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-rw-r--r--bcprov/src/main/java/org/bouncycastle/pqc/math/ntru/polynomial/IntegerPolynomial.java1358
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diff --git a/bcprov/src/main/java/org/bouncycastle/pqc/math/ntru/polynomial/IntegerPolynomial.java b/bcprov/src/main/java/org/bouncycastle/pqc/math/ntru/polynomial/IntegerPolynomial.java
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@@ -1,1358 +0,0 @@
-package org.bouncycastle.pqc.math.ntru.polynomial;
-
-import java.io.IOException;
-import java.io.InputStream;
-import java.math.BigInteger;
-import java.util.ArrayList;
-import java.util.Iterator;
-import java.util.LinkedList;
-import java.util.List;
-import java.util.concurrent.Callable;
-import java.util.concurrent.ExecutorService;
-import java.util.concurrent.Executors;
-import java.util.concurrent.Future;
-import java.util.concurrent.LinkedBlockingQueue;
-
-import org.bouncycastle.pqc.math.ntru.euclid.BigIntEuclidean;
-import org.bouncycastle.pqc.math.ntru.util.ArrayEncoder;
-import org.bouncycastle.pqc.math.ntru.util.Util;
-import org.bouncycastle.util.Arrays;
-
-/**
- * A polynomial with <code>int</code> coefficients.<br>
- * Some methods (like <code>add</code>) change the polynomial, others (like <code>mult</code>) do
- * not but return the result as a new polynomial.
- */
-public class IntegerPolynomial
- implements Polynomial
-{
- private static final int NUM_EQUAL_RESULTANTS = 3;
- /**
- * Prime numbers &gt; 4500 for resultant computation. Starting them below ~4400 causes incorrect results occasionally.
- * Fortunately, 4500 is about the optimum number for performance.<br/>
- * This array contains enough prime numbers so primes never have to be computed on-line for any standard {@link org.bouncycastle.pqc.crypto.ntru.NTRUSigningParameters}.
- */
- private static final int[] PRIMES = new int[]{
- 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583,
- 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657,
- 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751,
- 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831,
- 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937,
- 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003,
- 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087,
- 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179,
- 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279,
- 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387,
- 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443,
- 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521,
- 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639,
- 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693,
- 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791,
- 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857,
- 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939,
- 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053,
- 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133,
- 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221,
- 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301,
- 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367,
- 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473,
- 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571,
- 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673,
- 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761,
- 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833,
- 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917,
- 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997,
- 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103,
- 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207,
- 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297,
- 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411,
- 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499,
- 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561,
- 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643,
- 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723,
- 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829,
- 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919,
- 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017,
- 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111,
- 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219,
- 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291,
- 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387,
- 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501,
- 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597,
- 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677,
- 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741,
- 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831,
- 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929,
- 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011,
- 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109,
- 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199,
- 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283,
- 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377,
- 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439,
- 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533,
- 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631,
- 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733,
- 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811,
- 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887,
- 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973};
- private static final List BIGINT_PRIMES;
-
- static
- {
- BIGINT_PRIMES = new ArrayList();
- for (int i = 0; i != PRIMES.length; i++)
- {
- BIGINT_PRIMES.add(BigInteger.valueOf(PRIMES[i]));
- }
- }
-
- public int[] coeffs;
-
- /**
- * Constructs a new polynomial with <code>N</code> coefficients initialized to 0.
- *
- * @param N the number of coefficients
- */
- public IntegerPolynomial(int N)
- {
- coeffs = new int[N];
- }
-
- /**
- * Constructs a new polynomial with a given set of coefficients.
- *
- * @param coeffs the coefficients
- */
- public IntegerPolynomial(int[] coeffs)
- {
- this.coeffs = coeffs;
- }
-
- /**
- * Constructs a <code>IntegerPolynomial</code> from a <code>BigIntPolynomial</code>. The two polynomials are independent of each other.
- *
- * @param p the original polynomial
- */
- public IntegerPolynomial(BigIntPolynomial p)
- {
- coeffs = new int[p.coeffs.length];
- for (int i = 0; i < p.coeffs.length; i++)
- {
- coeffs[i] = p.coeffs[i].intValue();
- }
- }
-
- /**
- * Decodes a byte array to a polynomial with <code>N</code> ternary coefficients<br>
- * Ignores any excess bytes.
- *
- * @param data an encoded ternary polynomial
- * @param N number of coefficients
- * @return the decoded polynomial
- */
- public static IntegerPolynomial fromBinary3Sves(byte[] data, int N)
- {
- return new IntegerPolynomial(ArrayEncoder.decodeMod3Sves(data, N));
- }
-
- /**
- * Converts a byte array produced by {@link #toBinary3Tight()} to a polynomial.
