[15:]) >> 6) - b7 := 2097151 & (load3(b[18:]) >> 3) - b8 := 2097151 & load3(b[21:]) - b9 := 2097151 & (load4(b[23:]) >> 5) - b10 := 2097151 & (load3(b[26:]) >> 2) - b11 := (load4(b[28:]) >> 7) - c0 := 2097151 & load3(c[:]) - c1 := 2097151 & (load4(c[2:]) >> 5) - c2 := 2097151 & (load3(c[5:]) >> 2) - c3 := 2097151 & (load4(c[7:]) >> 7) - c4 := 2097151 & (load4(c[10:]) >> 4) - c5 := 2097151 & (load3(c[13:]) >> 1) - c6 := 2097151 & (load4(c[15:]) >> 6) - c7 := 2097151 & (load3(c[18:]) >> 3) - c8 := 2097151 & load3(c[21:]) - c9 := 2097151 & (load4(c[23:]) >> 5) - c10 := 2097151 & (load3(c[26:]) >> 2) - c11 := (load4(c[28:]) >> 7) - var carry [23]int64 - - s0 := c0 + a0*b0 - s1 := c1 + a0*b1 + a1*b0 - s2 := c2 + a0*b2 + a1*b1 + a2*b0 - s3 := c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0 - s4 := c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0 - s5 := c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0 - s6 := c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0 - s7 := c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0 - s8 := c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0 - s9 := c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0 - s10 := c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0 - s11 := c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0 - s12 := a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1 - s13 := a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2 - s14 := a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3 - s15 := a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4 - s16 := a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5 - s17 := a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6 - s18 := a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7 - s19 := a8*b11 + a9*b10 + a10*b9 + a11*b8 - s20 := a9*b11 + a10*b10 + a11*b9 - s21 := a10*b11 + a11*b10 - s22 := a11 * b11 - s23 := int64(0) - - carry[0] = (s0 + (1 << 20)) >> 21 - s1 += carry[0] - s0 -= carry[0] << 21 - carry[2] = (s2 + (1 << 20)) >> 21 - s3 += carry[2] - s2 -= carry[2] << 21 - carry[4] = (s4 + (1 << 20)) >> 21 - s5 += carry[4] - s4 -= carry[4] << 21 - carry[6] = (s6 + (1 << 20)) >> 21 - s7 += carry[6] - s6 -= carry[6] << 21 - carry[8] = (s8 + (1 << 20)) >> 21 - s9 += carry[8] - s8 -= carry[8] << 21 - carry[10] = (s10 + (1 << 20)) >> 21 - s11 += carry[10] - s10 -= carry[10] << 21 - carry[12] = (s12 + (1 << 20)) >> 21 - s13 += carry[12] - s12 -= carry[12] << 21 - carry[14] = (s14 + (1 << 20)) >> 21 - s15 += carry[14] - s14 -= carry[14] << 21 - carry[16] = (s16 + (1 << 20)) >> 21 - s17 += carry[16] - s16 -= carry[16] << 21 - carry[18] = (s18 + (1 << 20)) >> 21 - s19 += carry[18] - s18 -= carry[18] << 21 - carry[20] = (s20 + (1 << 20)) >> 21 - s21 += carry[20] - s20 -= carry[20] << 21 - carry[22] = (s22 + (1 << 20)) >> 21 - s23 += carry[22] - s22 -= carry[22] << 21 - - carry[1] = (s1 + (1 << 20)) >> 21 - s2 += carry[1] - s1 -= carry[1] << 21 - carry[3] = (s3 + (1 << 20)) >> 21 - s4 += carry[3] - s3 -= carry[3] << 21 - carry[5] = (s5 + (1 << 20)) >> 21 - s6 += carry[5] - s5 -= carry[5] << 21 - carry[7] = (s7 + (1 << 20)) >> 21 - s8 += carry[7] - s7 -= carry[7] << 21 - carry[9] = (s9 + (1 << 20)) >> 21 - s10 += carry[9] - s9 -= carry[9] << 21 - carry[11] = (s11 + (1 << 20)) >> 21 - s12 += carry[11] - s11 -= carry[11] << 21 - carry[13] = (s13 + (1 << 20)) >> 21 - s14 += carry[13] - s13 -= carry[13] << 21 - carry[15] = (s15 + (1 << 20)) >> 21 - s16 += carry[15] - s15 -= carry[15] << 21 - carry[17] = (s17 + (1 << 20)) >> 21 - s18 += carry[17] - s17 -= carry[17] << 21 - carry[19] = (s19 + (1 << 20)) >> 21 - s20 += carry[19] - s19 -= carry[19] << 21 - carry[21] = (s21 + (1 << 20)) >> 21 - s22 += carry[21] - s21 -= carry[21] << 21 - - s11 += s23 * 666643 - s12 += s23 * 470296 - s13 += s23 * 654183 - s14 -= s23 * 997805 - s15 += s23 * 136657 - s16 -= s23 * 683901 - s23 = 0 - - s10 += s22 * 666643 - s11 += s22 * 470296 - s12 += s22 * 654183 - s13 -= s22 * 997805 - s14 += s22 * 136657 - s15 -= s22 * 683901 - s22 = 0 - - s9 += s21 * 666643 - s10 += s21 * 470296 - s11 += s21 * 654183 - s12 -= s21 * 997805 - s13 += s21 * 136657 - s14 -= s21 * 683901 - s21 = 0 - - s8 += s20 * 666643 - s9 += s20 * 470296 - s10 += s20 * 654183 - s11 -= s20 * 997805 - s12 += s20 * 136657 - s13 -= s20 * 683901 - s20 = 0 - - s7 += s19 * 666643 - s8 += s19 * 470296 - s9 += s19 * 654183 - s10 -= s19 * 997805 - s11 += s19 * 136657 - s12 -= s19 * 683901 - s19 = 0 - - s6 += s18 * 666643 - s7 += s18 * 470296 - s8 += s18 * 654183 - s9 -= s18 * 997805 - s10 += s18 * 136657 - s11 -= s18 * 683901 - s18 = 0 - - carry[6] = (s6 + (1 << 20)) >> 21 - s7 += carry[6] - s6 -= carry[6] << 21 - carry[8] = (s8 + (1 << 20)) >> 21 - s9 += carry[8] - s8 -= carry[8] << 21 - carry[10] = (s10 + (1 << 20)) >> 21 - s11 += carry[10] - s10 -= carry[10] << 21 - carry[12] = (s12 + (1 << 20)) >> 21 - s13 += carry[12] - s12 -= carry[12] << 21 - carry[14] = (s14 + (1 << 20)) >> 21 - s15 += carry[14] - s14 -= carry[14] << 21 - carry[16] = (s16 + (1 << 20)) >> 21 - s17 += carry[16] - s16 -= carry[16] << 21 - - carry[7] = (s7 + (1 << 20)) >> 21 - s8 += carry[7] - s7 -= carry[7] << 21 - carry[9] = (s9 + (1 << 20)) >> 21 - s10 += carry[9] - s9 -= carry[9] << 21 - carry[11] = (s11 + (1 << 20)) >> 21 - s12 += carry[11] - s11 -= carry[11] << 21 - carry[13] = (s13 + (1 << 20)) >> 21 - s14 += carry[13] - s13 -= carry[13] << 21 - carry[15] = (s15 + (1 << 20)) >> 21 - s16 += carry[15] - s15 -= carry[15] << 21 - - s5 += s17 * 666643 - s6 += s17 * 470296 - s7 += s17 * 654183 - s8 -= s17 * 997805 - s9 += s17 * 136657 - s10 -= s17 * 683901 - s17 = 0 - - s4 += s16 * 666643 - s5 += s16 * 470296 - s6 += s16 * 654183 - s7 -= s16 * 997805 - s8 += s16 * 136657 - s9 -= s16 * 