SorryToPerson logo
返回
算法2026-04-26·10 分钟

算法知识库:密码学算法实现

JavaScript/TypeScript 实现密码学基础算法,如RSA加密、AES加密、数字签名等。

密码学算法实现

1. RSA 加密算法

ts
class RSA {
  private p: bigint;
  private q: bigint;
  private n: bigint;
  private phi: bigint;
  private e: bigint;
  private d: bigint;

  constructor(bitLength: number = 1024) {
    this.generateKeys(bitLength);
  }

  private generateKeys(bitLength: number): void {
    // 生成两个大质数
    this.p = this.generatePrime(bitLength / 2);
    this.q = this.generatePrime(bitLength / 2);

    this.n = this.p * this.q;
    this.phi = (this.p - 1n) * (this.q - 1n);

    // 选择公钥指数 e
    this.e = 65537n;

    // 计算私钥指数 d
    this.d = this.modInverse(this.e, this.phi);
  }

  private generatePrime(bitLength: number): bigint {
    let prime: bigint;
    do {
      prime = this.randomBigInt(bitLength);
    } while (!this.isPrime(prime));
    return prime;
  }

  private randomBigInt(bits: number): bigint {
    const bytes = Math.ceil(bits / 8);
    const array = new Uint8Array(bytes);
    crypto.getRandomValues(array);
    array[0] |= 0x80; // 确保最高位为1
    return BigInt(
      '0x' +
        Array.from(array)
          .map((b) => b.toString(16).padStart(2, '0'))
          .join(''),
    );
  }

  private isPrime(n: bigint): boolean {
    if (n < 2n) return false;
    if (n === 2n || n === 3n) return true;
    if (n % 2n === 0n || n % 3n === 0n) return false;

    let i = 5n;
    while (i * i <= n) {
      if (n % i === 0n || n % (i + 2n) === 0n) return false;
      i += 6n;
    }

    return true;
  }

  private modInverse(a: bigint, m: bigint): bigint {
    let m0 = m;
    let y = 0n;
    let x = 1n;

    if (m === 1n) return 0n;

    while (a > 1n) {
      const q = a / m;
      let t = m;
      m = a % m;
      a = t;
      t = y;
      y = x - q * y;
      x = t;
    }

    if (x < 0n) x += m0;

    return x;
  }

  encrypt(message: string): string {
    const messageBytes = new TextEncoder().encode(message);
    const encrypted: bigint[] = [];

    for (let i = 0; i < messageBytes.length; i += 1) {
      const m = BigInt(messageBytes[i]);
      const c = this.modPow(m, this.e, this.n);
      encrypted.push(c);
    }

    return encrypted.map((c) => c.toString()).join(',');
  }

  decrypt(encryptedMessage: string): string {
    const encrypted = encryptedMessage.split(',').map((c) => BigInt(c));
    const decrypted: number[] = [];

    for (const c of encrypted) {
      const m = this.modPow(c, this.d, this.n);
      decrypted.push(Number(m));
    }

    return new TextDecoder().decode(new Uint8Array(decrypted));
  }

  private modPow(base: bigint, exponent: bigint, modulus: bigint): bigint {
    let result = 1n;
    base = base % modulus;

    while (exponent > 0n) {
      if (exponent % 2n === 1n) {
        result = (result * base) % modulus;
      }
      exponent = exponent / 2n;
      base = (base * base) % modulus;
    }

    return result;
  }

  getPublicKey(): { n: bigint; e: bigint } {
    return { n: this.n, e: this.e };
  }
}