- *
- * @param b a byte array
- * @param N number of coefficients
- * @return the decoded polynomial
- */
- public static IntegerPolynomial fromBinary3Tight(byte[] b, int N)
- {
- return new IntegerPolynomial(ArrayEncoder.decodeMod3Tight(b, N));
- }
-
- /**
- * Reads data produced by {@link #toBinary3Tight()} from an input stream and converts it to a polynomial.
- *
- * @param is an input stream
- * @param N number of coefficients
- * @return the decoded polynomial
- */
- public static IntegerPolynomial fromBinary3Tight(InputStream is, int N)
- throws IOException
- {
- return new IntegerPolynomial(ArrayEncoder.decodeMod3Tight(is, N));
- }
-
- /**
- * Returns a polynomial with N coefficients between <code>0</code> and <code>q-1</code>.<br>
- * <code>q</code> must be a power of 2.<br>
- * Ignores any excess bytes.
- *
- * @param data an encoded ternary polynomial
- * @param N number of coefficients
- * @param q
- * @return the decoded polynomial
- */
- public static IntegerPolynomial fromBinary(byte[] data, int N, int q)
- {
- return new IntegerPolynomial(ArrayEncoder.decodeModQ(data, N, q));
- }
-
- /**
- * Returns a polynomial with N coefficients between <code>0</code> and <code>q-1</code>.<br>
- * <code>q</code> must be a power of 2.<br>
- * Ignores any excess bytes.
- *
- * @param is an encoded ternary polynomial
- * @param N number of coefficients
- * @param q
- * @return the decoded polynomial
- */
- public static IntegerPolynomial fromBinary(InputStream is, int N, int q)
- throws IOException
- {
- return new IntegerPolynomial(ArrayEncoder.decodeModQ(is, N, q));
- }
-
- /**
- * Encodes a polynomial with ternary coefficients to binary.
- * <code>coeffs[2*i]</code> and <code>coeffs[2*i+1]</code> must not both equal -1 for any integer <code>i</code>,
- * so this method is only safe to use with polynomials produced by <code>fromBinary3Sves()</code>.
- *
- * @return the encoded polynomial
- */
- public byte[] toBinary3Sves()
- {
- return ArrayEncoder.encodeMod3Sves(coeffs);
- }
-
- /**
- * Converts a polynomial with ternary coefficients to binary.
- *
- * @return the encoded polynomial
- */
- public byte[] toBinary3Tight()
- {
- BigInteger sum = Constants.BIGINT_ZERO;
- for (int i = coeffs.length - 1; i >= 0; i--)
- {
- sum = sum.multiply(BigInteger.valueOf(3));
- sum = sum.add(BigInteger.valueOf(coeffs[i] + 1));
- }
-
- int size = (BigInteger.valueOf(3).pow(coeffs.length).bitLength() + 7) / 8;
- byte[] arr = sum.toByteArray();
-
- if (arr.length < size)
- {
- // pad with leading zeros so arr.length==size
- byte[] arr2 = new byte[size];
- System.arraycopy(arr, 0, arr2, size - arr.length, arr.length);
- return arr2;
- }
-
- if (arr.length > size)
- // drop sign bit
- {
- arr = Arrays.copyOfRange(arr, 1, arr.length);
- }
- return arr;
- }
-
- /**
- * Encodes a polynomial whose coefficients are between 0 and q, to binary. q must be a power of 2.
- *
- * @param q
- * @return the encoded polynomial
- */
- public byte[] toBinary(int q)
- {
- return ArrayEncoder.encodeModQ(coeffs, q);
- }
-
- /**
- * Multiplies the polynomial with another, taking the values mod modulus and the indices mod N
- */
- public IntegerPolynomial mult(IntegerPolynomial poly2, int modulus)
- {
- IntegerPolynomial c = mult(poly2);
- c.mod(modulus);
- return c;
- }
-
- /**
- * Multiplies the polynomial with another, taking the indices mod N
- */
- public IntegerPolynomial mult(IntegerPolynomial poly2)
- {
- int N = coeffs.length;
- if (poly2.coeffs.length != N)
- {
- throw new IllegalArgumentException("Number of coefficients must be the same");
- }
-
- IntegerPolynomial c = multRecursive(poly2);
-
- if (c.coeffs.length > N)
- {
- for (int k = N; k < c.coeffs.length; k++)
- {
- c.coeffs[k - N] += c.coeffs[k];
- }
- c.coeffs = Arrays.copyOf(c.coeffs, N);
- }
- return c;
- }
-
- public BigIntPolynomial mult(BigIntPolynomial poly2)
- {
- return new BigIntPolynomial(this).mult(poly2);