683901 - s16 = 0 - - s3 += s15 * 666643 - s4 += s15 * 470296 - s5 += s15 * 654183 - s6 -= s15 * 997805 - s7 += s15 * 136657 - s8 -= s15 * 683901 - s15 = 0 - - s2 += s14 * 666643 - s3 += s14 * 470296 - s4 += s14 * 654183 - s5 -= s14 * 997805 - s6 += s14 * 136657 - s7 -= s14 * 683901 - s14 = 0 - - s1 += s13 * 666643 - s2 += s13 * 470296 - s3 += s13 * 654183 - s4 -= s13 * 997805 - s5 += s13 * 136657 - s6 -= s13 * 683901 - s13 = 0 - - s0 += s12 * 666643 - s1 += s12 * 470296 - s2 += s12 * 654183 - s3 -= s12 * 997805 - s4 += s12 * 136657 - s5 -= s12 * 683901 - s12 = 0 - - carry[0] = (s0 + (1 << 20)) >> 21 - s1 += carry[0] - s0 -= carry[0] << 21 - carry[2] = (s2 + (1 << 20)) >> 21 - s3 += carry[2] - s2 -= carry[2] << 21 - carry[4] = (s4 + (1 << 20)) >> 21 - s5 += carry[4] - s4 -= carry[4] << 21 - carry[6] = (s6 + (1 << 20)) >> 21 - s7 += carry[6] - s6 -= carry[6] << 21 - carry[8] = (s8 + (1 << 20)) >> 21 - s9 += carry[8] - s8 -= carry[8] << 21 - carry[10] = (s10 + (1 << 20)) >> 21 - s11 += carry[10] - s10 -= carry[10] << 21 - - carry[1] = (s1 + (1 << 20)) >> 21 - s2 += carry[1] - s1 -= carry[1] << 21 - carry[3] = (s3 + (1 << 20)) >> 21 - s4 += carry[3] - s3 -= carry[3] << 21 - carry[5] = (s5 + (1 << 20)) >> 21 - s6 += carry[5] - s5 -= carry[5] << 21 - carry[7] = (s7 + (1 << 20)) >> 21 - s8 += carry[7] - s7 -= carry[7] << 21 - carry[9] = (s9 + (1 << 20)) >> 21 - s10 += carry[9] - s9 -= carry[9] << 21 - carry[11] = (s11 + (1 << 20)) >> 21 - s12 += carry[11] - s11 -= carry[11] << 21 - - s0 += s12 * 666643 - s1 += s12 * 470296 - s2 += s12 * 654183 - s3 -= s12 * 997805 - s4 += s12 * 136657 - s5 -= s12 * 683901 - s12 = 0 - - carry[0] = s0 >> 21 - s1 += carry[0] - s0 -= carry[0] << 21 - carry[1] = s1 >> 21 - s2 += carry[1] - s1 -= carry[1] << 21 - carry[2] = s2 >> 21 - s3 += carry[2] - s2 -= carry[2] << 21 - carry[3] = s3 >> 21 - s4 += carry[3] - s3 -= carry[3] << 21 - carry[4] = s4 >> 21 - s5 += carry[4] - s4 -= carry[4] << 21 - carry[5] = s5 >> 21 - s6 += carry[5] - s5 -= carry[5] << 21 - carry[6] = s6 >> 21 - s7 += carry[6] - s6 -= carry[6] << 21 - carry[7] = s7 >> 21 - s8 += carry[7] - s7 -= carry[7] << 21 - carry[8] = s8 >> 21 - s9 += carry[8] - s8 -= carry[8] << 21 - carry[9] = s9 >> 21 - s10 += carry[9] - s9 -= carry[9] << 21 - carry[10] = s10 >> 21 - s11 += carry[10] - s10 -= carry[10] << 21 - carry[11] = s11 >> 21 - s12 += carry[11] - s11 -= carry[11] << 21 - - s0 += s12 * 666643 - s1 += s12 * 470296 - s2 += s12 * 654183 - s3 -= s12 * 997805 - s4 += s12 * 136657 - s5 -= s12 * 683901 - s12 = 0 - - carry[0] = s0 >> 21 - s1 += carry[0] - s0 -= carry[0] << 21 - carry[1] = s1 >> 21 - s2 += carry[1] - s1 -= carry[1] << 21 - carry[2] = s2 >> 21 - s3 += carry[2] - s2 -= carry[2] << 21 - carry[3] = s3 >> 21 - s4 += carry[3] - s3 -= carry[3] << 21 - carry[4] = s4 >> 21 - s5 += carry[4] - s4 -= carry[4] << 21 - carry[5] = s5 >> 21 - s6 += carry[5] - s5 -= carry[5] << 21 - carry[6] = s6 >> 21 - s7 += carry[6] - s6 -= carry[6] << 21 - carry[7] = s7 >> 21 - s8 += carry[7] - s7 -= carry[7] << 21 - carry[8] = s8 >> 21 - s9 += carry[8] - s8 -= carry[8] << 21 - carry[9] = s9 >> 21 - s10 += carry[9] - s9 -= carry[9] << 21 - carry[10] = s10 >> 21 - s11 += carry[10] - s10 -= carry[10] << 21 - - s[0] = byte(s0 >> 0) - s[1] = byte(s0 >> 8) - s[2] = byte((s0 >> 16) | (s1 << 5)) - s[3] = byte(s1 >> 3) - s[4] = byte(s1 >> 11) - s[5] = byte((s1 >> 19) | (s2 << 2)) - s[6] = byte(s2 >> 6) - s[7] = byte((s2 >> 14) | (s3 << 7)) - s[8] = byte(s3 >> 1) - s[9] = byte(s3 >> 9) - s[10] = byte((s3 >> 17) | (s4 << 4)) - s[11] = byte(s4 >> 4) - s[12] = byte(s4 >> 12) - s[13] = byte((s4 >> 20) | (s5 << 1)) - s[14] = byte(s5 >> 7) - s[15] = byte((s5 >> 15) | (s6 << 6)) - s[16] = byte(s6 >> 2) - s[17] = byte(s6 >> 10) - s[18] = byte((s6 >> 18) | (s7 << 3)) - s[19] = byte(s7 >> 5) - s[20] = byte(s7 >> 13) - s[21] = byte(s8 >> 0) - s[22] = byte(s8 >> 8) - s[23] = byte((s8 >> 16) | (s9 << 5)) - s[24] = byte(s9 >> 3) - s[25] = byte(s9 >> 11) - s[26] = byte((s9 >> 19) | (s10 << 2)) - s[27] = byte(s10 >> 6) - s[28] = byte((s10 >> 14) | (s11 << 7)) - s[29] = byte(s11 >> 1) - s[30] = byte(s11 >> 9) - s[31] = byte(s11 >> 17) -} - -// Input: -// s[0]+256*s[1]+...+256^63*s[63] = s -// -// Output: -// s[0]+256*s[1]+...+256^31*s[31] = s mod l -// where l = 2^252 + 27742317777372353535851937790883648493. -func ScReduce(out *[32]byte, s *[64]byte) { - s0 := 2097151 & load3(s[:]) - s1 := 2097151 & (load4(s[2:]) >> 5) - s2 := 2097151 & (load3(s[5:]) >> 2) - s3 := 2097151 & (load4(s[7:]) >> 7) - s4 := 2097151 & (load4(s[10:]) >> 4) - s5 := 2097151 & (load3(s[13:]) >> 1) - s6 := 2097151 & (load4(s[15:]) >> 6) - s7 := 2097151 & (load3(s[18:]) >> 3) - s8 := 2097151 & load3(s[21:]) - s9 := 2097151 & (load4(s[23:]) >> 5) - s10 := 2097151 & (load3(s[26:]) >> 2) - s11 := 2097151 & (load4(s[28:]) >> 7) - s12 := 2097151 & (load4(s[31:]) >> 4) - s13 := 2097151 & (load3(s[34:]) >> 1) - s14 := 2097151 & (load4(s[36:]) >> 6) - s15 := 2097151 & (load3(s[39:]) >> 3) - s16 := 2097151 & load3(s[42:]) - s17 := 2097151 & (load4(s[44:]) >> 5) - s18 := 2097151 & (load3(s[47:]) >> 2) - s19 := 2097151 & (load4(s[49:]) >> 7) - s20 := 2097151 & (load4(s[52:]) >> 4) - s21 := 2097151 & (load3(s[55:]) >> 1) - s22 := 2097151 & (load4(s[57:]) >> 6) - s23 := (load4(s[60:]) >> 3) - - s11 += s23 * 666643 - s12 += s23 * 470296 - s13 += s23 * 654183 - s14 -= s23 * 997805 - s15 += s23 * 136657 - s16 -= s23 * 683901 - s23 = 0 - - s10 += s22 * 666643 - s11 += s22 * 470296 - s12 += s22 * 654183 - s13 -= s22 * 997805 - s14 += s22 * 136657 - s15 -= s22 * 683901 - s22 = 0 - - s9 += s21 * 666643 - s10 += s21 * 470296 - s11 += s21 * 654183 - s12 -= s21 * 997805 - s13 += s21 * 136657 - s14 -= s21 * 683901 - s21 = 0 - - s8 += s20 * 666643 - s9 += s20 * 470296 - s10 += s20 * 654183 - s11 -= s20 * 997805 - s12 += s20 * 136657 - s13 -= s20 * 683901 - s20 = 0 - - s7 += s19 * 666643 - s8 += s19 * 470296 - s9 += s19 * 654183 - s10 -= s19 * 997805 - s11 += s19 * 136657 - s12 -= s19 * 683901 - s19 = 0 - - s6 += s18 * 666643 - s7 += s18 * 470296 - s8 += s18 * 654183 - s9 -= s18 * 997805 - s10 += s18 * 136657 - s11 -= s18 * 683901 - s18 = 0 - - var carry [17]int64 - - carry[6] = (s6 + (1 << 20)) >> 21 - s7 += carry[6] - s6 -= carry[6] << 21 - carry[8] = (s8 + (1 << 20)) >> 21 - s9 += carry[8] - s8 -= carry[8] << 21 - carry[10] = (s10 + (1 << 20)) >> 21 - s11 += carry[10] - s10 -= carry[10] << 21 - carry[12] = (s12 + (1 << 20)) >> 21 - s13 += carry[12] - s12 -= carry[12] << 21 - carry[14] = (s14 + (1 << 20)) >> 21 - s15 += carry[14] - s14 -= carry[14] << 21 - carry[16] = (s16 + (1 << 20)) >> 21 - s17 += carry[16] - s16 -= carry[16] << 21 - - carry[7] = (s7 + (1 << 20)) >> 21 - s8 += carry[7] - s7 -= carry[7] << 21 - carry[9] = (s9 + (1 << 20)) >> 21 - s10 += carry[9] - s9 -= carry[9] << 21 - carry[11] = (s11 + (1 << 20)) >> 21 - s12 += carry[11] - s11 -= carry[11] << 21 - carry[13] = (s13 + (1 << 20)) >> 21 - s14 += carry[13] - s13 -= carry[13] << 21 - carry[15] = (s15 + (1 << 20)) >> 21 - s16 += carry[15] - s15 -= carry[15] << 21 - - s5 += s17 * 666643 - s6 += s17 * 470296 - s7 += s17 * 654183 - s8 -= s17 * 997805 - s9 += s17 * 136657 - s10 -= s17 * 683901 - s17 = 0 - - s4 += s16 * 666643 - s5 += s16 * 470296 - s6 += s16 * 654183 - s7 -= s16 * 997805 - s8 += s16 * 136657 - s9 -= s16 * 683901 - s16 = 0 - - s3 += s15 * 666643 - s4 += s15 * 470296 - s5 += s15 * 654183 - s6 -= s15 * 997805 - s7 += s15 * 136657 - s8 -= s15 * 683901 - s15 = 0 - - s2 += s14 * 666643 - s3 += s14 * 470296 - s4 += s14 * 654183 - s5 -= s14 * 997805 - s6 += s14 * 136657 - s7 -= s14 * 683901 - s14 = 0 - - s1 += s13 * 666643 - s2 += s13 * 470296 - s3 += s13 * 654183 - s4 -= s13 * 997805 - s5 += s13 * 136657 - s6 -= s13 * 683901 - s13 = 0 - - s0 += s12 * 666643 - s1 += s12 * 470296 - s2 += s12 * 654183 - s3 -= s12 * 997805 - s4 += s12 * 136657 - s5 -= s12 * 683901 - s12 = 0 - - carry[0] = (s0 + (1 << 20)) >> 21 - s1 += carry[0] - s0 -= carry[0] << 21 - carry[2] = (s2 + (1 << 20)) >> 21 - s3 += carry[2] - s2 -= carry[2] << 21 - carry[4] = (s4 + (1 << 20)) >> 21 - s5 += carry[4] - s4 -= carry[4] << 21 - carry[6] = (s6 + (1 << 20)) >> 21 - s7 += carry[6] - s6 -= carry[6] << 21 - carry[8] = (s8 + (1 << 20)) >> 21 - s9 += carry[8] - s8 -= carry[8] << 21 - carry[10] = (s10 + (1 << 20)) >> 21 - s11 += carry[10] - s10 -= carry[10] << 21 - - carry[1] = (s1 + (1 << 20)) >> 21 - s2 += carry[1] - s1 -= carry[1] << 21 - carry[3] = (s3 + (1 << 20)) >> 21 - s4 += carry[3] - s3 -= carry[3] << 21 - carry[5] = (s5 + (1 << 20)) >> 21 - s6 += carry[5] - s5 -= carry[5] << 21 - carry[7] = (s7 + (1 << 20)) >> 21 - s8 += carry[7] - s7 -= carry[7] << 21 - carry[9] = (s9 + (1 << 20)) >> 21 - s10 += carry[9] - s9 -= carry[9] << 21 - carry[11] = (s11 + (1 << 20)) >> 21 - s12 += carry[11] - s11 -= carry[11] << 21 - - s0 += s12 * 666643 - s1 += s12 * 470296 - s2 += s12 * 654183 - s3 -= s12 * 997805 - s4 += s12 * 136657 - s5 -= s12 * 683901 - s12 = 0 - - carry[0] = s0 >> 21 - s1 += carry[0] - s0 -= carry[0] << 21 - carry[1] = s1 >> 21 - s2 += carry[1] - s1 -= carry[1] << 21 - carry[2] = s2 >> 21 - s3 += carry[2] - s2 -= carry[2] << 21 - carry[3] = s3 >> 21 - s4 += carry[3] - s3 -= carry[3] << 21 - carry[4] = s4 >> 21 - s5 += carry[4] - s4 -= carry[4] << 21 - carry[5] = s5 >> 21 - s6 += carry[5] - s5 -= carry[5] << 21 - carry[6] = s6 >> 21 - s7 += carry[6] - s6 -= carry[6] << 21 - carry[7] = s7 >> 21 - s8 += carry[7] - s7 -= carry[7] << 21 - carry[8] = s8 >> 21 - s9 += carry[8] - s8 -= carry[8] << 21 - carry[9] = s9 >> 21 - s10 += carry[9] - s9 -= carry[9] << 21 - carry[10] = s10 >> 21 - s11 += carry[10] - s10 -= carry[10] << 21 - carry[11] = s11 >> 21 - s12 += carry[11] - s11 -= carry[11] << 21 - - s0 += s12 * 666643 - s1 += s12 * 470296 - s2 += s12 * 654183 - s3 -= s12 * 997805 - s4 += s12 * 136657 - s5 -= s12 * 683901 - s12 = 0 - - carry[0] = s0 >> 21 - s1 += carry[0] - s0 -= carry[0] << 21 - carry[1] = s1 >> 21 - s2 += carry[1] - s1 -= carry[1] << 21 - carry[2] = s2 >> 21 - s3 += carry[2] - s2 -= carry[2] << 21 - carry[3] = s3 >> 21 - s4 += carry[3] - s3 -= carry[3] << 21 - carry[4] = s4 >> 21 - s5 += carry[4] - s4 -= carry[4] << 21 - carry[5] = s5 >> 21 - s6 += carry[5] - s5 -= carry[5] << 21 - carry[6] = s6 >> 21 - s7 += carry[6] - s6 -= carry[6] << 21 - carry[7] = s7 >> 21 - s8 += carry[7] - s7 -= carry[7] << 21 - carry[8] = s8 >> 21 - s9 += carry[8] - s8 -= carry[8] << 21 - carry[9] = s9 >> 21 - s10 += carry[9] - s9 -= carry[9] << 21 - carry[10] = s10 >> 21 - s11 += carry[10] - s10 -= carry[10] << 21 - - out[0] = byte(s0 >> 0) - out[1] = byte(s0 >> 8) - out[2] = byte((s0 >> 16) | (s1 << 5)) - out[3] = byte(s1 >> 3) - out[4] = byte(s1 >> 11) - out[5] = byte((s1 >> 19) | (s2 << 2)) - out[6] = byte(s2 >> 6) - out[7] = byte((s2 >> 14) | (s3 << 7)) - out[8] = byte(s3 >> 1) - out[9] = byte(s3 >> 9) - out[10] = byte((s3 >> 17) | (s4 << 4)) - out[11] = byte(s4 >> 4) - out[12] = byte(s4 >> 12) - out[13] = byte((s4 >> 20) | (s5 << 1)) - out[14] = byte(s5 >> 7) - out[15] = byte((s5 >> 15) | (s6 << 6)) - out[16] = byte(s6 >> 2) - out[17] = byte(s6 >> 10) - out[18] = byte((s6 >> 18) | (s7 << 3)) - out[19] = byte(s7 >> 5) - out[20] = byte(s7 >> 13) - out[21] = byte(s8 >> 0) - out[22] = byte(s8 >> 8) - out[23] = byte((s8 >> 16) | (s9 << 5)) - out[24] = byte(s9 >> 3) - out[25] = byte(s9 >> 11) - out[26] = byte((s9 >> 19) | (s10 << 2)) - out[27] = byte(s10 >> 6) - out[28] = byte((s10 >> 14) | (s11 << 7)) - out[29] = byte(s11 >> 1) - out[30] = byte(s11 >> 