加密解密 CTR IGE DH等

// Use of this source code is governed by a license
// that can be found in the LICENSE file.

// Package dh implements the Diffie-Hellman key exchange over
// multiplicative groups of integers modulo a prime.
// This also defines some commen groups described in RFC 3526.
package dh

import (
	cryptorand "crypto/rand"
	"errors"
	"io"
	"math/big"
)

var zero *big.Int = big.NewInt(0)
var one *big.Int = big.NewInt(1)
var two *big.Int = big.NewInt(2)

// IsSafePrime returns true, if the prime of the group is
// a so called safe-prime. For a group with a safe-prime prime
// number the Decisional-Diffie-Hellman-Problem (DDH) is a
// 'hard' problem. The n argument is the number of iterations
// for the probabilistic prime test.
// It's recommend to use DDH-safe groups for DH-exchanges.
func IsSafePrimeGroup(g *Group, n int) bool {
	q := new(big.Int).Sub(g.P, one)
	q = q.Div(q, two)
	return q.ProbablyPrime(n)
}

// PublicKey is the type of DH public keys.
type PublicKey *big.Int

// PrivateKey is the type of DH private keys.
type PrivateKey *big.Int

// Group represents a mathematical group defined
// by a large prime and a generator.
type Group struct {
	P *big.Int // The prime
	G *big.Int // The generator
}

// GenerateKey generates a public/private key pair using entropy from rand.
// If rand is nil, crypto/rand.Reader will be used.
func (g *Group) GenerateKey(rand io.Reader) (private PrivateKey, public PublicKey, err error) {
	if g.P == nil {
		panic("crypto/dh: group prime is nil")
	}
	if g.G == nil {
		panic("crypto/dh: group generator is nil")
	}
	if rand == nil {
		rand = cryptorand.Reader
	}

	// Ensure, that p.G ^ privateKey > than g.P
	// (only modulo calculations are safe)
	// The minimal (and common) value for p.G is 2
	// So 2 ^ (1 + 'bitsize of p.G') > than g.P
	min := big.NewInt(int64(g.P.BitLen() + 1)) //生成一个不小于p的大数
	bytes := make([]byte, (g.P.BitLen()+7)/8)  //bit/8 = byte, +7 是为了补空，放置少除了，然后长度不够

	for private == nil {
		_, err = io.ReadFull(rand, bytes)
		if err != nil {
			private = nil
			return
		}
		// Clear bits in the first byte to increase
		// the probability that the candidate is < g.P.
		bytes[0] = 0
		if private == nil {
			private = new(big.Int)
		}
		(*private).SetBytes(bytes)   //将读到的数据设置进private中
		if (*private).Cmp(min) < 0 { //private 小于 一个不小于p的数。 如x < y返回-1；如x > y返回+1；否则返回0。
			private = nil
		}
	}

	public = new(big.Int).Exp(g.G, private, g.P) //x**y mod |m| =  A = g**a mod p
	return
}

// PublicKey returns the public key corresponding to the given private one.
func (g *Group) PublicKey(private PrivateKey) (public PublicKey) {
	public = new(big.Int).Exp(g.G, private, g.P)
	return
}

//private returns a non-nil error if the given public key is
// not a possible element of the group. This means, that the
// public key is < 0 or > g.P.
func (g *Group) Check(peersPublic PublicKey) (err error) {
	if !((*peersPublic).Cmp(zero) >= 0 && (*peersPublic).Cmp(g.P) == -1) {
		err = errors.New("peer's public is not a possible group element")
	}
	return
}

// ComputeSecret returns the secret computed from
// the own private and the peer's public key.
func (g *Group) ComputeSecret(private PrivateKey, peersPublic PublicKey) (secret *big.Int) {
	secret = new(big.Int).Exp(peersPublic, private, g.P)
	return
}

给定椭圆曲线上的一个点P，一个整数k，求解Q=kP很容易；给定一个点P、Q，知道Q=kP，求整数k确是一个难题。ECDH即建立在此数学难题之上

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)