vendor.github.com.cloudflare.circl.sign.ed448.ed448.go Maven / Gradle / Ivy
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// Package ed448 implements Ed448 signature scheme as described in RFC-8032.
//
// This package implements two signature variants.
//
// | Scheme Name | Sign Function | Verification | Context |
// |-------------|-------------------|---------------|-------------------|
// | Ed448 | Sign | Verify | Yes, can be empty |
// | Ed448Ph | SignPh | VerifyPh | Yes, can be empty |
// | All above | (PrivateKey).Sign | VerifyAny | As above |
//
// Specific functions for sign and verify are defined. A generic signing
// function for all schemes is available through the crypto.Signer interface,
// which is implemented by the PrivateKey type. A correspond all-in-one
// verification method is provided by the VerifyAny function.
//
// Both schemes require a context string for domain separation. This parameter
// is passed using a SignerOptions struct defined in this package.
//
// References:
//
// - RFC8032: https://rfc-editor.org/rfc/rfc8032.txt
// - EdDSA for more curves: https://eprint.iacr.org/2015/677
// - High-speed high-security signatures: https://doi.org/10.1007/s13389-012-0027-1
package ed448
import (
"bytes"
"crypto"
cryptoRand "crypto/rand"
"crypto/subtle"
"errors"
"fmt"
"io"
"strconv"
"github.com/cloudflare/circl/ecc/goldilocks"
"github.com/cloudflare/circl/internal/sha3"
"github.com/cloudflare/circl/sign"
)
const (
// ContextMaxSize is the maximum length (in bytes) allowed for context.
ContextMaxSize = 255
// PublicKeySize is the length in bytes of Ed448 public keys.
PublicKeySize = 57
// PrivateKeySize is the length in bytes of Ed448 private keys.
PrivateKeySize = 114
// SignatureSize is the length in bytes of signatures.
SignatureSize = 114
// SeedSize is the size, in bytes, of private key seeds. These are the private key representations used by RFC 8032.
SeedSize = 57
)
const (
paramB = 456 / 8 // Size of keys in bytes.
hashSize = 2 * paramB // Size of the hash function's output.
)
// SignerOptions implements crypto.SignerOpts and augments with parameters
// that are specific to the Ed448 signature schemes.
type SignerOptions struct {
// Hash must be crypto.Hash(0) for both Ed448 and Ed448Ph.
crypto.Hash
// Context is an optional domain separation string for signing.
// Its length must be less or equal than 255 bytes.
Context string
// Scheme is an identifier for choosing a signature scheme.
Scheme SchemeID
}
// SchemeID is an identifier for each signature scheme.
type SchemeID uint
const (
ED448 SchemeID = iota
ED448Ph
)
// PublicKey is the type of Ed448 public keys.
type PublicKey []byte
// Equal reports whether pub and x have the same value.
func (pub PublicKey) Equal(x crypto.PublicKey) bool {
xx, ok := x.(PublicKey)
return ok && bytes.Equal(pub, xx)
}
// PrivateKey is the type of Ed448 private keys. It implements crypto.Signer.
type PrivateKey []byte
// Equal reports whether priv and x have the same value.
func (priv PrivateKey) Equal(x crypto.PrivateKey) bool {
xx, ok := x.(PrivateKey)
return ok && subtle.ConstantTimeCompare(priv, xx) == 1
}
// Public returns the PublicKey corresponding to priv.
func (priv PrivateKey) Public() crypto.PublicKey {
publicKey := make([]byte, PublicKeySize)
copy(publicKey, priv[SeedSize:])
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[:SeedSize])
return seed
}
func (priv PrivateKey) Scheme() sign.Scheme { return sch }
func (pub PublicKey) Scheme() sign.Scheme { return sch }
func (priv PrivateKey) MarshalBinary() (data []byte, err error) {
privateKey := make(PrivateKey, PrivateKeySize)
copy(privateKey, priv)
return privateKey, nil
}
func (pub PublicKey) MarshalBinary() (data []byte, err error) {
publicKey := make(PublicKey, PublicKeySize)
copy(publicKey, pub)
return publicKey, nil
}
// Sign creates a signature of a message given a key pair.
// This function supports all the two signature variants defined in RFC-8032,
// namely Ed448 (or pure EdDSA) and Ed448Ph.
// The opts.HashFunc() must return zero to the specify Ed448 variant. This can
// be achieved by passing crypto.Hash(0) as the value for opts.