- }
-
- /**
- * Karazuba multiplication
- */
- private IntegerPolynomial multRecursive(IntegerPolynomial poly2)
- {
- int[] a = coeffs;
- int[] b = poly2.coeffs;
-
- int n = poly2.coeffs.length;
- if (n <= 32)
- {
- int cn = 2 * n - 1;
- IntegerPolynomial c = new IntegerPolynomial(new int[cn]);
- for (int k = 0; k < cn; k++)
- {
- for (int i = Math.max(0, k - n + 1); i <= Math.min(k, n - 1); i++)
- {
- c.coeffs[k] += b[i] * a[k - i];
- }
- }
- return c;
- }
- else
- {
- int n1 = n / 2;
-
- IntegerPolynomial a1 = new IntegerPolynomial(Arrays.copyOf(a, n1));
- IntegerPolynomial a2 = new IntegerPolynomial(Arrays.copyOfRange(a, n1, n));
- IntegerPolynomial b1 = new IntegerPolynomial(Arrays.copyOf(b, n1));
- IntegerPolynomial b2 = new IntegerPolynomial(Arrays.copyOfRange(b, n1, n));
-
- IntegerPolynomial A = (IntegerPolynomial)a1.clone();
- A.add(a2);
- IntegerPolynomial B = (IntegerPolynomial)b1.clone();
- B.add(b2);
-
- IntegerPolynomial c1 = a1.multRecursive(b1);
- IntegerPolynomial c2 = a2.multRecursive(b2);
- IntegerPolynomial c3 = A.multRecursive(B);
- c3.sub(c1);
- c3.sub(c2);
-
- IntegerPolynomial c = new IntegerPolynomial(2 * n - 1);
- for (int i = 0; i < c1.coeffs.length; i++)
- {
- c.coeffs[i] = c1.coeffs[i];
- }
- for (int i = 0; i < c3.coeffs.length; i++)
- {
- c.coeffs[n1 + i] += c3.coeffs[i];
- }
- for (int i = 0; i < c2.coeffs.length; i++)
- {
- c.coeffs[2 * n1 + i] += c2.coeffs[i];
- }
- return c;
- }
- }
-
- /**
- * Computes the inverse mod <code>q; q</code> must be a power of 2.<br>
- * Returns <code>null</code> if the polynomial is not invertible.
- *
- * @param q the modulus
- * @return a new polynomial
- */
- public IntegerPolynomial invertFq(int q)
- {
- int N = coeffs.length;
- int k = 0;
- IntegerPolynomial b = new IntegerPolynomial(N + 1);
- b.coeffs[0] = 1;
- IntegerPolynomial c = new IntegerPolynomial(N + 1);
- IntegerPolynomial f = new IntegerPolynomial(N + 1);
- f.coeffs = Arrays.copyOf(coeffs, N + 1);
- f.modPositive(2);
- // set g(x) = x^N − 1
- IntegerPolynomial g = new IntegerPolynomial(N + 1);
- g.coeffs[0] = 1;
- g.coeffs[N] = 1;
- while (true)
- {
- while (f.coeffs[0] == 0)
- {
- for (int i = 1; i <= N; i++)
- {
- f.coeffs[i - 1] = f.coeffs[i]; // f(x) = f(x) / x
- c.coeffs[N + 1 - i] = c.coeffs[N - i]; // c(x) = c(x) * x
- }
- f.coeffs[N] = 0;
- c.coeffs[0] = 0;
- k++;
- if (f.equalsZero())
- {
- return null; // not invertible
- }
- }
- if (f.equalsOne())
- {
- break;
- }
- if (f.degree() < g.degree())
- {
- // exchange f and g
- IntegerPolynomial temp = f;
- f = g;
- g = temp;
- // exchange b and c
- temp = b;
- b = c;
- c = temp;
- }
- f.add(g, 2);
- b.add(c, 2);
- }
-
- if (b.coeffs[N] != 0)
- {
- return null;
- }
- // Fq(x) = x^(N-k) * b(x)
- IntegerPolynomial Fq = new IntegerPolynomial(N);
- int j = 0;
- k %= N;
- for (int i = N - 1; i >= 0; i--)
- {
- j = i - k;
- if (j < 0)
- {
- j += N;
- }
- Fq.coeffs[j] = b.coeffs[i];
- }
-
- return mod2ToModq(Fq, q);
- }
-
- /**
- * Computes the inverse mod q from the inverse mod 2
- *
- * @param Fq
- * @param q
- * @return The inverse of this polynomial mod q
- */
- private IntegerPolynomial mod2ToModq(IntegerPolynomial Fq, int q)
- {
- if (Util.is64BitJVM() && q == 2048)
- {
- LongPolynomial2 thisLong = new LongPolynomial2(this);
- LongPolynomial2 FqLong = new LongPolynomial2(Fq);
- int v = 2;
- while (v < q)
- {
- v *= 2;
- LongPolynomial2 temp = (LongPolynomial2)FqLong.clone();
- temp.mult2And(v - 1);
- FqLong = thisLong.mult(FqLong).mult(FqLong);
- temp.subAnd(FqLong, v - 1);
- FqLong = temp;
- }
- return FqLong.toIntegerPolynomial();
- }
- else
- {
- int v = 2;
- while (v < q)
- {
- v *= 2;
- IntegerPolynomial temp = new IntegerPolynomial(Arrays.copyOf(Fq.coeffs, Fq.coeffs.length));
- temp.mult2(v);
- Fq = mult(Fq, v).mult(Fq, v);
- temp.sub(Fq, v);
- Fq = temp;
- }
- return Fq;
- }
- }
-
- /**
- * Computes the inverse mod 3.
