org.bouncycastle.pqc.crypto.hqc.FastFourierTransform Maven / Gradle / Ivy

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The Bouncy Castle Crypto package is a Java implementation of cryptographic algorithms. This jar contains JCE provider and lightweight API for the Bouncy Castle Cryptography APIs for JDK 1.5 to JDK 1.8.
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package org.bouncycastle.pqc.crypto.hqc;

class FastFourierTransform
{
    static void fastFourierTransform(int[] output, int[] elements, int noCoefs, int fft)
    {
        int m = HQCParameters.PARAM_M;
        int mSize = 1 << (HQCParameters.PARAM_M - 1);

        int fftSize = 1 << fft;

        int[] f0 = new int[fftSize];
        int[] f1 = new int[fftSize];
        int[] deltas = new int[m - 1];
        int[] u = new int[mSize];
        int[] v = new int[mSize];

        // Step 1: Compute betas
        int[] betas = new int[m - 1];
        int[] betaSum = new int[mSize];

        computeFFTBetas(betas, m);
        computeSubsetSum(betaSum, betas, m - 1);

        // Step 2: Compute radix
        computeRadix(f0, f1, elements, fft, fft);

        // Step 3: Compute deltas
        for (int i = 0; i < m - 1; i++)
        {
            deltas[i] = GFCalculator.mult(betas[i], betas[i]) ^ betas[i];
        }

        // Step 5:
        computeFFTRec(u, f0, (noCoefs + 1) / 2, m - 1, fft - 1, deltas, fft, m);
        computeFFTRec(v, f1, noCoefs / 2, m - 1, fft - 1, deltas, fft, m);

        // Step 6.7
        int k = 1;
        k = 1 << (m - 1);

        System.arraycopy(v, 0, output, k, k);

        output[0] = u[0];
        output[k] ^= u[0];

        for (int i = 1; i < k; i++)
        {
            output[i] = u[i] ^ GFCalculator.mult(betaSum[i], v[i]);
            output[k + i] ^= output[i];
        }
    }

    static void computeFFTBetas(int[] betas, int m)
    {
        for (int i = 0; i < m - 1; i++)
        {
            betas[i] = 1 << (m - 1 - i);
        }
    }

    static void computeSubsetSum(int[] subsetSum, int[] set, int size)
    {
        subsetSum[0] = 0;

        for (int i = 0; i < size; i++)
        {
            for (int j = 0; j < (1 << i); j++)
            {
                subsetSum[(1 << i) + j] = set[i] ^ subsetSum[j];
            }
        }
    }

    static void computeRadix(int[] f0, int[] f1, int[] f, int mf, int fft)
    {
        switch (mf)
        {
        case 4:
            f0[4] = f[8] ^ f[12];
            f0[6] = f[12] ^ f[14];
            f0[7] = f[14] ^ f[15];
            f1[5] = f[11] ^ f[13];
            f1[6] = f[13] ^ f[14];
            f1[7] = f[15];
            f0[5] = f[10] ^ f[12] ^ f1[5];
            f1[4] = f[9] ^ f[13] ^ f0[5];

            f0[0] = f[0];
            f1[3] = f[7] ^ f[11] ^ f[15];
            f0[3] = f[6] ^ f[10] ^ f[14] ^ f1[3];
            f0[2] = f[4] ^ f0[4] ^ f0[3] ^ f1[3];
            f1[1] = f[3] ^ f[5] ^ f[9] ^ f[13] ^ f1[3];
            f1[2] = f[3] ^ f1[1] ^ f0[3];
            f0[1] = f[2] ^ f0[2] ^ f1[1];
            f1[0] = f[1] ^ f0[1];
            return;

        case 3:
            f0[0] = f[0];
            f0[2] = f[4] ^ f[6];
            f0[3] = f[6] ^ f[7];
            f1[1] = f[3] ^ f[5] ^ f[7];
            f1[2] = f[5] ^ f[6];
            f1[3] = f[7];
            f0[1] = f[2] ^ f0[2] ^ f1[1];
            f1[0] = f[1] ^ f0[1];
            return;

        case 2:
            f0[0] = f[0];
            f0[1] = f[2] ^ f[3];
            f1[0] = f[1] ^ f0[1];
            f1[1] = f[3];
            return;

        case 1:
            f0[0] = f[0];
            f1[0] = f[1];
            return;

        default:
            computeRadixBig(f0, f1, f, mf, fft);
            break;
        }
    }

    static void computeRadixBig(int[] f0, int[] f1, int[] f, int mf, int fft)
    {
        int n = 1;
        n <<= (mf - 2);
        int fftSize = 1 << (fft - 2);

        int Q[] = new int[2 * fftSize];
        int R[] = new int[2 * fftSize];

        int Q0[] = new int[fftSize];
        int Q1[] = new int[fftSize];
        int R0[] = new int[fftSize];
        int R1[] = new int[fftSize];