// Use an Options struct to pass a bool indicating that the ed448Ph variant
// should be used.
// The struct can also be optionally used to pass a context string for signing.
func (priv PrivateKey) Sign(
rand io.Reader,
message []byte,
opts crypto.SignerOpts,
) (signature []byte, err error) {
var ctx string
var scheme SchemeID
if o, ok := opts.(SignerOptions); ok {
ctx = o.Context
scheme = o.Scheme
}
switch true {
case scheme == ED448 && opts.HashFunc() == crypto.Hash(0):
return Sign(priv, message, ctx), nil
case scheme == ED448Ph && opts.HashFunc() == crypto.Hash(0):
return SignPh(priv, message, ctx), nil
default:
return nil, errors.New("ed448: bad hash algorithm")
}
}
// 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(PrivateKey, SeedSize)
if _, err := io.ReadFull(rand, seed); err != nil {
return nil, nil, err
}
privateKey := NewKeyFromSeed(seed)
publicKey := make([]byte, PublicKeySize)
copy(publicKey, privateKey[SeedSize:])
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 {
privateKey := make([]byte, PrivateKeySize)
newKeyFromSeed(privateKey, seed)
return privateKey
}
func newKeyFromSeed(privateKey, seed []byte) {
if l := len(seed); l != SeedSize {
panic("ed448: bad seed length: " + strconv.Itoa(l))
}
var h [hashSize]byte
H := sha3.NewShake256()
_, _ = H.Write(seed)
_, _ = H.Read(h[:])
s := &goldilocks.Scalar{}
deriveSecretScalar(s, h[:paramB])
copy(privateKey[:SeedSize], seed)
_ = goldilocks.Curve{}.ScalarBaseMult(s).ToBytes(privateKey[SeedSize:])
}
func signAll(signature []byte, privateKey PrivateKey, message, ctx []byte, preHash bool) {
if len(ctx) > ContextMaxSize {
panic(fmt.Errorf("ed448: bad context length: " + strconv.Itoa(len(ctx))))
}
H := sha3.NewShake256()
var PHM []byte
if preHash {
var h [64]byte
_, _ = H.Write(message)
_, _ = H.Read(h[:])
PHM = h[:]
H.Reset()
} else {
PHM = message
}
// 1. Hash the 57-byte private key using SHAKE256(x, 114).
var h [hashSize]byte
_, _ = H.Write(privateKey[:SeedSize])
_, _ = H.Read(h[:])
s := &goldilocks.Scalar{}
deriveSecretScalar(s, h[:paramB])
prefix := h[paramB:]
// 2. Compute SHAKE256(dom4(F, C) || prefix || PH(M), 114).
var rPM [hashSize]byte
H.Reset()
writeDom(&H, ctx, preHash)
_, _ = H.Write(prefix)
_, _ = H.Write(PHM)
_, _ = H.Read(rPM[:])
// 3. Compute the point [r]B.
r := &goldilocks.Scalar{}
r.FromBytes(rPM[:])
R := (&[paramB]byte{})[:]
if err := (goldilocks.Curve{}.ScalarBaseMult(r).ToBytes(R)); err != nil {
panic(err)
}
// 4. Compute SHAKE256(dom4(F, C) || R || A || PH(M), 114)
var hRAM [hashSize]byte
H.Reset()
writeDom(&H, ctx, preHash)
_, _ = H.Write(R)
_, _ = H.Write(privateKey[SeedSize:])
_, _ = H.Write(PHM)
_, _ = H.Read(hRAM[:])
// 5. Compute S = (r + k * s) mod order.
k := &goldilocks.Scalar{}
k.FromBytes(hRAM[:])
S := &goldilocks.Scalar{}
S.Mul(k, s)
S.Add(S, r)
// 6. The signature is the concatenation of R and S.
copy(signature[:paramB], R[:])
copy(signature[paramB:], S[:])
}
// Sign signs the message with privateKey and returns a signature.
// This function supports the signature variant defined in RFC-8032: Ed448,
// also known as the pure version of EdDSA.
// It will panic if len(privateKey) is not PrivateKeySize.
func Sign(priv PrivateKey, message []byte, ctx string) []byte {
signature := make([]byte, SignatureSize)
signAll(signature, priv, message, []byte(ctx), false)
return signature
}
// SignPh creates a signature of a message given a keypair.