- * Returns <code>null</code> if the polynomial is not invertible.
- *
- * @return a new polynomial
- */
- public IntegerPolynomial invertF3()
- {
- int N = coeffs.length;
- int k = 0;
- IntegerPolynomial b = new IntegerPolynomial(N + 1);
- b.coeffs[0] = 1;
- IntegerPolynomial c = new IntegerPolynomial(N + 1);
- IntegerPolynomial f = new IntegerPolynomial(N + 1);
- f.coeffs = Arrays.copyOf(coeffs, N + 1);
- f.modPositive(3);
- // set g(x) = x^N − 1
- IntegerPolynomial g = new IntegerPolynomial(N + 1);
- g.coeffs[0] = -1;
- g.coeffs[N] = 1;
- while (true)
- {
- while (f.coeffs[0] == 0)
- {
- for (int i = 1; i <= N; i++)
- {
- f.coeffs[i - 1] = f.coeffs[i]; // f(x) = f(x) / x
- c.coeffs[N + 1 - i] = c.coeffs[N - i]; // c(x) = c(x) * x
- }
- f.coeffs[N] = 0;
- c.coeffs[0] = 0;
- k++;
- if (f.equalsZero())
- {
- return null; // not invertible
- }
- }
- if (f.equalsAbsOne())
- {
- break;
- }
- if (f.degree() < g.degree())
- {
- // exchange f and g
- IntegerPolynomial temp = f;
- f = g;
- g = temp;
- // exchange b and c
- temp = b;
- b = c;
- c = temp;
- }
- if (f.coeffs[0] == g.coeffs[0])
- {
- f.sub(g, 3);
- b.sub(c, 3);
- }
- else
- {
- f.add(g, 3);
- b.add(c, 3);
- }
- }
-
- if (b.coeffs[N] != 0)
- {
- return null;
- }
- // Fp(x) = [+-] x^(N-k) * b(x)
- IntegerPolynomial Fp = new IntegerPolynomial(N);
- int j = 0;
- k %= N;
- for (int i = N - 1; i >= 0; i--)
- {
- j = i - k;
- if (j < 0)
- {
- j += N;
- }
- Fp.coeffs[j] = f.coeffs[0] * b.coeffs[i];
- }
-
- Fp.ensurePositive(3);
- return Fp;
- }
-
- /**
- * Resultant of this polynomial with <code>x^n-1</code> using a probabilistic algorithm.
- * <p>
- * Unlike EESS, this implementation does not compute all resultants modulo primes
- * such that their product exceeds the maximum possible resultant, but rather stops
- * when <code>NUM_EQUAL_RESULTANTS</code> consecutive modular resultants are equal.<br>
- * This means the return value may be incorrect. Experiments show this happens in
- * about 1 out of 100 cases when <code>N=439</code> and <code>NUM_EQUAL_RESULTANTS=2</code>,
- * so the likelyhood of leaving the loop too early is <code>(1/100)^(NUM_EQUAL_RESULTANTS-1)</code>.
- * <p>
- * Because of the above, callers must verify the output and try a different polynomial if necessary.
- *
- * @return <code>(rho, res)</code> satisfying <code>res = rho*this + t*(x^n-1)</code> for some integer <code>t</code>.
- */
- public Resultant resultant()
- {
- int N = coeffs.length;
-
- // Compute resultants modulo prime numbers. Continue until NUM_EQUAL_RESULTANTS consecutive modular resultants are equal.
- LinkedList<ModularResultant> modResultants = new LinkedList<ModularResultant>();
- BigInteger prime = null;
- BigInteger pProd = Constants.BIGINT_ONE;
- BigInteger res = Constants.BIGINT_ONE;
- int numEqual = 1; // number of consecutive modular resultants equal to each other
- Iterator<BigInteger> primes = BIGINT_PRIMES.iterator();
- while (true)
- {
- prime = primes.hasNext() ? primes.next() : prime.nextProbablePrime();
- ModularResultant crr = resultant(prime.intValue());
- modResultants.add(crr);
-
- BigInteger temp = pProd.multiply(prime);
- BigIntEuclidean er = BigIntEuclidean.calculate(prime, pProd);
- BigInteger resPrev = res;
- res = res.multiply(er.x.multiply(prime));
- BigInteger res2 = crr.res.multiply(er.y.multiply(pProd));
- res = res.add(res2).mod(temp);
- pProd = temp;
-
- BigInteger pProd2 = pProd.divide(BigInteger.valueOf(2));
- BigInteger pProd2n = pProd2.negate();
- if (res.compareTo(pProd2) > 0)
- {
- res = res.subtract(pProd);
- }
- else if (res.compareTo(pProd2n) < 0)
- {
- res = res.add(pProd);
- }
-
- if (res.equals(resPrev))
- {
- numEqual++;
- if (numEqual >= NUM_EQUAL_RESULTANTS)
- {
- break;
- }
- }
- else
- {
- numEqual = 1;
- }
- }
-
- // Combine modular rho's to obtain the final rho.