9) - out[31] = byte(s11 >> 17) -} - -// order is the order of Curve25519 in little-endian form. -var order = [4]uint64{0x5812631a5cf5d3ed, 0x14def9dea2f79cd6, 0, 0x1000000000000000} - -// ScMinimal returns true if the given scalar is less than the order of the -// curve. -func ScMinimal(scalar *[32]byte) bool { - for i := 3; ; i-- { - v := binary.LittleEndian.Uint64(scalar[i*8:]) - if v > order[i] { - return false - } else if v < order[i] { - break - } else if i == 0 { - return false - } - } - - return true -} diff --git a/vendor/golang.org/x/crypto/ssh/cipher.go b/vendor/golang.org/x/crypto/ssh/cipher.go index bddbde5d..f8bdf498 100644 --- a/vendor/golang.org/x/crypto/ssh/cipher.go +++ b/vendor/golang.org/x/crypto/ssh/cipher.go @@ -394,6 +394,10 @@ func (c *gcmCipher) readCipherPacket(seqNum uint32, r io.Reader) ([]byte, error) } c.incIV() + if len(plain) == 0 { + return nil, errors.New("ssh: empty packet") + } + padding := plain[0] if padding < 4 { // padding is a byte, so it automatically satisfies @@ -710,6 +714,10 @@ func (c *chacha20Poly1305Cipher) readCipherPacket(seqNum uint32, r io.Reader) ([ plain := c.buf[4:contentEnd] s.XORKeyStream(plain, plain) + if len(plain) == 0 { + return nil, errors.New("ssh: empty packet") + } + padding := plain[0] if padding < 4 { // padding is a byte, so it automatically satisfies diff --git a/vendor/golang.org/x/crypto/ssh/server.go b/vendor/golang.org/x/crypto/ssh/server.go index 6a58e120..bf5364c3 100644 --- a/vendor/golang.org/x/crypto/ssh/server.go +++ b/vendor/golang.org/x/crypto/ssh/server.go @@ -633,6 +633,30 @@ userAuthLoop: } authFailures++ + if config.MaxAuthTries > 0 && authFailures >= config.MaxAuthTries { + // If we have hit the max attempts, don't bother sending the + // final SSH_MSG_USERAUTH_FAILURE message, since there are + // no more authentication methods which can be attempted, + // and this message may cause the client to re-attempt + // authentication while we send the disconnect message. + // Continue, and trigger the disconnect at the start of + // the loop. + // + // The SSH specification is somewhat confusing about this, + // RFC 4252 Section 5.1 requires each authentication failure + // be responded to with a respective SSH_MSG_USERAUTH_FAILURE + // message, but Section 4 says the server should disconnect + // after some number of attempts, but it isn't explicit which + // message should take precedence (i.e. should there be a failure + // message than a disconnect message, or if we are going to + // disconnect, should we only send that message.) + // + // Either way, OpenSSH disconnects immediately after the last + // failed authnetication attempt, and given they are typically + // considered the golden implementation it seems reasonable + // to match that behavior. + continue + } var failureMsg userAuthFailureMsg if config.PasswordCallback != nil { |