用Java实现Hill密码加解密

Hill密码是一种基于矩阵乘法的密码算法，它可以用于加密和解密任意长度的文本，同时也可以抵御一定程度的密码分析攻击。下面是用Java实现Hill密码加解密的示例代码：

import java.util.Scanner;

public class HillCipher {
    // 矩阵加法
    public static int[][] matrixAdd(int[][] A, int[][] B) {
        int[][] C = new int[A.length][A[0].length];
        for (int i = 0; i < A.length; i++) {
            for (int j = 0; j < A[0].length; j++) {
                C[i][j] = A[i][j] + B[i][j];
            }
        }
        return C;
    }

    // 矩阵乘法
    public static int[][] matrixMul(int[][] A, int[][] B) {
        int[][] C = new int[A.length][B[0].length];
        for (int i = 0; i < A.length; i++) {
            for (int j = 0; j < B[0].length; j++) {
                for (int k = 0; k < B.length; k++) {
                    C[i][j] += A[i][k] * B[k][j];
                }
            }
        }
        return C;
    }

    // 矩阵求逆
    public static int[][] matrixInverse(int[][] A) {
        int n = A.length;
        int[][] B = new int[n][n];
        int[][] C = new int[n][2 * n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                B[i][j] = A[i][j];
            }
            C[i][i] = 1;
        }
        for (int k = 0; k < n; k++) {
            int maxRow = k;
            for (int i = k + 1; i < n; i++) {
                if (Math.abs(B[i][k]) > Math.abs(B[maxRow][k])) {
                    maxRow = i;
                }
            }
            if (maxRow != k) {
                int[] tmp = B[k];
                B[k] = B[maxRow];
                B[maxRow] = tmp;
                tmp = C[k];
                C[k] = C[maxRow];
                C[maxRow] = tmp;
            }
            if (B[k][k] == 0) {
                throw new RuntimeException("Matrix is singular.");
            }
            int inv = 1 / B[k][k];
            for (int j = 0; j < n; j++) {
                B[k][j] *= inv;
                C[k][j] *= inv;
            }
            for (int i = 0; i < n; i++) {
                if (i != k) {
                    int f = B[i][k];
                    for (int j = 0; j < n; j++) {
                        B[i][j] -= f * B[k][j];
                        C[i][j] -= f * C[k][j];
                    }
                }
            }
        }
        for (int i = 0; i < n; i++) {
            for (int j = n; j < 2 * n; j++) {
                C[i][j] /= B[i][i];
            }
        }
        int[][] D = new int[n][n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                D[i][j] = C[i][j + n];
            }
        }
        return D;
    }

    // 加密函数
    public static String encrypt(String plaintext, int[][] key) {
        int n = key.length;
        int m = (plaintext.length() + n - 1) / n * n;
        int[][] P = new int[m / n][n];
        int k = 0;
        for (int i = 0; i < m / n; i++) {
            for (int j = 0; j < n; j++) {
                if (k < plaintext.length()) {
                    P[i][j] = plaintext.charAt(k) - 'a';
                    k++;
                } else {
                    P[i][j] = 0;
                }
            }
        }
        int[][] C = new int[m / n][n];
        for (int i = 0; i < m / n; i++) {
            int[][] Pi = new int[1][n];
            for (int j = 0; j < n; j++) {
                Pi[0][j] = P[i][j];
            }
            int[][] Ci = matrixMul(Pi, key);
            for (int j = 0; j < n; j++) {
                C[i][j] = Ci[0][j];
            }
        }
        StringBuilder ciphertext = new StringBuilder();
        for (int i = 0; i < m / n; i++) {
            for (int j = 0; j < n; j++) {
                ciphertext.append((char) (C[i][j] % 26 + 'a'));
            }
        }
        return ciphertext.toString();
    }

    // 解密函数
    public static String decrypt(String ciphertext, int[][] key) {
        int n = key.length;
        int m = ciphertext.length();
        int[][] C = new int[m / n][n];
        int k = 0;
        for (int i = 0; i < m / n; i++) {
            for (int j = 0; j < n; j++) {
                C[i][j] = ciphertext.charAt(k) - 'a';
                k++;
            }
        }
        int[][] keyInv = matrixInverse(key);
        int[][] P = new int[m / n][n];
        for (int i = 0; i < m / n; i++) {
            int[][] Ci = new int[1][n];
            for (int j = 0; j < n; j++) {
                Ci[0][j] = C[i][j];
            }
            int[][] Pi = matrixMul(Ci, keyInv);
            for (int j = 0; j < n; j++) {
                P[i][j] = Pi[0][j];
            }
        }
        StringBuilder plaintext = new StringBuilder();
        for (int i = 0; i < m / n; i++) {
            for (int j = 0; j < n; j++) {
                plaintext.append((char) (P[i][j] % 26 + 'a'));
            }
        }
        return plaintext.toString();
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        System.out.print("请输入明文：");
        String plaintext = sc.nextLine();
        System.out.print("请输入密钥：");
        int[][] key = new int[3][3];
        for (int i = 0; i < 3; i++) {
            for (int j = 0; j < 3; j++) {
                key[i][j] = sc.nextInt();
            }
        }
        String ciphertext = encrypt(plaintext, key);
        System.out.println("密文为：" + ciphertext);
        String decryptedText = decrypt(ciphertext, key);
        System.out.println("解密后明文为：" + decryptedText);
    }
}

上面的代码中，我们定义了`matrixAdd`、`matrixMul`和`matrixInverse`三个函数来实现矩阵加法、矩阵乘法和矩阵求逆操作。然后，我们定义了`encrypt`和`decrypt`两个函数来实现加密和解密操作。最后，在`main`函数中，我们通过键盘输入明文和密钥，然后输出加密后的密文和解密后的明文。