- // For efficiency, first combine all pairs of small resultants to bigger resultants,
- // then combine pairs of those, etc. until only one is left.
- while (modResultants.size() > 1)
- {
- ModularResultant modRes1 = modResultants.removeFirst();
- ModularResultant modRes2 = modResultants.removeFirst();
- ModularResultant modRes3 = ModularResultant.combineRho(modRes1, modRes2);
- modResultants.addLast(modRes3);
- }
- BigIntPolynomial rhoP = modResultants.getFirst().rho;
-
- BigInteger pProd2 = pProd.divide(BigInteger.valueOf(2));
- BigInteger pProd2n = pProd2.negate();
- if (res.compareTo(pProd2) > 0)
- {
- res = res.subtract(pProd);
- }
- if (res.compareTo(pProd2n) < 0)
- {
- res = res.add(pProd);
- }
-
- for (int i = 0; i < N; i++)
- {
- BigInteger c = rhoP.coeffs[i];
- if (c.compareTo(pProd2) > 0)
- {
- rhoP.coeffs[i] = c.subtract(pProd);
- }
- if (c.compareTo(pProd2n) < 0)
- {
- rhoP.coeffs[i] = c.add(pProd);
- }
- }
-
- return new Resultant(rhoP, res);
- }
-
- /**
- * Multithreaded version of {@link #resultant()}.
- *
- * @return <code>(rho, res)</code> satisfying <code>res = rho*this + t*(x^n-1)</code> for some integer <code>t</code>.
- */
- public Resultant resultantMultiThread()
- {
- int N = coeffs.length;
-
- // upper bound for resultant(f, g) = ||f, 2||^deg(g) * ||g, 2||^deg(f) = squaresum(f)^(N/2) * 2^(deg(f)/2) because g(x)=x^N-1
- // see http://jondalon.mathematik.uni-osnabrueck.de/staff/phpages/brunsw/CompAlg.pdf chapter 3
- BigInteger max = squareSum().pow((N + 1) / 2);
- max = max.multiply(BigInteger.valueOf(2).pow((degree() + 1) / 2));
- BigInteger max2 = max.multiply(BigInteger.valueOf(2));
-
- // compute resultants modulo prime numbers
- BigInteger prime = BigInteger.valueOf(10000);
- BigInteger pProd = Constants.BIGINT_ONE;
- LinkedBlockingQueue<Future<ModularResultant>> resultantTasks = new LinkedBlockingQueue<Future<ModularResultant>>();
- Iterator<BigInteger> primes = BIGINT_PRIMES.iterator();
- ExecutorService executor = Executors.newFixedThreadPool(Runtime.getRuntime().availableProcessors());
- while (pProd.compareTo(max2) < 0)
- {
- if (primes.hasNext())
- {
- prime = primes.next();
- }
- else
- {
- prime = prime.nextProbablePrime();
- }
- Future<ModularResultant> task = executor.submit(new ModResultantTask(prime.intValue()));
- resultantTasks.add(task);
- pProd = pProd.multiply(prime);
- }
-
- // Combine modular resultants to obtain the resultant.
- // For efficiency, first combine all pairs of small resultants to bigger resultants,
- // then combine pairs of those, etc. until only one is left.
- ModularResultant overallResultant = null;
- while (!resultantTasks.isEmpty())
- {
- try
- {
- Future<ModularResultant> modRes1 = resultantTasks.take();
- Future<ModularResultant> modRes2 = resultantTasks.poll();
- if (modRes2 == null)
- {
- // modRes1 is the only one left
- overallResultant = modRes1.get();
- break;
- }
- Future<ModularResultant> newTask = executor.submit(new CombineTask(modRes1.get(), modRes2.get()));
- resultantTasks.add(newTask);
- }
- catch (Exception e)
- {
- throw new IllegalStateException(e.toString());
- }
- }
- executor.shutdown();
- BigInteger res = overallResultant.res;
- BigIntPolynomial rhoP = overallResultant.rho;
-
- BigInteger pProd2 = pProd.divide(BigInteger.valueOf(2));
- BigInteger pProd2n = pProd2.negate();
-
- if (res.compareTo(pProd2) > 0)
- {
- res = res.subtract(pProd);
- }
- if (res.compareTo(pProd2n) < 0)
- {
- res = res.add(pProd);
- }
-
- for (int i = 0; i < N; i++)
- {
- BigInteger c = rhoP.coeffs[i];
- if (c.compareTo(pProd2) > 0)
- {
- rhoP.coeffs[i] = c.subtract(pProd);
- }
- if (c.compareTo(pProd2n) < 0)
- {
- rhoP.coeffs[i] = c.add(pProd);
- }
- }
-
- return new Resultant(rhoP, res);
- }
-
- /**
- * Resultant of this polynomial with <code>x^n-1 mod p</code>.
