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// 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 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”.
package ed25519
import (
"bytes"
"crypto"
"crypto/internal/edwards25519"
cryptorand "crypto/rand"
"crypto/sha512"
"errors"
"io"
"strconv"
)
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.
type PublicKey []byte
// Any methods implemented on PublicKey might need to also be implemented on
// PrivateKey, as the latter embeds the former and will expose its methods.
// Equal reports whether pub and x have the same value.
func (pub PublicKey) Equal(x crypto.PublicKey) bool {
xx, ok := x.(PublicKey)
if !ok {
return false
}
return bytes.Equal(pub, xx)
}
// 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)
}
// Equal reports whether priv and x have the same value.
func (priv PrivateKey) Equal(x crypto.PrivateKey) bool {
xx, ok := x.(PrivateKey)
if !ok {
return false
}
return bytes.Equal(priv, xx)
}
// 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 {
return bytes.Clone(priv[:SeedSize])
}
// Sign signs the given message with priv. rand is ignored.
//
// If opts.HashFunc() is [crypto.SHA512], the pre-hashed variant Ed25519ph is used
// and message is expected to be a SHA-512 hash, otherwise opts.HashFunc() must
// be [crypto.Hash](0) and the message must not be hashed, as Ed25519 performs two
// passes over messages to be signed.
//
// A value of type [Options] can be used as opts, or crypto.Hash(0) or
// crypto.SHA512 directly to select plain Ed25519 or Ed25519ph, respectively.
func (priv PrivateKey) Sign(rand io.Reader, message []byte, opts crypto.SignerOpts) (signature []byte, err error) {
hash := opts.HashFunc()
context := ""
if opts, ok := opts.(*Options); ok {
context = opts.Context
}
if l := len(context); l > 255 {
return nil, errors.New("ed25519: bad Ed25519ph context length: " + strconv.Itoa(l))
}
switch {
case hash == crypto.SHA512: // Ed25519ph
if l := len(message); l != sha512.Size {
return nil, errors.New("ed25519: bad Ed25519ph message hash length: " + strconv.Itoa(l))
}
signature := make([]byte, SignatureSize)
sign(signature, priv, message, domPrefixPh, context)
return signature, nil
case hash == crypto.Hash(0) && context != "": // Ed25519ctx
signature := make([]byte, SignatureSize)
sign(signature, priv, message, domPrefixCtx, context)
return signature, nil
case hash == crypto.Hash(0): // Ed25519
return Sign(priv, message), nil
default:
return nil, errors.New("ed25519: expected opts.HashFunc() zero (unhashed message, for standard Ed25519) or SHA-512 (for Ed25519ph)")
}
}
// Options can be used with [PrivateKey.Sign] or [VerifyWithOptions]
// to select Ed25519 variants.
type Options struct {
// Hash can be zero for regular Ed25519, or crypto.SHA512 for Ed25519ph.
Hash crypto.Hash
// Context, if not empty, selects Ed25519ctx or provides the context string
// for Ed25519ph. It can be at most 255 bytes in length.
Context string
}
// HashFunc returns o.Hash.
func (o *Options) HashFunc() crypto.Hash { return o.Hash }
// 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
}
// 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 {
// Outline the function body so that the returned key can be stack-allocated.
privateKey := make([]byte, PrivateKeySize)
newKeyFromSeed(privateKey, seed)
return privateKey
}
func newKeyFromSeed(privateKey, seed []byte) {
if l := len(seed); l != SeedSize {
panic("ed25519: bad seed length: " + strconv.Itoa(l))
}
h := sha512.Sum512(seed)
s, err := edwards25519.NewScalar().SetBytesWithClamping(h[:32])
if err != nil {
panic("ed25519: internal error: setting scalar failed")
}
A := (&edwards25519.Point{}).ScalarBaseMult(s)
publicKey := A.Bytes()
copy(privateKey, seed)
copy(privateKey[32:], publicKey)
}
// 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 {
// Outline the function body so that the returned signature can be
// stack-allocated.
signature := make([]byte, SignatureSize)
sign(signature, privateKey, message, domPrefixPure, "")
return signature
}
// Domain separation prefixes used to disambiguate Ed25519/Ed25519ph/Ed25519ctx.
