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