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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
// 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
// This code is a port of the public domain, “ref10” implementation of ed25519
// from SUPERCOP.
import (
cryptorand "crypto/rand"
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
// 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
// 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 {
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
privateKey := make([]byte, PrivateKeySize)
copy(privateKey, seed)
copy(privateKey[32:], publicKeyBytes[:])
return privateKey
// 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()
var digest1, messageDigest, hramDigest [64]byte
var expandedSecretKey [32]byte
copy(expandedSecretKey[:], digest1[:])
expandedSecretKey[0] &= 248
expandedSecretKey[31] &= 63
expandedSecretKey[31] |= 64
var messageDigestReduced [32]byte
edwards25519.ScReduce(&messageDigestReduced, &messageDigest)
var R edwards25519.ExtendedGroupElement
edwards25519.GeScalarMultBase(&R, &messageDigestReduced)
var encodedR [32]byte
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
// 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()
var digest [64]byte
var hReduced [32]byte
edwards25519.ScReduce(&hReduced, &digest)
var R edwards25519.ProjectiveGroupElement
var s [32]byte
copy(s[:], sig[32:])
// 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
return bytes.Equal(sig[:32], checkR[:])