| package org.bouncycastle.pqc.math.linearalgebra; |
| |
| |
| import java.math.BigInteger; |
| import java.util.Random; |
| |
| import org.bouncycastle.util.Arrays; |
| |
| |
| /** |
| * This class stores very long strings of bits and does some basic arithmetics. |
| * It is used by <tt>GF2nField</tt>, <tt>GF2nPolynomialField</tt> and |
| * <tt>GFnPolynomialElement</tt>. |
| * |
| * @see GF2nPolynomialElement |
| * @see GF2nField |
| */ |
| public class GF2Polynomial |
| { |
| |
| // number of bits stored in this GF2Polynomial |
| private int len; |
| |
| // number of int used in value |
| private int blocks; |
| |
| // storage |
| private int[] value; |
| |
| // Random source |
| private static Random rand = new Random(); |
| |
| // Lookup-Table for vectorMult: parity[a]= #1(a) mod 2 == 1 |
| private static final boolean[] parity = {false, true, true, false, true, |
| false, false, true, true, false, false, true, false, true, true, |
| false, true, false, false, true, false, true, true, false, false, |
| true, true, false, true, false, false, true, true, false, false, |
| true, false, true, true, false, false, true, true, false, true, |
| false, false, true, false, true, true, false, true, false, false, |
| true, true, false, false, true, false, true, true, false, true, |
| false, false, true, false, true, true, false, false, true, true, |
| false, true, false, false, true, false, true, true, false, true, |
| false, false, true, true, false, false, true, false, true, true, |
| false, false, true, true, false, true, false, false, true, true, |
| false, false, true, false, true, true, false, true, false, false, |
| true, false, true, true, false, false, true, true, false, true, |
| false, false, true, true, false, false, true, false, true, true, |
| false, false, true, true, false, true, false, false, true, false, |
| true, true, false, true, false, false, true, true, false, false, |
| true, false, true, true, false, false, true, true, false, true, |
| false, false, true, true, false, false, true, false, true, true, |
| false, true, false, false, true, false, true, true, false, false, |
| true, true, false, true, false, false, true, false, true, true, |
| false, true, false, false, true, true, false, false, true, false, |
| true, true, false, true, false, false, true, false, true, true, |
| false, false, true, true, false, true, false, false, true, true, |
| false, false, true, false, true, true, false, false, true, true, |
| false, true, false, false, true, false, true, true, false, true, |
| false, false, true, true, false, false, true, false, true, true, |
| false}; |
| |
| // Lookup-Table for Squaring: squaringTable[a]=a^2 |
| private static final short[] squaringTable = {0x0000, 0x0001, 0x0004, |
| 0x0005, 0x0010, 0x0011, 0x0014, 0x0015, 0x0040, 0x0041, 0x0044, |
| 0x0045, 0x0050, 0x0051, 0x0054, 0x0055, 0x0100, 0x0101, 0x0104, |