// See RFC 8032, Section 2 and Section 5.1.
const (
// domPrefixPure is empty for pure Ed25519.
domPrefixPure = ""
// domPrefixPh is dom2(phflag=1) for Ed25519ph. It must be followed by the
// uint8-length prefixed context.
domPrefixPh = "SigEd25519 no Ed25519 collisions\x01"
// domPrefixCtx is dom2(phflag=0) for Ed25519ctx. It must be followed by the
// uint8-length prefixed context.
domPrefixCtx = "SigEd25519 no Ed25519 collisions\x00"
)
func sign(signature, privateKey, message []byte, domPrefix, context string) {
if l := len(privateKey); l != PrivateKeySize {
panic("ed25519: bad private key length: " + strconv.Itoa(l))
}
seed, publicKey := privateKey[:SeedSize], privateKey[SeedSize:]
h := sha512.Sum512(seed)
s, err := edwards25519.NewScalar().SetBytesWithClamping(h[:32])
if err != nil {
panic("ed25519: internal error: setting scalar failed")
}
prefix := h[32:]
mh := sha512.New()
if domPrefix != domPrefixPure {
mh.Write([]byte(domPrefix))
mh.Write([]byte{byte(len(context))})
mh.Write([]byte(context))
}
mh.Write(prefix)
mh.Write(message)
messageDigest := make([]byte, 0, sha512.Size)
messageDigest = mh.Sum(messageDigest)
r, err := edwards25519.NewScalar().SetUniformBytes(messageDigest)
if err != nil {
panic("ed25519: internal error: setting scalar failed")
}
R := (&edwards25519.Point{}).ScalarBaseMult(r)
kh := sha512.New()
if domPrefix != domPrefixPure {
kh.Write([]byte(domPrefix))
kh.Write([]byte{byte(len(context))})
kh.Write([]byte(context))
}
kh.Write(R.Bytes())
kh.Write(publicKey)
kh.Write(message)
hramDigest := make([]byte, 0, sha512.Size)
hramDigest = kh.Sum(hramDigest)
k, err := edwards25519.NewScalar().SetUniformBytes(hramDigest)
if err != nil {
panic("ed25519: internal error: setting scalar failed")
}
S := edwards25519.NewScalar().MultiplyAdd(k, s, r)
copy(signature[:32], R.Bytes())
copy(signature[32:], S.Bytes())
}
// 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 verify(publicKey, message, sig, domPrefixPure, "")
}
// VerifyWithOptions reports whether sig is a valid signature of message by
// publicKey. A valid signature is indicated by returning a nil error. It will
// panic if len(publicKey) is not [PublicKeySize].
//
// If opts.Hash is [crypto.SHA512], the pre-hashed variant Ed25519ph is used and
// message is expected to be a SHA-512 hash, otherwise opts.Hash must be
// [crypto.Hash](0) and the message must not be hashed, as Ed25519 performs two
// passes over messages to be signed.
func VerifyWithOptions(publicKey PublicKey, message, sig []byte, opts *Options) error {
switch {
case opts.Hash == crypto.SHA512: // Ed25519ph
if l := len(message); l != sha512.Size {
return errors.New("ed25519: bad Ed25519ph message hash length: " + strconv.Itoa(l))
}
if l := len(opts.Context); l > 255 {
return errors.New("ed25519: bad Ed25519ph context length: " + strconv.Itoa(l))
}
if !verify(publicKey, message, sig, domPrefixPh, opts.Context) {
return errors.New("ed25519: invalid signature")
}
return nil
case opts.Hash == crypto.Hash(0) && opts.Context != "": // Ed25519ctx
if l := len(opts.Context); l > 255 {
return errors.New("ed25519: bad Ed25519ctx context length: " + strconv.Itoa(l))
}
if !verify(publicKey, message, sig, domPrefixCtx, opts.Context) {
return errors.New("ed25519: invalid signature")
}
return nil
case opts.Hash == crypto.Hash(0): // Ed25519
if !verify(publicKey, message, sig, domPrefixPure, "") {
return errors.New("ed25519: invalid signature")
}
return nil
default:
return errors.New("ed25519: expected opts.Hash zero (unhashed message, for standard Ed25519) or SHA-512 (for Ed25519ph)")
}
}
func verify(publicKey PublicKey, message, sig []byte, domPrefix, context string) 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
}
A, err := (&edwards25519.Point{}).SetBytes(publicKey)
if err != nil {
return false
}
kh := sha512.New()
if domPrefix != domPrefixPure {
kh.Write([]byte(domPrefix))
kh.Write([]byte{byte(len(context))})
kh.Write([]byte(context))
}
kh.Write(sig[:32])
kh.Write(publicKey)
kh.Write(message)
hramDigest := make([]byte, 0, sha512.Size)
hramDigest = kh.Sum(hramDigest)
k, err := edwards25519.NewScalar().SetUniformBytes(hramDigest)
if err != nil {
panic("ed25519: internal error: setting scalar failed")
}
S, err := edwards25519.NewScalar().SetCanonicalBytes(sig[32:])
if err != nil {
return false
}
// [S]B = R + [k]A --> [k](-A) + [S]B = R
minusA := (&edwards25519.Point{}).Negate(A)
R := (&edwards25519.Point{}).VarTimeDoubleScalarBaseMult(k, minusA, S)
return bytes.Equal(sig[:32], R.Bytes())
}