Source: ed25519.go in package crypto/ed25519

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

This code is a port of the public domain, “ref10” implementation of ed25519 from SUPERCOP.


import (
	"bytes"
	"crypto"
	"crypto/ed25519/internal/edwards25519"
	cryptorand "crypto/rand"
	"crypto/sha512"
	"errors"
	"io"
	"strconv"
)

PublicKeySize is the size, in bytes, of public keys as used in this package.

PrivateKeySize is the size, in bytes, of private keys as used in this package.

SignatureSize is the size, in bytes, of signatures generated and verified by this package.

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 {
	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.

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))
	}

	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)

	copy(privateKey, seed)
	copy(privateKey[32:], publicKeyBytes[:])
}

Sign signs the message with privateKey and returns a signature. It will panic if len(privateKey) is not PrivateKeySize.

Outline the function body so that the returned signature can be stack-allocated.

	signature := make([]byte, SignatureSize)
	sign(signature, privateKey, message)
	return signature
}

func sign(signature, privateKey, message []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)

	copy(signature[:], encodedR[:])
	copy(signature[32:], s[:])
}

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[:])