秘钥交换算法

可以如下定义离散对数：首先定义一个素数p的原根，为其各次幂产生从1 到p-1的所有整数根，也就是说，如果a是素数p的一个原根，那么数值 a mod p,a2 mod p,…,ap-1 mod p 是各不相同的整数，并且以某种排列方式组成了从1到p-1的所有整数. 对于一个整数b和素数p的一个原根a，可以找到惟一的指数i，使得 b = a^i mod p 其中0 ≤ i ≤ （p-1） 指数i称为b的以a为基数的模p的离散对数或者指数.该值被记为inda,p(b).

package main
import (
	"crypto"
	"crypto/elliptic"
	"crypto/rand"
	"fmt"
	"io"
	"math/big"
	"golang.org/x/crypto/curve25519"
)
// ECDH 秘钥交换算法的主接口
type ECDH interface {
	GenerateKey(io.Reader) (crypto.PrivateKey, crypto.PublicKey, error)
	Marshal(crypto.PublicKey) []byte
	Unmarshal([]byte) (crypto.PublicKey, bool)
	GenerateSharedSecret(crypto.PrivateKey, crypto.PublicKey) ([]byte, error)
}
type ellipticECDH struct {
	ECDH
	curve elliptic.Curve
}
type ellipticPublicKey struct {
	elliptic.Curve
	X, Y *big.Int
}
type ellipticPrivateKey struct {
	D []byte
}
// NewEllipticECDH 指定一种椭圆曲线算法用于创建一个ECDH的实例
// 关于椭圆曲线算法标准库里面实现了4种: 见crypto/elliptic
func NewEllipticECDH(curve elliptic.Curve) ECDH {
	return &ellipticECDH{
		curve: curve,
	}
}
// GenerateKey 基于标准库的NIST椭圆曲线算法生成秘钥对
func (e *ellipticECDH) GenerateKey(rand io.Reader) (crypto.PrivateKey, crypto.PublicKey, error) {
	var d []byte
	var x, y *big.Int
	var priv *ellipticPrivateKey
	var pub *ellipticPublicKey
	var err error
	d, x, y, err = elliptic.GenerateKey(e.curve, rand)
	if err != nil {
		return nil, nil, err
	}
	priv = &ellipticPrivateKey{
		D: d,
	}
	pub = &ellipticPublicKey{
		Curve: e.curve,
		X:     x,
		Y:     y,
	}
	return priv, pub, nil
}
// Marshal用于公钥的序列化
func (e *ellipticECDH) Marshal(p crypto.PublicKey) []byte {
	pub := p.(*ellipticPublicKey)
	return elliptic.Marshal(e.curve, pub.X, pub.Y)
}
// Unmarshal用于公钥的反序列化
func (e *ellipticECDH) Unmarshal(data []byte) (crypto.PublicKey, bool) {
	var key *ellipticPublicKey
	var x, y *big.Int
	x, y = elliptic.Unmarshal(e.curve, data)
	if x == nil || y == nil {
		return key, false
	}
	key = &ellipticPublicKey{
		Curve: e.curve,
		X:     x,
		Y:     y,
	}
	return key, true
}
// GenerateSharedSecret 通过自己的私钥和对方的公钥协商一个共享密码
func (e *ellipticECDH) GenerateSharedSecret(privKey crypto.PrivateKey, pubKey crypto.PublicKey) ([]byte, error) {
	priv := privKey.(*ellipticPrivateKey)
	pub := pubKey.(*ellipticPublicKey)
	x, _ := e.curve.ScalarMult(pub.X, pub.Y, priv.D)
	return x.Bytes(), nil
}
// NewCurve25519ECDH 使用密码学家Daniel J. Bernstein的椭圆曲线算法:Curve25519来创建ECDH实例
// 因为Curve25519独立于NIST之外, 没在标准库实现, 需要单独为期实现一套接口来支持ECDH
func NewCurve25519ECDH() ECDH {
	return &curve25519ECDH{}
}
type curve25519ECDH struct {
	ECDH
}
// GenerateKey 基于curve25519椭圆曲线算法生成秘钥对
func (e *curve25519ECDH) GenerateKey(rand io.Reader) (crypto.PrivateKey, crypto.PublicKey, error) {
	var pub, priv [32]byte
	var err error
	_, err = io.ReadFull(rand, priv[:])
	if err != nil {
		return nil, nil, err
	}
	priv[0] &= 248
	priv[31] &= 127
	priv[31] |= 64
	curve25519.ScalarBaseMult(&pub, &priv)
	return &priv, &pub, nil
}
// 实现公钥的序列化
func (e *curve25519ECDH) Marshal(p crypto.PublicKey) []byte {
	pub := p.(*[32]byte)
	return pub[:]
}
// 实现公钥的反序列化
func (e *curve25519ECDH) Unmarshal(data []byte) (crypto.PublicKey, bool) {
	var pub [32]byte
	if len(data) != 32 {
		return nil, false
	}
	copy(pub[:], data)
	return &pub, true
}
// 实现秘钥协商接口
func (e *curve25519ECDH) GenerateSharedSecret(privKey crypto.PrivateKey, pubKey crypto.PublicKey) ([]byte, error) {
	var priv, pub, secret *[32]byte
	priv = privKey.(*[32]byte)
	pub = pubKey.(*[32]byte)
	secret = new([32]byte)
	curve25519.ScalarMult(secret, priv, pub)
	return secret[:], nil
}
func test(e ECDH) {
	var privKey1, privKey2 crypto.PrivateKey
	var pubKey1, pubKey2 crypto.PublicKey
	var pubKey1Buf, pubKey2Buf []byte
	var err error
	var ok bool
	var secret1, secret2 []byte
	// 准备2对秘钥对,A: privKey1,pubKey1 B:privKey2,pubKey2
	privKey1, pubKey1, err = e.GenerateKey(rand.Reader)
	if err != nil {
		fmt.Println(err)
	}
	privKey2, pubKey2, err = e.GenerateKey(rand.Reader)
	if err != nil {
		fmt.Println(err)
	}
	pubKey1Buf = e.Marshal(pubKey1)
	pubKey2Buf = e.Marshal(pubKey2)
	pubKey1, ok = e.Unmarshal(pubKey1Buf)
	if !ok {
		fmt.Println("Unmarshal does not work")
	}
	pubKey2, ok = e.Unmarshal(pubKey2Buf)
	if !ok {
		fmt.Println("Unmarshal does not work")
	}
	// A 通过B给的公钥协商共享密码
	secret1, err = e.GenerateSharedSecret(privKey1, pubKey2)
	if err != nil {
		fmt.Println(err)
	}
	// B 通过A给的公钥协商共享密码
	secret2, err = e.GenerateSharedSecret(privKey2, pubKey1)
	if err != nil {
		fmt.Println(err)
	}
	// A B在没暴露直接的私钥的情况下, 协商出了一个共享密码
	fmt.Printf("The secret1 shared keys: %x\n", secret1)
	fmt.Printf("The secret2 shared keys: %x\n", secret2)
}
func main() {
	e1 := NewEllipticECDH(elliptic.P521())
	e2 := NewCurve25519ECDH()
	test(e1)
	test(e2)
}