// This function supports the signature variant defined in RFC-8032: Ed448ph,
// meaning it internally hashes the message using SHAKE-256.
// Context could be passed to this function, which length should be no more than
// 255. It can be empty.
func SignPh(priv PrivateKey, message []byte, ctx string) []byte {
signature := make([]byte, SignatureSize)
signAll(signature, priv, message, []byte(ctx), true)
return signature
}
func verify(public PublicKey, message, signature, ctx []byte, preHash bool) bool {
if len(public) != PublicKeySize ||
len(signature) != SignatureSize ||
len(ctx) > ContextMaxSize ||
!isLessThanOrder(signature[paramB:]) {
return false
}
P, err := goldilocks.FromBytes(public)
if err != nil {
return false
}
H := sha3.NewShake256()
var PHM []byte
if preHash {
var h [64]byte
_, _ = H.Write(message)
_, _ = H.Read(h[:])
PHM = h[:]
H.Reset()
} else {
PHM = message
}
var hRAM [hashSize]byte
R := signature[:paramB]
writeDom(&H, ctx, preHash)
_, _ = H.Write(R)
_, _ = H.Write(public)
_, _ = H.Write(PHM)
_, _ = H.Read(hRAM[:])
k := &goldilocks.Scalar{}
k.FromBytes(hRAM[:])
S := &goldilocks.Scalar{}
S.FromBytes(signature[paramB:])
encR := (&[paramB]byte{})[:]
P.Neg()
_ = goldilocks.Curve{}.CombinedMult(S, k, P).ToBytes(encR)
return bytes.Equal(R, encR)
}
// VerifyAny returns true if the signature is valid. Failure cases are invalid
// signature, or when the public key cannot be decoded.
// This function supports all the two signature variants defined in RFC-8032,
// namely Ed448 (or pure EdDSA) and Ed448Ph.
// The opts.HashFunc() must return zero, this can be achieved by passing
// crypto.Hash(0) as the value for opts.
// Use a SignerOptions struct to pass a context string for signing.
func VerifyAny(public PublicKey, message, signature []byte, opts crypto.SignerOpts) bool {
var ctx string
var scheme SchemeID
if o, ok := opts.(SignerOptions); ok {
ctx = o.Context
scheme = o.Scheme
}
switch true {
case scheme == ED448 && opts.HashFunc() == crypto.Hash(0):
return Verify(public, message, signature, ctx)
case scheme == ED448Ph && opts.HashFunc() == crypto.Hash(0):
return VerifyPh(public, message, signature, ctx)
default:
return false
}
}
// Verify returns true if the signature is valid. Failure cases are invalid
// signature, or when the public key cannot be decoded.
// This function supports the signature variant defined in RFC-8032: Ed448,
// also known as the pure version of EdDSA.
func Verify(public PublicKey, message, signature []byte, ctx string) bool {
return verify(public, message, signature, []byte(ctx), false)
}
// VerifyPh returns true if the signature is valid. Failure cases are invalid
// signature, or when the public key cannot be decoded.
// This function supports the signature variant defined in RFC-8032: Ed448ph,
// meaning it internally hashes the message using SHAKE-256.
// Context could be passed to this function, which length should be no more than
// 255. It can be empty.
func VerifyPh(public PublicKey, message, signature []byte, ctx string) bool {
return verify(public, message, signature, []byte(ctx), true)
}
func deriveSecretScalar(s *goldilocks.Scalar, h []byte) {
h[0] &= 0xFC // The two least significant bits of the first octet are cleared,
h[paramB-1] = 0x00 // all eight bits the last octet are cleared, and
h[paramB-2] |= 0x80 // the highest bit of the second to last octet is set.
s.FromBytes(h[:paramB])
}
// isLessThanOrder returns true if 0 <= x < order and if the last byte of x is zero.
func isLessThanOrder(x []byte) bool {
order := goldilocks.Curve{}.Order()
i := len(order) - 1
for i > 0 && x[i] == order[i] {
i--
}
return x[paramB-1] == 0 && x[i] < order[i]
}
func writeDom(h io.Writer, ctx []byte, preHash bool) {
dom4 := "SigEd448"
_, _ = h.Write([]byte(dom4))
if preHash {
_, _ = h.Write([]byte{byte(0x01), byte(len(ctx))})
} else {
_, _ = h.Write([]byte{byte(0x00), byte(len(ctx))})
}
_, _ = h.Write(ctx)
}
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