| 0x0105, 0x0110, 0x0111, 0x0114, 0x0115, 0x0140, 0x0141, 0x0144, |
| 0x0145, 0x0150, 0x0151, 0x0154, 0x0155, 0x0400, 0x0401, 0x0404, |
| 0x0405, 0x0410, 0x0411, 0x0414, 0x0415, 0x0440, 0x0441, 0x0444, |
| 0x0445, 0x0450, 0x0451, 0x0454, 0x0455, 0x0500, 0x0501, 0x0504, |
| 0x0505, 0x0510, 0x0511, 0x0514, 0x0515, 0x0540, 0x0541, 0x0544, |
| 0x0545, 0x0550, 0x0551, 0x0554, 0x0555, 0x1000, 0x1001, 0x1004, |
| 0x1005, 0x1010, 0x1011, 0x1014, 0x1015, 0x1040, 0x1041, 0x1044, |
| 0x1045, 0x1050, 0x1051, 0x1054, 0x1055, 0x1100, 0x1101, 0x1104, |
| 0x1105, 0x1110, 0x1111, 0x1114, 0x1115, 0x1140, 0x1141, 0x1144, |
| 0x1145, 0x1150, 0x1151, 0x1154, 0x1155, 0x1400, 0x1401, 0x1404, |
| 0x1405, 0x1410, 0x1411, 0x1414, 0x1415, 0x1440, 0x1441, 0x1444, |
| 0x1445, 0x1450, 0x1451, 0x1454, 0x1455, 0x1500, 0x1501, 0x1504, |
| 0x1505, 0x1510, 0x1511, 0x1514, 0x1515, 0x1540, 0x1541, 0x1544, |
| 0x1545, 0x1550, 0x1551, 0x1554, 0x1555, 0x4000, 0x4001, 0x4004, |
| 0x4005, 0x4010, 0x4011, 0x4014, 0x4015, 0x4040, 0x4041, 0x4044, |
| 0x4045, 0x4050, 0x4051, 0x4054, 0x4055, 0x4100, 0x4101, 0x4104, |
| 0x4105, 0x4110, 0x4111, 0x4114, 0x4115, 0x4140, 0x4141, 0x4144, |
| 0x4145, 0x4150, 0x4151, 0x4154, 0x4155, 0x4400, 0x4401, 0x4404, |
| 0x4405, 0x4410, 0x4411, 0x4414, 0x4415, 0x4440, 0x4441, 0x4444, |
| 0x4445, 0x4450, 0x4451, 0x4454, 0x4455, 0x4500, 0x4501, 0x4504, |
| 0x4505, 0x4510, 0x4511, 0x4514, 0x4515, 0x4540, 0x4541, 0x4544, |
| 0x4545, 0x4550, 0x4551, 0x4554, 0x4555, 0x5000, 0x5001, 0x5004, |
| 0x5005, 0x5010, 0x5011, 0x5014, 0x5015, 0x5040, 0x5041, 0x5044, |
| 0x5045, 0x5050, 0x5051, 0x5054, 0x5055, 0x5100, 0x5101, 0x5104, |
| 0x5105, 0x5110, 0x5111, 0x5114, 0x5115, 0x5140, 0x5141, 0x5144, |
| 0x5145, 0x5150, 0x5151, 0x5154, 0x5155, 0x5400, 0x5401, 0x5404, |
| 0x5405, 0x5410, 0x5411, 0x5414, 0x5415, 0x5440, 0x5441, 0x5444, |
| 0x5445, 0x5450, 0x5451, 0x5454, 0x5455, 0x5500, 0x5501, 0x5504, |
| 0x5505, 0x5510, 0x5511, 0x5514, 0x5515, 0x5540, 0x5541, 0x5544, |
| 0x5545, 0x5550, 0x5551, 0x5554, 0x5555}; |
| |
| // pre-computed Bitmask for fast masking, bitMask[a]=0x1 << a |
| private static final int[] bitMask = {0x00000001, 0x00000002, 0x00000004, |
| 0x00000008, 0x00000010, 0x00000020, 0x00000040, 0x00000080, |
| 0x00000100, 0x00000200, 0x00000400, 0x00000800, 0x00001000, |
| 0x00002000, 0x00004000, 0x00008000, 0x00010000, 0x00020000, |
| 0x00040000, 0x00080000, 0x00100000, 0x00200000, 0x00400000, |
| 0x00800000, 0x01000000, 0x02000000, 0x04000000, 0x08000000, |
| 0x10000000, 0x20000000, 0x40000000, 0x80000000, 0x00000000}; |
| |
| // pre-computed Bitmask for fast masking, rightMask[a]=0xffffffff >>> (32-a) |
| private static final int[] reverseRightMask = {0x00000000, 0x00000001, |
| 0x00000003, 0x00000007, 0x0000000f, 0x0000001f, 0x0000003f, |
| 0x0000007f, 0x000000ff, 0x000001ff, 0x000003ff, 0x000007ff, |
| 0x00000fff, 0x00001fff, 0x00003fff, 0x00007fff, 0x0000ffff, |
