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