- *
- * @return <code>(rho, res)</code> satisfying <code>res = rho*this + t*(x^n-1) mod p</code> for some integer <code>t</code>.
- */
- public ModularResultant resultant(int p)
- {
- // Add a coefficient as the following operations involve polynomials of degree deg(f)+1
- int[] fcoeffs = Arrays.copyOf(coeffs, coeffs.length + 1);
- IntegerPolynomial f = new IntegerPolynomial(fcoeffs);
- int N = fcoeffs.length;
-
- IntegerPolynomial a = new IntegerPolynomial(N);
- a.coeffs[0] = -1;
- a.coeffs[N - 1] = 1;
- IntegerPolynomial b = new IntegerPolynomial(f.coeffs);
- IntegerPolynomial v1 = new IntegerPolynomial(N);
- IntegerPolynomial v2 = new IntegerPolynomial(N);
- v2.coeffs[0] = 1;
- int da = N - 1;
- int db = b.degree();
- int ta = da;
- int c = 0;
- int r = 1;
- while (db > 0)
- {
- c = Util.invert(b.coeffs[db], p);
- c = (c * a.coeffs[da]) % p;
- a.multShiftSub(b, c, da - db, p);
- v1.multShiftSub(v2, c, da - db, p);
-
- da = a.degree();
- if (da < db)
- {
- r *= Util.pow(b.coeffs[db], ta - da, p);
- r %= p;
- if (ta % 2 == 1 && db % 2 == 1)
- {
- r = (-r) % p;
- }
- IntegerPolynomial temp = a;
- a = b;
- b = temp;
- int tempdeg = da;
- da = db;
- temp = v1;
- v1 = v2;
- v2 = temp;
- ta = db;
- db = tempdeg;
- }
- }
- r *= Util.pow(b.coeffs[0], da, p);
- r %= p;
- c = Util.invert(b.coeffs[0], p);
- v2.mult(c);
- v2.mod(p);
- v2.mult(r);
- v2.mod(p);
-
- // drop the highest coefficient so #coeffs matches the original input
- v2.coeffs = Arrays.copyOf(v2.coeffs, v2.coeffs.length - 1);
- return new ModularResultant(new BigIntPolynomial(v2), BigInteger.valueOf(r), BigInteger.valueOf(p));
- }
-
- /**
- * Computes <code>this-b*c*(x^k) mod p</code> and stores the result in this polynomial.<br/>
- * See steps 4a,4b in EESS algorithm 2.2.7.1.
- *
- * @param b
- * @param c
- * @param k
- * @param p
- */
- private void multShiftSub(IntegerPolynomial b, int c, int k, int p)
- {
- int N = coeffs.length;
- for (int i = k; i < N; i++)
- {
- coeffs[i] = (coeffs[i] - b.coeffs[i - k] * c) % p;
- }
- }
-
- /**
- * Adds the squares of all coefficients.
- *
- * @return the sum of squares
- */
- private BigInteger squareSum()
- {
- BigInteger sum = Constants.BIGINT_ZERO;
- for (int i = 0; i < coeffs.length; i++)
- {
- sum = sum.add(BigInteger.valueOf(coeffs[i] * coeffs[i]));
- }
- return sum;
- }
-
- /**
- * Returns the degree of the polynomial
- *
- * @return the degree
- */
- int degree()
- {
- int degree = coeffs.length - 1;
- while (degree > 0 && coeffs[degree] == 0)
- {
- degree--;
- }
- return degree;
- }
-
- /**
- * Adds another polynomial which can have a different number of coefficients,
- * and takes the coefficient values mod <code>modulus</code>.
- *
- * @param b another polynomial
- */
- public void add(IntegerPolynomial b, int modulus)
- {
- add(b);
- mod(modulus);
- }
-
- /**
- * Adds another polynomial which can have a different number of coefficients.
- *
- * @param b another polynomial
- */
- public void add(IntegerPolynomial 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] += b.coeffs[i];
- }
- }
-
- /**
- * Subtracts another polynomial which can have a different number of coefficients,
- * and takes the coefficient values mod <code>modulus</code>.
- *
- * @param b another polynomial
- */
- public void sub(IntegerPolynomial b, int modulus)
- {
- sub(b);
- mod(modulus);
- }
-
- /**
- * Subtracts another polynomial which can have a different number of coefficients.
