DH加密算法使用简介 - 邵俊桦的博客

RSA与DH算法

迪菲—赫尔曼密钥交换是使用和RSA相似的技术吗？

RSA

RSA可以用于加密和签名，用公钥和私钥可以对文件做验证。

但RSA无法解决前向加密的问题，如果RSA的私钥泄漏，之前的消息均可用私钥解密出来。

RSA可以做密钥传输，B使用A的密钥对中的公钥加密数据，只有B用它的私钥才能解开。但RSA的公钥也不能在公网中传递，依然会有被中间人攻击的可能。

DH

DH的使用双方均有一对密钥，如果一方的公钥和私钥泄漏，依然无法破解之前的数据。

DH算法本身不包含身份认证机制，如果AB在交换公钥时被截获，C插入一对DH密钥，分别与AB通信，则可以截取信息。

Curve25519椭圆曲线算法

从 Ed25519 转换为 Curve25519 公钥

Curve25519是一种高水平的DH函数，提供128位的安全心，是最快的ECC曲线。

使用一个32字节的私钥，再根据私钥计算出32字节公钥。

B用户的公钥+A用户的私钥、A用户的公钥+B用户的私钥可以计算出一个32字节的共享密钥提供给两个用户使用，做AES加密。

Ed25519加密解密很快,生成时间短而且安全性更高,rsa则加密解密稍慢,生成时间长,安全性没有ed25519高,只是rsa基本都是默认,所以用的人更多,但是建议转换为ed25519,网站软件现在基本都支持了.

验签逻辑

curve25519_sign

将 Curve25519的私钥转换为 Ed25519的公钥
使用 Curve25519的私钥和 Ed25519的公钥对数据进行签名。
返回加密结果

curve25519_verify

参数：加密数据，Curve25519公钥，原始数据

将 Cureve25519的公钥转换成 Ed25519的公钥。
使用 Ed25519的公钥计算出签名数据，将签名数据从加密数据中提取出来。
再将原始数据与签名数据拼接生成验证体数据A 。
使用 Ed25519的公钥，验证体数据A，原始数据，生成验证体数据B。
验证解密结果是否成功

void curve25519_keygen(unsigned char* curve25519_pubkey_out,
                       const unsigned char* curve25519_privkey_in)
{
  ge_p3 ed; /* Ed25519 pubkey point */
  fe ed_y, ed_y_plus_one, one_minus_ed_y, inv_one_minus_ed_y;
  fe mont_x;

  /* Perform a fixed-base multiplication of the Edwards base point,
     (which is efficient due to precalculated tables), then convert
     to the Curve25519 montgomery-format public key.  In particular,
     convert Curve25519's "montgomery" x-coordinate into an Ed25519
     "edwards" y-coordinate:

     mont_x = (ed_y + 1) / (1 - ed_y)
     
     with projective coordinates:

     mont_x = (ed_y + ed_z) / (ed_z - ed_y)

     NOTE: ed_y=1 is converted to mont_x=0 since fe_invert is mod-exp
  */

  ge_scalarmult_base(&ed, curve25519_privkey_in);
  fe_add(ed_y_plus_one, ed.Y, ed.Z);
  fe_sub(one_minus_ed_y, ed.Z, ed.Y);  
  fe_invert(inv_one_minus_ed_y, one_minus_ed_y);
  fe_mul(mont_x, ed_y_plus_one, inv_one_minus_ed_y);
  fe_tobytes(curve25519_pubkey_out, mont_x);
}

int curve25519_sign(unsigned char* signature_out,
                    const unsigned char* curve25519_privkey,
                    const unsigned char* msg, const unsigned long msg_len,
                    const unsigned char* random)
{
  ge_p3 ed_pubkey_point; /* Ed25519 pubkey point */
  unsigned char ed_pubkey[32]; /* Ed25519 encoded pubkey */
  unsigned char *sigbuf; /* working buffer */
  unsigned char sign_bit = 0;

  if ((sigbuf = malloc(msg_len + 128)) == 0) {
    memset(signature_out, 0, 64);
    return -1;
  }

  /* Convert the Curve25519 privkey to an Ed25519 public key */
  ge_scalarmult_base(&ed_pubkey_point, curve25519_privkey);
  ge_p3_tobytes(ed_pubkey, &ed_pubkey_point);
  sign_bit = ed_pubkey[31] & 0x80;

  /* Perform an Ed25519 signature with explicit private key */
  crypto_sign_modified(sigbuf, msg, msg_len, curve25519_privkey,
                       ed_pubkey, random);
  memmove(signature_out, sigbuf, 64);

  /* Encode the sign bit into signature (in unused high bit of S) */
   signature_out[63] &= 0x7F; /* bit should be zero already, but just in case */
   signature_out[63] |= sign_bit;

   free(sigbuf);
   return 0;
}

int curve25519_verify(const unsigned char* signature,
                      const unsigned char* curve25519_pubkey,
                      const unsigned char* msg, const unsigned long msg_len)
{
  fe mont_x, mont_x_minus_one, mont_x_plus_one, inv_mont_x_plus_one;
  fe one;
  fe ed_y;
  unsigned char ed_pubkey[32];
  unsigned long long some_retval;
  unsigned char *verifybuf = NULL; /* working buffer */
  unsigned char *verifybuf2 = NULL; /* working buffer #2 */
  int result;

  if ((verifybuf = malloc(msg_len + 64)) == 0) {
    result = -1;
    goto err;
  }

  if ((verifybuf2 = malloc(msg_len + 64)) == 0) {
    result = -1;
    goto err;
  }

  /* Convert the Curve25519 public key into an Ed25519 public key.  In
     particular, convert Curve25519's "montgomery" x-coordinate into an
     Ed25519 "edwards" y-coordinate:

     ed_y = (mont_x - 1) / (mont_x + 1)

     NOTE: mont_x=-1 is converted to ed_y=0 since fe_invert is mod-exp

     Then move the sign bit into the pubkey from the signature.
  */
  fe_frombytes(mont_x, curve25519_pubkey);
  fe_1(one);
  fe_sub(mont_x_minus_one, mont_x, one);
  fe_add(mont_x_plus_one, mont_x, one);
  fe_invert(inv_mont_x_plus_one, mont_x_plus_one);
  fe_mul(ed_y, mont_x_minus_one, inv_mont_x_plus_one);
  fe_tobytes(ed_pubkey, ed_y);

  /* Copy the sign bit, and remove it from signature */
  ed_pubkey[31] &= 0x7F;  /* bit should be zero already, but just in case */
  ed_pubkey[31] |= (signature[63] & 0x80);
  memmove(verifybuf, signature, 64);
  verifybuf[63] &= 0x7F;

  memmove(verifybuf+64, msg, msg_len);

  /* Then perform a normal Ed25519 verification, return 0 on success */
  /* The below call has a strange API: */
  /* verifybuf = R || S || message */
  /* verifybuf2 = internal to next call gets a copy of verifybuf, S gets 
     replaced with pubkey for hashing, then the whole thing gets zeroized
     (if bad sig), or contains a copy of msg (good sig) */
  result = crypto_sign_open(verifybuf2, &some_retval, verifybuf, 64 + msg_len, ed_pubkey);

  err:

  if (verifybuf != NULL) {
    free(verifybuf);
  }

  if (verifybuf2 != NULL) {
    free(verifybuf2);
  }

  return result;
}

RSA与DH算法的区别，Curve25519椭圆曲线算法的验签逻辑

RSA与DH算法

RSA

DH

Curve25519椭圆曲线算法

验签逻辑