104 lines
2.3 KiB
Go
104 lines
2.3 KiB
Go
|
// Copyright 2018 (c) NSPCC
|
||
|
|
//
|
||
|
|
// Package gf127 implements the GF(2^127) arithmetic
|
||
|
|
// modulo reduction polynomial x^127 + x^63 + 1 .
|
||
|
|
// This is rather straight-forward re-implementation of C library
|
||
|
|
// available here https://github.com/srijs/hwsl2-core .
|
||
|
|
// Interfaces are highly influenced by math/big .
|
||
|
|
package gf127
|
||
|
|
|
||
|
|
import (
|
||
|
|
"encoding/binary"
|
||
|
|
"encoding/hex"
|
||
|
|
"errors"
|
||
|
|
)
|
||
|
|
|
||
|
|
// GF127 represents element of GF(2^127)
|
||
|
|
type GF127 [2]uint64
|
||
|
|
|
||
|
|
const msb64 = 0x8000000000000000
|
||
|
|
const byteSize = 16
|
||
|
|
|
||
|
|
// x127x64 represents x^127 + x^63. Used in assembly file.
|
||
|
|
var x127x63 = GF127{msb64, msb64}
|
||
|
|
|
||
|
|
// New constructs new element of GF(2^127) as hi*x^64 + lo.
|
||
|
|
// It is assumed that hi has zero MSB.
|
||
|
|
func New(lo, hi uint64) *GF127 {
|
||
|
|
return &GF127{lo, hi}
|
||
|
|
}
|
||
|
|
|
||
|
|
// String returns hex-encoded representation, starting with MSB.
|
||
|
|
func (c *GF127) String() string {
|
||
|
|
return hex.EncodeToString(c.ByteArray())
|
||
|
|
}
|
||
|
|
|
||
|
|
// Equals checks if two reduced (zero MSB) elements of GF(2^127) are equal
|
||
|
|
func (c *GF127) Equals(b *GF127) bool {
|
||
|
|
return c[0] == b[0] && c[1] == b[1]
|
||
|
|
}
|
||
|
|
|
||
|
|
// ByteArray represents element of GF(2^127) as byte array of length 16.
|
||
|
|
func (c *GF127) ByteArray() (buf []byte) {
|
||
|
|
buf = make([]byte, 16)
|
||
|
|
binary.BigEndian.PutUint64(buf[:8], c[1])
|
||
|
|
binary.BigEndian.PutUint64(buf[8:], c[0])
|
||
|
|
return
|
||
|
|
}
|
||
|
|
|
||
|
|
// MarshalBinary implements encoding.BinaryMarshaler.
|
||
|
|
func (c *GF127) MarshalBinary() (data []byte, err error) {
|
||
|
|
return c.ByteArray(), nil
|
||
|
|
}
|
||
|
|
|
||
|
|
// UnmarshalBinary implements encoding.BinaryUnmarshaler.
|
||
|
|
func (c *GF127) UnmarshalBinary(data []byte) error {
|
||
|
|
if len(data) != byteSize {
|
||
|
|
return errors.New("data must be 16-bytes long")
|
||
|
|
}
|
||
|
|
|
||
|
|
c[0] = binary.BigEndian.Uint64(data[8:])
|
||
|
|
c[1] = binary.BigEndian.Uint64(data[:8])
|
||
|
|
if c[1]&msb64 != 0 {
|
||
|
|
return errors.New("MSB must be zero")
|
||
|
|
}
|
||
|
|
|
||
|
|
return nil
|
||
|
|
}
|
||
|
|
|
||
|
|
// Mul sets c to the product a*b and returns c.
|
||
|
|
func (c *GF127) Mul(a, b *GF127) *GF127 {
|
||
|
|
Mul(a, b, c)
|
||
|
|
return c
|
||
|
|
}
|
||
|
|
|
||
|
|
// Add sets c to the sum a+b and returns c.
|
||
|
|
func (c *GF127) Add(a, b *GF127) *GF127 {
|
||
|
|
Add(a, b, c)
|
||
|
|
return c
|
||
|
|
}
|
||
|
|
|
||
|
|
// Mul1 copies a to b.
|
||
|
|
func Mul1(a, b *GF127) {
|
||
|
|
b[0] = a[0]
|
||
|
|
b[1] = a[1]
|
||
|
|
}
|
||
|
|
|
||
|
|
// And sets c to a & b (bitwise-and).
|
||
|
|
func And(a, b, c *GF127) {
|
||
|
|
c[0] = a[0] & b[0]
|
||
|
|
c[1] = a[1] & b[1]
|
||
|
|
}
|
||
|
|
|
||
|
|
// Add sets c to a+b.
|
||
|
|
func Add(a, b, c *GF127)
|
||
|
|
|
||
|
|
// Mul sets c to a*b.
|
||
|
|
func Mul(a, b, c *GF127)
|
||
|
|
|
||
|
|
// Mul10 sets y to a*x.
|
||
|
|
func Mul10(a, b *GF127)
|
||
|
|
|
||
|
|
// Mul11 sets y to a*(x+1).
|
||
|
|
func Mul11(a, b *GF127)
|