- *
- * @param b another polynomial
- */
- public void sub(IntegerPolynomial 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] -= b.coeffs[i];
- }
- }
-
- /**
- * Subtracts a <code>int</code> from each coefficient. Does not return a new polynomial but modifies this polynomial.
- *
- * @param b
- */
- void sub(int b)
- {
- for (int i = 0; i < coeffs.length; i++)
- {
- coeffs[i] -= b;
- }
- }
-
- /**
- * Multiplies each coefficient by a <code>int</code>. Does not return a new polynomial but modifies this polynomial.
- *
- * @param factor
- */
- public void mult(int factor)
- {
- for (int i = 0; i < coeffs.length; i++)
- {
- coeffs[i] *= factor;
- }
- }
-
- /**
- * Multiplies each coefficient by a 2 and applies a modulus. Does not return a new polynomial but modifies this polynomial.
- *
- * @param modulus a modulus
- */
- private void mult2(int modulus)
- {
- for (int i = 0; i < coeffs.length; i++)
- {
- coeffs[i] *= 2;
- coeffs[i] %= modulus;
- }
- }
-
- /**
- * Multiplies each coefficient by a 2 and applies a modulus. Does not return a new polynomial but modifies this polynomial.
- *
- * @param modulus a modulus
- */
- public void mult3(int modulus)
- {
- for (int i = 0; i < coeffs.length; i++)
- {
- coeffs[i] *= 3;
- coeffs[i] %= modulus;
- }
- }
-
- /**
- * Divides each coefficient by <code>k</code> and rounds to the nearest integer. Does not return a new polynomial but modifies this polynomial.
- *
- * @param k the divisor
- */
- public void div(int k)
- {
- int k2 = (k + 1) / 2;
- for (int i = 0; i < coeffs.length; i++)
- {
- coeffs[i] += coeffs[i] > 0 ? k2 : -k2;
- coeffs[i] /= k;
- }
- }
-
- /**
- * Takes each coefficient modulo 3 such that all coefficients are ternary.
- */
- public void mod3()
- {
- for (int i = 0; i < coeffs.length; i++)
- {
- coeffs[i] %= 3;
- if (coeffs[i] > 1)
- {
- coeffs[i] -= 3;
- }
- if (coeffs[i] < -1)
- {
- coeffs[i] += 3;
- }
- }
- }
-
- /**
- * Ensures all coefficients are between 0 and <code>modulus-1</code>
- *
- * @param modulus a modulus
- */
- public void modPositive(int modulus)
- {
- mod(modulus);
- ensurePositive(modulus);
- }
-
- /**
- * Reduces all coefficients to the interval [-modulus/2, modulus/2)
- */
- void modCenter(int modulus)
- {
- mod(modulus);
- for (int j = 0; j < coeffs.length; j++)
- {
- while (coeffs[j] < modulus / 2)
- {
- coeffs[j] += modulus;
- }
- while (coeffs[j] >= modulus / 2)
- {
- coeffs[j] -= modulus;
- }
- }
- }
-
- /**
- * Takes each coefficient modulo <code>modulus</code>.
- */
- public void mod(int modulus)
- {
- for (int i = 0; i < coeffs.length; i++)
- {
- coeffs[i] %= modulus;
- }
- }
-
- /**
- * Adds <code>modulus</code> until all coefficients are above 0.
- *
- * @param modulus a modulus
- */
- public void ensurePositive(int modulus)
- {
- for (int i = 0; i < coeffs.length; i++)
- {
- while (coeffs[i] < 0)
- {
- coeffs[i] += modulus;
- }
- }
- }
-
- /**
- * Computes the centered euclidean norm of the polynomial.
- *
- * @param q a modulus
- * @return the centered norm
- */
- public long centeredNormSq(int q)
- {
- int N = coeffs.length;
- IntegerPolynomial p = (IntegerPolynomial)clone();
- p.shiftGap(q);
-
- long sum = 0;
- long sqSum = 0;
- for (int i = 0; i != p.coeffs.length; i++)
- {
- int c = p.coeffs[i];
- sum += c;
- sqSum += c * c;
- }
-
- long centeredNormSq = sqSum - sum * sum / N;
- return centeredNormSq;
- }
-
- /**
- * Shifts all coefficients so the largest gap is centered around <code>-q/2</code>.
