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package org.bouncycastle.pqc.math.ntru.polynomial;

import org.bouncycastle.util.Arrays;

/**
 * A polynomial class that combines two coefficients into one long value for
 * faster multiplication in 64 bit environments.
* Coefficients can be between 0 and 2047 and are stored in pairs in the bits 0..10 and 24..34 of a long number. */ public class LongPolynomial2 { private long[] coeffs; // each representing two coefficients in the original IntegerPolynomial private int numCoeffs; /** * Constructs a LongPolynomial2 from a IntegerPolynomial. The two polynomials are independent of each other. * * @param p the original polynomial. Coefficients must be between 0 and 2047. */ public LongPolynomial2(IntegerPolynomial p) { numCoeffs = p.coeffs.length; coeffs = new long[(numCoeffs + 1) / 2]; int idx = 0; for (int pIdx = 0; pIdx < numCoeffs; ) { int c0 = p.coeffs[pIdx++]; while (c0 < 0) { c0 += 2048; } long c1 = pIdx < numCoeffs ? p.coeffs[pIdx++] : 0; while (c1 < 0) { c1 += 2048; } coeffs[idx] = c0 + (c1 << 24); idx++; } } private LongPolynomial2(long[] coeffs) { this.coeffs = coeffs; } private LongPolynomial2(int N) { coeffs = new long[N]; } /** * Multiplies the polynomial with another, taking the indices mod N and the values mod 2048. */ public LongPolynomial2 mult(LongPolynomial2 poly2) { int N = coeffs.length; if (poly2.coeffs.length != N || numCoeffs != poly2.numCoeffs) { throw new IllegalArgumentException("Number of coefficients must be the same"); } LongPolynomial2 c = multRecursive(poly2); if (c.coeffs.length > N) { if (numCoeffs % 2 == 0) { for (int k = N; k < c.coeffs.length; k++) { c.coeffs[k - N] = (c.coeffs[k - N] + c.coeffs[k]) & 0x7FF0007FFL; } c.coeffs = Arrays.copyOf(c.coeffs, N); } else { for (int k = N; k < c.coeffs.length; k++) { c.coeffs[k - N] = c.coeffs[k - N] + (c.coeffs[k - 1] >> 24); c.coeffs[k - N] = c.coeffs[k - N] + ((c.coeffs[k] & 2047) << 24); c.coeffs[k - N] &= 0x7FF0007FFL; } c.coeffs = Arrays.copyOf(c.coeffs, N); c.coeffs[c.coeffs.length - 1] &= 2047; } } c = new LongPolynomial2(c.coeffs); c.numCoeffs = numCoeffs; return c; } public IntegerPolynomial toIntegerPolynomial() { int[] intCoeffs = new int[numCoeffs]; int uIdx = 0; for (int i = 0; i < coeffs.length; i++) { intCoeffs[uIdx++] = (int)(coeffs[i] & 2047); if (uIdx < numCoeffs) { intCoeffs[uIdx++] = (int)((coeffs[i] >> 24) & 2047); } } return new IntegerPolynomial(intCoeffs); } /** * Karazuba multiplication */ private LongPolynomial2 multRecursive(LongPolynomial2 poly2) { long[] a = coeffs; long[] b = poly2.coeffs; int n = poly2.coeffs.length; if (n <= 32) { int cn = 2 * n; LongPolynomial2 c = new LongPolynomial2(new long[cn]); for (int k = 0; k < cn; k++) { for (int i = Math.max(0, k - n + 1); i <= Math.min(k, n - 1); i++) { long c0 = a[k - i] * b[i]; long cu = c0 & 0x7FF000000L + (c0 & 2047); long co = (c0 >>> 48) & 2047; c.coeffs[k] = (c.coeffs[k] + cu) & 0x7FF0007FFL; c.coeffs[k + 1] = (c.coeffs[k + 1] + co) & 0x7FF0007FFL; } } return c; } else { int n1 = n / 2; LongPolynomial2 a1 = new LongPolynomial2(Arrays.copyOf(a, n1)); LongPolynomial2 a2 = new LongPolynomial2(Arrays.copyOfRange(a, n1, n)); LongPolynomial2 b1 = new LongPolynomial2(Arrays.copyOf(b, n1)); LongPolynomial2 b2 = new LongPolynomial2(Arrays.copyOfRange(b, n1, n)); LongPolynomial2 A = (LongPolynomial2)a1.clone(); A.add(a2); LongPolynomial2 B = (LongPolynomial2)b1.clone(); B.add(b2); LongPolynomial2 c1 = a1.multRecursive(b1); LongPolynomial2 c2 = a2.multRecursive(b2); LongPolynomial2 c3 = A.multRecursive(B); c3.sub(c1); c3.sub(c2); LongPolynomial2 c = new LongPolynomial2(2 * n); for (int i = 0; i < c1.coeffs.length; i++) { c.coeffs[i] = c1.coeffs[i] & 0x7FF0007FFL; } for (int i = 0; i < c3.coeffs.length; i++) { c.coeffs[n1 + i] = (c.coeffs[n1 + i] + c3.coeffs[i]) & 0x7FF0007FFL; } for (int i = 0; i < c2.coeffs.length; i++) { c.coeffs[2 * n1 + i] = (c.coeffs[2 * n1 + i] + c2.coeffs[i]) & 0x7FF0007FFL; } return c; } } /** * Adds another polynomial which can have a different number of coefficients. * * @param b another polynomial */ private void add(LongPolynomial2 b) { if (b.coeffs.length > coeffs.length) { coeffs = Arrays.copyOf(coeffs, b.coeffs.length); } for (int i = 0; i < b.coeffs.length; i++) { coeffs[i] = (coeffs[i] + b.coeffs[i]) & 0x7FF0007FFL; } } /** * Subtracts another polynomial which can have a different number of coefficients. * * @param b another polynomial */ private void sub(LongPolynomial2 b) { if (b.coeffs.length > coeffs.length) { coeffs = Arrays.copyOf(coeffs, b.coeffs.length); } for (int i = 0; i < b.coeffs.length; i++) { coeffs[i] = (0x0800000800000L + coeffs[i] - b.coeffs[i]) & 0x7FF0007FFL; } } /** * Subtracts another polynomial which must have the same number of coefficients, * and applies an AND mask to the upper and lower halves of each coefficients. * * @param b another polynomial * @param mask a bit mask less than 2048 to apply to each 11-bit coefficient */ public void subAnd(LongPolynomial2 b, int mask) { long longMask = (((long)mask) << 24) + mask; for (int i = 0; i < b.coeffs.length; i++) { coeffs[i] = (0x0800000800000L + coeffs[i] - b.coeffs[i]) & longMask; } } /** * Multiplies this polynomial by 2 and applies an AND mask to the upper and * lower halves of each coefficients. * * @param mask a bit mask less than 2048 to apply to each 11-bit coefficient */ public void mult2And(int mask) { long longMask = (((long)mask) << 24) + mask; for (int i = 0; i < coeffs.length; i++) { coeffs[i] = (coeffs[i] << 1) & longMask; } } public Object clone() { LongPolynomial2 p = new LongPolynomial2(coeffs.clone()); p.numCoeffs = numCoeffs; return p; } public boolean equals(Object obj) { if (obj instanceof LongPolynomial2) { return Arrays.areEqual(coeffs, ((LongPolynomial2)obj).coeffs); } else { return false; } } }




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