基于Ring-LWE的Java客户端-服务器加密聊天应用字符乱序问题

我正在为密码学与安全项目开发一款基于Ring-LWE的客户端-服务器架构Java安全聊天应用。目前已实现密钥交换、加密及解密逻辑，但出现字符被替换的问题，测试输出如下：

• hello -> gelko
• help -> gekp

我尝试过增大缩放因子和误差系数，但问题仍未解决。我清楚Ring-LWE不适用于实时语音和文件加密，此仅为项目用途。

包含Ring-LWE实现的Client.java代码 #

class RingLWE {
    private final int n = 512;
    private final int q = 12289;
    private final int scalingFactor = q / 256; //48

    private int[] s;

    public RingLWE() {
        Random random = new Random();
        s = new int[n];
        for (int i = 0; i < n; i++) {
            s[i] = random.nextInt(3) - 1; // Coefficients in {-1, 0, 1}
        }
    }

    // public key (a, b)
    public int[][] generatePublicKey() {
        Random random = new Random();
        int[] a = new int[n];
        int[] e = new int[n];
        int[] b = new int[n];

        // polynomial a
        for (int i = 0; i < n; i++) {
            a[i] = random.nextInt(q);
        }

        // error polynomial e
        for (int i = 0; i < n; i++) {
            e[i] = random.nextInt(3) - 1; // Coefficients in {-1, 0, 1}
        }

        // b = a * s + e mod q
        b = polyAdd(polyMul(a, s), e);
        for (int i = 0; i < n; i++) {
            b[i] = modq(b[i]);
        }

        return new int[][]{a, b};
    }

    public int[] encryptByte(int message, int[] a, int[] b) {
        Random random = new Random();

        // polynomial r
        int[] r = new int[n];
        for (int i = 0; i < n; i++) {
            r[i] = random.nextInt(3) - 1; // Coefficients in {-1, 0, 1}
        }

        // error polynomials e1 and e2
        int[] e1 = new int[n];
        int[] e2 = new int[n];
        for (int i = 0; i < n; i++) {
            e1[i] = random.nextInt(3) - 1;
            e2[i] = random.nextInt(3) - 1;
        }

        // u = a * r + e1 mod q
        int[] u = polyAdd(polyMul(a, r), e1);
        for (int i = 0; i < n; i++) {
            u[i] = modq(u[i]);
        }

        int[] m = new int[n];
        m[0] = message;

        // v = b * r + e2 + m * scalingFactor mod q
        int[] scaledM = scalarMul(m, scalingFactor);
        int[] v = polyAdd(polyAdd(polyMul(b, r), e2), scaledM);
        for (int i = 0; i < n; i++) {
            v[i] = modq(v[i]);
        }

        int[] ciphertext = new int[2 * n];
        System.arraycopy(u, 0, ciphertext, 0, n);
        System.arraycopy(v, 0, ciphertext, n, n);

        return ciphertext;
    }

    public int decryptByte(int[] ciphertext) {
        int[] u = new int[n];
        int[] v = new int[n];
        System.arraycopy(ciphertext, 0, u, 0, n);
        System.arraycopy(ciphertext, n, v, 0, n);

        // m' = v - u * s mod q
        int[] us = polyMul(u, s);
        int[] mPrime = polySub(v, us);
        for (int i = 0; i < n; i++) {
            mPrime[i] = modq(mPrime[i]);
        }

        int decryptedMessage = (int) Math.round((double) mPrime[0] / scalingFactor);
        decryptedMessage = decryptedMessage % 256;
        if (decryptedMessage < 0) decryptedMessage += 256;

        return decryptedMessage;
    }

    // Polynomial multiplication modulo x^n + 1
    private int[] polyMul(int[] a, int[] b) {
        int[] result = new int[n];
        for (int i = 0; i < n; i++) {
            long sum = 0;
            for (int j = 0; j < n; j++) {
                int index = (i - j) % n;
                if (index < 0) index += n;
                int sign = (((i - j) >= 0) ? 1 : -1);
                sum += (long) sign * a[j] * b[index];
            }
            result[i] = modq((int) sum);
        }
        return result;
    }

    private int[] polyAdd(int[] a, int[] b) {
        int[] result = new int[n];
        for (int i = 0; i < n; i++) {
            result[i] = modq(a[i] + b[i]);
        }
        return result;
    }

    private int[] polySub(int[] a, int[] b) {
        int[] result = new int[n];
        for (int i = 0; i < n; i++) {
            result[i] = modq(a[i] - b[i]);
        }
        return result;
    }
    
    private int[] scalarMul(int[] a, int scalar) {
        int[] result = new int[n];
        for (int i = 0; i < n; i++) {
            result[i] = modq(a[i] * scalar);
        }
        return result;
    }

    private int modq(int x) {
        int result = x % q;
        if (result < 0) result += q;
        return result;
    }
}

内容的提问来源于stack exchange，提问作者SDG8