2. AES 加密算法 (简化版)

ts
class AES {
  private static S_BOX = [
    0x63, 0x7c, 0x77, 0x7b, 0xf2, 0x6b, 0x6f, 0xc5, 0x30, 0x01, 0x67, 0x2b, 0xfe, 0xd7, 0xab, 0x76, 0xca, 0x82, 0xc9, 0x7d, 0xfa, 0x59, 0x47, 0xf0, 0xad, 0xd4, 0xa2, 0xaf, 0x9c, 0xa4, 0x72, 0xc0,
    0xb7, 0xfd, 0x93, 0x26, 0x36, 0x3f, 0xf7, 0xcc, 0x34, 0xa5, 0xe5, 0xf1, 0x71, 0xd8, 0x31, 0x15, 0x04, 0xc7, 0x23, 0xc3, 0x18, 0x96, 0x05, 0x9a, 0x07, 0x12, 0x80, 0xe2, 0xeb, 0x27, 0xb2, 0x75,
    0x09, 0x83, 0x2c, 0x1a, 0x1b, 0x6e, 0x5a, 0xa0, 0x52, 0x3b, 0xd6, 0xb3, 0x29, 0xe3, 0x2f, 0x84, 0x53, 0xd1, 0x00, 0xed, 0x20, 0xfc, 0xb1, 0x5b, 0x6a, 0xcb, 0xbe, 0x39, 0x4a, 0x4c, 0x58, 0xcf,
    0xd0, 0xef, 0xaa, 0xfb, 0x43, 0x4d, 0x33, 0x85, 0x45, 0xf9, 0x02, 0x7f, 0x50, 0x3c, 0x9f, 0xa8, 0x51, 0xa3, 0x40, 0x8f, 0x92, 0x9d, 0x38, 0xf5, 0xbc, 0xb6, 0xda, 0x21, 0x10, 0xff, 0xf3, 0xd2,
    0xcd, 0x0c, 0x13, 0xec, 0x5f, 0x97, 0x44, 0x17, 0xc4, 0xa7, 0x7e, 0x3d, 0x64, 0x5d, 0x19, 0x73, 0x60, 0x81, 0x4f, 0xdc, 0x22, 0x2a, 0x90, 0x88, 0x46, 0xee, 0xb8, 0x14, 0xde, 0x5e, 0x0b, 0xdb,
    0xe0, 0x32, 0x3a, 0x0a, 0x49, 0x06, 0x24, 0x5c, 0xc2, 0xd3, 0xac, 0x62, 0x91, 0x95, 0xe4, 0x79, 0xe7, 0xc8, 0x37, 0x6d, 0x8d, 0xd5, 0x4e, 0xa9, 0x6c, 0x56, 0xf4, 0xea, 0x65, 0x7a, 0xae, 0x08,
    0xba, 0x78, 0x25, 0x2e, 0x1c, 0xa6, 0xb4, 0xc6, 0xe8, 0xdd, 0x74, 0x1f, 0x4b, 0xbd, 0x8b, 0x8a, 0x70, 0x3e, 0xb5, 0x66, 0x48, 0x03, 0xf6, 0x0e, 0x61, 0x35, 0x57, 0xb9, 0x86, 0xc1, 0x1d, 0x9e,
    0xe1, 0xf8, 0x98, 0x11, 0x69, 0xd9, 0x8e, 0x94, 0x9b, 0x1e, 0x87, 0xe9, 0xce, 0x55, 0x28, 0xdf, 0x8c, 0xa1, 0x89, 0x0d, 0xbf, 0xe6, 0x42, 0x68, 0x41, 0x99, 0x2d, 0x0f, 0xb0, 0x54, 0xbb, 0x16,
  ];

  static encrypt(plaintext: string, key: string): string {
    // 简化版 AES 实现,实际应用中应使用标准库
    const keyBytes = new TextEncoder().encode(key);
    const dataBytes = new TextEncoder().encode(plaintext);

    // 简单的 XOR 加密作为示例
    const encrypted = dataBytes.map((byte, i) => byte ^ keyBytes[i % keyBytes.length]);

    return btoa(String.fromCharCode(...encrypted));
  }

  static decrypt(encrypted: string, key: string): string {
    const encryptedBytes = new Uint8Array(
      atob(encrypted)
        .split('')
        .map((c) => c.charCodeAt(0)),
    );
    const keyBytes = new TextEncoder().encode(key);

    const decrypted = encryptedBytes.map((byte, i) => byte ^ keyBytes[i % keyBytes.length]);

    return new TextDecoder().decode(decrypted);
  }
}

3. 数字签名 (RSA 签名)

ts
class DigitalSignature {
  private rsa: RSA;

  constructor() {
    this.rsa = new RSA();
  }

  sign(message: string): string {
    const hash = SHA256.hash(message);
    return this.rsa.encrypt(hash);
  }

  verify(message: string, signature: string, publicKey: { n: bigint; e: bigint }): boolean {
    const hash = SHA256.hash(message);
    const rsaVerify = new RSA();
    // 设置公钥进行验证
    const decryptedHash = rsaVerify.decrypt(signature);
    return decryptedHash === hash;
  }
}

4. 哈希函数 (SHA-256)

ts
// 使用之前实现的 SHA256 类
class SHA256 {
  // ... (之前实现的 SHA256 代码)
}

5. 密钥交换 (Diffie-Hellman)

ts
class DiffieHellman {
  private p: bigint;
  private g: bigint;
  private privateKey: bigint;
  public publicKey: bigint;

  constructor(p?: bigint, g?: bigint) {
    this.p = p || 23n; // 质数
    this.g = g || 5n; // 生成元
    this.privateKey = this.randomBigInt(8); // 8位随机数
    this.publicKey = this.modPow(this.g, this.privateKey, this.p);
  }

  computeSharedSecret(otherPublicKey: bigint): bigint {
    return this.modPow(otherPublicKey, this.privateKey, this.p);
  }

  private randomBigInt(bits: number): bigint {
    const bytes = Math.ceil(bits / 8);
    const array = new Uint8Array(bytes);
    crypto.getRandomValues(array);
    return BigInt(
      '0x' +
        Array.from(array)
          .map((b) => b.toString(16).padStart(2, '0'))
          .join(''),
    );
  }

  private modPow(base: bigint, exponent: bigint, modulus: bigint): bigint {
    let result = 1n;
    base = base % modulus;

    while (exponent > 0n) {
      if (exponent % 2n === 1n) {
        result = (result * base) % modulus;
      }
      exponent = exponent / 2n;
      base = (base * base) % modulus;
    }

    return result;
  }
}

6. 实现要点

  • RSA 基于大数分解困难性。
  • AES 提供对称加密。
  • 数字签名确保消息完整性和认证。
  • Diffie-Hellman 实现密钥交换。
  • 实际应用中应使用标准密码学库。
算法密码学JavaScript