        Utils.copyBytes(f, 3 * n, Q, 0, 2 * n);
        Utils.copyBytes(f, 3 * n, Q, n, 2 * n);
        Utils.copyBytes(f, 0, R, 0, 4 * n);

        for (int i = 0; i < n; ++i)
        {
            Q[i] ^= f[2 * n + i];
            R[n + i] ^= Q[i];
        }

        computeRadix(Q0, Q1, Q, mf - 1, fft);
        computeRadix(R0, R1, R, mf - 1, fft);

        Utils.copyBytes(R0, 0, f0, 0, 2 * n);
        Utils.copyBytes(Q0, 0, f0, n, 2 * n);
        Utils.copyBytes(R1, 0, f1, 0, 2 * n);
        Utils.copyBytes(Q1, 0, f1, n, 2 * n);
    }

    static void computeFFTRec(int[] output, int[] func, int noCoeffs, int noOfBetas, int noCoeffsPlus, int[] betaSet, int fft, int m)
    {
        int fftSize = 1 << (fft - 2);
        int mSize = 1 << (m - 2);

        int[] fx0 = new int[fftSize];
        int[] fx1 = new int[fftSize];
        int[] gammaSet = new int[m - 2];
        int[] deltaSet = new int[m - 2];
        int k = 1;
        int[] gammaSumSet = new int[mSize];
        int[] uSet = new int[mSize];
        int[] vSet = new int[mSize];
        int[] tempSet = new int[m - fft + 1];

        int x = 0;
        if (noCoeffsPlus == 1)
        {
            for (int i = 0; i < noOfBetas; i++)
            {
                tempSet[i] = GFCalculator.mult(betaSet[i], func[1]);
            }

            output[0] = func[0];
            x = 1;
            for (int j = 0; j < noOfBetas; j++)
            {
                for (int t = 0; t < x; t++)
                {
                    output[x + t] = output[t] ^ tempSet[j];
                }
                x <<= 1;
            }
            return;
        }

        if (betaSet[noOfBetas - 1] != 1)
        {
            int betaMPow = 1;
            x = 1;
            x <<= noCoeffsPlus;
            for (int i = 1; i < x; i++)
            {
                betaMPow = GFCalculator.mult(betaMPow, betaSet[noOfBetas - 1]);
                func[i] = GFCalculator.mult(betaMPow, func[i]);
            }
        }

        computeRadix(fx0, fx1, func, noCoeffsPlus, fft);

        for (int i = 0; i < noOfBetas - 1; i++)
        {
            gammaSet[i] = GFCalculator.mult(betaSet[i], GFCalculator.inverse(betaSet[noOfBetas - 1]));
            deltaSet[i] = GFCalculator.mult(gammaSet[i], gammaSet[i]) ^ gammaSet[i];
        }

        computeSubsetSum(gammaSumSet, gammaSet, noOfBetas - 1);

        computeFFTRec(uSet, fx0, (noCoeffs + 1) / 2, noOfBetas - 1, noCoeffsPlus - 1, deltaSet, fft, m);

        k = 1;
        k <<= ((noOfBetas - 1) & 0xf);
        if (noCoeffs <= 3)
        {
            output[0] = uSet[0];
            output[k] = uSet[0] ^ fx1[0];
            for (int i = 1; i < k; i++)
            {
                output[i] = uSet[i] ^ GFCalculator.mult(gammaSumSet[i], fx1[0]);
                output[k + i] = output[i] ^ fx1[0];
            }
        }
        else
        {
            computeFFTRec(vSet, fx1, noCoeffs / 2, noOfBetas - 1, noCoeffsPlus - 1, deltaSet, fft, m);

//            int[] tmp = new int[3*k];
//            System.arraycopy(output, 0, tmp, 0 , output.length);
//            System.arraycopy(vSet, 0, tmp, k , 2*k);
            System.arraycopy(vSet, 0, output, k, k);

            output[0] = uSet[0];
            output[k] ^= uSet[0];
            for (int i = 1; i < k; i++)
            {
                output[i] = uSet[i] ^ GFCalculator.mult(gammaSumSet[i], vSet[i]);
                output[k + i] ^= output[i];
            }


        }
    }

    static void fastFourierTransformGetError(byte[] errorSet, int[] input, int mSize, int[] logArrays)
    {
        int m = HQCParameters.PARAM_M;
        int gfMulOrder = HQCParameters.GF_MUL_ORDER;

        int[] gammaSet = new int[m - 1];
        int[] gammaSumSet = new int[mSize];
        int k = mSize;

        computeFFTBetas(gammaSet, m);
        computeSubsetSum(gammaSumSet, gammaSet, m - 1);

        errorSet[0] ^= 1 ^ Utils.toUnsigned16Bits(-input[0] >> 15);
        errorSet[0] ^= 1 ^ Utils.toUnsigned16Bits(-input[k] >> 15);

        for (int i = 1; i < k; i++)
        {
            int tmp = gfMulOrder - logArrays[gammaSumSet[i]];
            errorSet[tmp] ^= 1 ^ Math.abs(-input[i] >> 15);

            tmp = gfMulOrder - logArrays[gammaSumSet[i] ^ 1];
            errorSet[tmp] ^= 1 ^ Math.abs(-input[k + i] >> 15);
        }
    }
}