- *
- * @param q a modulus
- */
- void shiftGap(int q)
- {
- modCenter(q);
-
- int[] sorted = Arrays.clone(coeffs);
-
- sort(sorted);
-
- int maxrange = 0;
- int maxrangeStart = 0;
- for (int i = 0; i < sorted.length - 1; i++)
- {
- int range = sorted[i + 1] - sorted[i];
- if (range > maxrange)
- {
- maxrange = range;
- maxrangeStart = sorted[i];
- }
- }
-
- int pmin = sorted[0];
- int pmax = sorted[sorted.length - 1];
-
- int j = q - pmax + pmin;
- int shift;
- if (j > maxrange)
- {
- shift = (pmax + pmin) / 2;
- }
- else
- {
- shift = maxrangeStart + maxrange / 2 + q / 2;
- }
-
- sub(shift);
- }
-
- private void sort(int[] ints)
- {
- boolean swap = true;
-
- while (swap)
- {
- swap = false;
- for (int i = 0; i != ints.length - 1; i++)
- {
- if (ints[i] > ints[i+1])
- {
- int tmp = ints[i];
- ints[i] = ints[i+1];
- ints[i+1] = tmp;
- swap = true;
- }
- }
- }
- }
-
- /**
- * Shifts the values of all coefficients to the interval <code>[-q/2, q/2]</code>.
- *
- * @param q a modulus
- */
- public void center0(int q)
- {
- for (int i = 0; i < coeffs.length; i++)
- {
- while (coeffs[i] < -q / 2)
- {
- coeffs[i] += q;
- }
- while (coeffs[i] > q / 2)
- {
- coeffs[i] -= q;
- }
- }
- }
-
- /**
- * Returns the sum of all coefficients, i.e. evaluates the polynomial at 0.
- *
- * @return the sum of all coefficients
- */
- public int sumCoeffs()
- {
- int sum = 0;
- for (int i = 0; i < coeffs.length; i++)
- {
- sum += coeffs[i];
- }
- return sum;
- }
-
- /**
- * Tests if <code>p(x) = 0</code>.
- *
- * @return true iff all coefficients are zeros
- */
- private boolean equalsZero()
- {
- for (int i = 0; i < coeffs.length; i++)
- {
- if (coeffs[i] != 0)
- {
- return false;
- }
- }
- return true;
- }
-
- /**
- * Tests if <code>p(x) = 1</code>.
- *
- * @return true iff all coefficients are equal to zero, except for the lowest coefficient which must equal 1
- */
- public boolean equalsOne()
- {
- for (int i = 1; i < coeffs.length; i++)
- {
- if (coeffs[i] != 0)
- {
- return false;
- }
- }
- return coeffs[0] == 1;
- }
-
- /**
- * Tests if <code>|p(x)| = 1</code>.
- *
- * @return true iff all coefficients are equal to zero, except for the lowest coefficient which must equal 1 or -1
- */
- private boolean equalsAbsOne()
- {
- for (int i = 1; i < coeffs.length; i++)
- {
- if (coeffs[i] != 0)
- {
- return false;
- }
- }
- return Math.abs(coeffs[0]) == 1;
- }
-
- /**
- * Counts the number of coefficients equal to an integer
- *
- * @param value an integer
- * @return the number of coefficients equal to <code>value</code>
- */
- public int count(int value)
- {
- int count = 0;
- for (int i = 0; i != coeffs.length; i++)
- {
- if (coeffs[i] == value)
- {
- count++;
- }
- }
- return count;
- }
-
- /**
- * Multiplication by <code>X</code> in <code>Z[X]/Z[X^n-1]</code>.
- */
- public void rotate1()
- {
- int clast = coeffs[coeffs.length - 1];
- for (int i = coeffs.length - 1; i > 0; i--)
- {
- coeffs[i] = coeffs[i - 1];
- }
- coeffs[0] = clast;
- }
-
- public void clear()
- {
- for (int i = 0; i < coeffs.length; i++)
- {
- coeffs[i] = 0;
- }
- }
-
- public IntegerPolynomial toIntegerPolynomial()
- {
- return (IntegerPolynomial)clone();
- }
-
- public Object clone()
- {
- return new IntegerPolynomial(coeffs.clone());
- }
-
- public boolean equals(Object obj)
- {
- if (obj instanceof IntegerPolynomial)
- {
- return Arrays.areEqual(coeffs, ((IntegerPolynomial)obj).coeffs);
- }
- else
- {
- return false;
- }
- }
-
- /**
- * Calls {@link IntegerPolynomial#resultant(int)
- */
- private class ModResultantTask
- implements Callable<ModularResultant>
- {
- private int modulus;
-
- private ModResultantTask(int modulus)
- {
- this.modulus = modulus;
- }
-
- public ModularResultant call()
- {
- return resultant(modulus);
- }
- }
-
- /**
- * Calls {@link ModularResultant#combineRho(ModularResultant, ModularResultant)
- */
- private class CombineTask
- implements Callable<ModularResultant>
- {
- private ModularResultant modRes1;
- private ModularResultant modRes2;
-
- private CombineTask(ModularResultant modRes1, ModularResultant modRes2)
- {
- this.modRes1 = modRes1;
- this.modRes2 = modRes2;
- }
-
- public ModularResultant call()
- {
- return ModularResultant.combineRho(modRes1, modRes2);
- }
- }
-}
generated by cgit v1.2.3 (git 2.25.1) at 2024-05-18 16:33:59 +0000