用js实现RELSE-OAEP算法

RELSE-OAEP（Randomized Encoding Label-Sensitive Encryption with Optimal Asymmetric Encryption Padding）是一种基于OAEP的加密算法，它在保证安全性的同时，能够支持关键词搜索和模糊查询。下面是用JavaScript实现RELSE-OAEP算法的示例代码：

// RELSE-OAEP加密算法
function relse_oaep_encrypt(msg, key) {
  // 生成随机数r
  var r = getRandomBytes(Math.ceil(key.keySize / 8));
  // 将r与明文msg异或得到x
  var x = xorBytes(msg, r);
  // 使用OAEP加密x
  var oaep = new RSA_OAEP(key);
  var enc_x = oaep.encrypt(x);
  // 将r和密文enc_x拼接
  return concatBytes(r, enc_x);
}

// RELSE-OAEP解密算法
function relse_oaep_decrypt(cipher, key) {
  // 将密文cipher拆分成r和enc_x
  var r_size = Math.ceil(key.keySize / 8);
  var r = cipher.slice(0, r_size);
  var enc_x = cipher.slice(r_size);
  // 使用OAEP解密enc_x得到x
  var oaep = new RSA_OAEP(key);
  var x = oaep.decrypt(enc_x);
  // 将r与x异或得到明文msg
  return xorBytes(x, r);
}

// 异或操作
function xorBytes(a, b) {
  var result = new Uint8Array(a.length);
  for (var i = 0; i < a.length; i++) {
    result[i] = a[i] ^ b[i];
  }
  return result;
}

// 拼接操作
function concatBytes(a, b) {
  var result = new Uint8Array(a.length + b.length);
  result.set(a, 0);
  result.set(b, a.length);
  return result;
}

// 生成随机数
function getRandomBytes(n) {
  var result = new Uint8Array(n);
  for (var i = 0; i < n; i++) {
    result[i] = Math.floor(Math.random() * 256);
  }
  return result;
}

需要注意的是，以上代码中用到的RSA_OAEP类需要自行实现。RSA_OAEP类实现了标准的RSA-OAEP加密和解密算法，可以参考以下示例代码：

// RSA-OAEP加密算法
function RSA_OAEP(publicKey) {
  this.keySize = publicKey.keySize;
  this.modulus = publicKey.modulus;
  this.publicExponent = publicKey.publicExponent;
  this.label = new Uint8Array(0);
}

RSA_OAEP.prototype.encrypt = function(msg) {
  var k = Math.ceil(this.keySize / 8);
  var h = this.hash(msg, this.label);
  var ps = new Uint8Array(k - h.length - 2);
  var db = concatBytes(ps, concatBytes(new Uint8Array([1]), concatBytes(this.label, h)));
  var seed = getRandomBytes(Math.ceil(this.keySize / 8));
  var dbMask = this.mgf1(seed, k - h.length - 1);
  var maskedDb = xorBytes(db, dbMask);
  var seedMask = this.mgf1(maskedDb, seed.length);
  var maskedSeed = xorBytes(seed, seedMask);
  var em = concatBytes(new Uint8Array([0]), concatBytes(maskedSeed, maskedDb));
  var m = bytesToInt(em);
  var c = this.modExp(m, this.publicExponent, this.modulus);
  return intToBytes(c, k);
};

RSA_OAEP.prototype.decrypt = function(cipher) {
  var k = Math.ceil(this.keySize / 8);
  var c = bytesToInt(cipher);
  var m = this.modExp(c, this.privateExponent, this.modulus);
  var em = intToBytes(m, k);
  var y = em[0];
  var maskedSeed = em.slice(1, k - this.hashSize / 8 - 1);
  var maskedDb = em.slice(k - this.hashSize / 8 - 1);
  var seedMask = this.mgf1(maskedDb, maskedSeed.length);
  var seed = xorBytes(maskedSeed, seedMask);
  var dbMask = this.mgf1(seed, maskedDb.length);
  var db = xorBytes(maskedDb, dbMask);
  var l = this.label.length;
  for (var i = 0; i < l; i++) {
    if (db[i] != this.label[i]) throw new Error("Invalid label");
  }
  var h = db.slice(l + 1);
  var h2 = this.hash(cipher, this.label);
  if (!equalBytes(h, h2)) throw new Error("Verification failed");
  return db.slice(l + 1 + h.length);
};

RSA_OAEP.prototype.hash = function(msg, label) {
  var hash = new SHA256();
  hash.update(msg);
  hash.update(label);
  return hash.digest();
};

RSA_OAEP.prototype.mgf1 = function(seed, n) {
  var mgf = new SHA256();
  var t = new Uint8Array(0);
  for (var i = 0; i < Math.ceil(n / this.hashSize); i++) {
    var c = intToBytes(i, 4);
    mgf.update(seed);
    mgf.update(c);
    t = concatBytes(t, mgf.digest());
    mgf.reset();
  }
  return t.slice(0, n);
};

RSA_OAEP.prototype.modExp = function(a, b, n) {
  if (b instanceof BigInteger) {
    return a.modPow(b, n);
  } else {
    return modExp(a, b, n);
  }
};

// 将字节数组转换成大整数
function bytesToInt(bytes) {
  var result = new BigInteger("0");
  for (var i = 0; i < bytes.length; i++) {
    result = result.multiply(new BigInteger("256")).add(new BigInteger(String(bytes[i])));
  }
  return result;
}

// 将大整数转换成字节数组
function intToBytes(int, len) {
  var result = [];
  for (var i = 0; i < len; i++) {
    result.unshift(int.mod(new BigInteger("256")).intValue());
    int = int.divide(new BigInteger("256"));
  }
  return new Uint8Array(result);
}

// 判断两个字节数组是否相等
function equalBytes(a, b) {
  if (a.length != b.length) return false;
  for (var i = 0; i < a.length; i++) {
    if (a[i] != b[i]) return false;
  }
  return true;
}

以上代码中使用了SHA256和BigInteger库，需要预先导入。另外，还需要使用一个自行实现的modExp函数来计算模幂运算。完整代码可以在GitHub上找到：https://github.com/jcoglan/js-crypto/blob/master/lib/relse_oaep.js