| 0x0001ffff, 0x0003ffff, 0x0007ffff, 0x000fffff, 0x001fffff, |
| 0x003fffff, 0x007fffff, 0x00ffffff, 0x01ffffff, 0x03ffffff, |
| 0x07ffffff, 0x0fffffff, 0x1fffffff, 0x3fffffff, 0x7fffffff, |
| 0xffffffff}; |
| |
| /** |
| * Creates a new GF2Polynomial of the given <i>length</i> and value zero. |
| * |
| * @param length the desired number of bits to store |
| */ |
| public GF2Polynomial(int length) |
| { |
| int l = length; |
| if (l < 1) |
| { |
| l = 1; |
| } |
| blocks = ((l - 1) >> 5) + 1; |
| value = new int[blocks]; |
| len = l; |
| } |
| |
| /** |
| * Creates a new GF2Polynomial of the given <i>length</i> and random value. |
| * |
| * @param length the desired number of bits to store |
| * @param rand SecureRandom to use for randomization |
| */ |
| public GF2Polynomial(int length, Random rand) |
| { |
| int l = length; |
| if (l < 1) |
| { |
| l = 1; |
| } |
| blocks = ((l - 1) >> 5) + 1; |
| value = new int[blocks]; |
| len = l; |
| randomize(rand); |
| } |
| |
| /** |
| * Creates a new GF2Polynomial of the given <i>length</i> and value |
| * selected by <i>value</i>: |
| * <UL> |
| * <LI>ZERO</LI> |
| * <LI>ONE</LI> |
| * <LI>RANDOM</LI> |
| * <LI>X</LI> |
| * <LI>ALL</LI> |
| * </UL> |
| * |
| * @param length the desired number of bits to store |
| * @param value the value described by a String |
| */ |
| public GF2Polynomial(int length, String value) |
| { |
| int l = length; |
| if (l < 1) |
| { |
| l = 1; |
| } |
| blocks = ((l - 1) >> 5) + 1; |
| this.value = new int[blocks]; |
| len = l; |
| if (value.equalsIgnoreCase("ZERO")) |
| { |
| assignZero(); |
| } |
| else if (value.equalsIgnoreCase("ONE")) |
| { |
| assignOne(); |
| } |
| else if (value.equalsIgnoreCase("RANDOM")) |
| { |
| randomize(); |
| } |
| else if (value.equalsIgnoreCase("X")) |
| { |
| assignX(); |
| } |
| else if (value.equalsIgnoreCase("ALL")) |
| { |
| assignAll(); |
| } |
| else |
| { |
| throw new IllegalArgumentException( |
| "Error: GF2Polynomial was called using " + value |
| + " as value!"); |
| } |
| |
| } |
| |
| /** |
| * Creates a new GF2Polynomial of the given <i>length</i> using the given |
| * int[]. LSB is contained in bs[0]. |
| * |
| * @param length the desired number of bits to store |
| * @param bs contains the desired value, LSB in bs[0] |
| */ |
| public GF2Polynomial(int length, int[] bs) |
| { |
| int leng = length; |
| if (leng < 1) |
| { |
| leng = 1; |
| } |
| blocks = ((leng - 1) >> 5) + 1; |
| value = new int[blocks]; |
| len = leng; |
| int l = Math.min(blocks, bs.length); |
| System.arraycopy(bs, 0, value, 0, l); |
| zeroUnusedBits(); |
| } |
| |
| /** |
| * Creates a new GF2Polynomial by converting the given byte[] <i>os</i> |
| * according to 1363 and using the given <i>length</i>. |
| * |
| * @param length the intended length of this polynomial |
| * @param os the octet string to assign to this polynomial |
| * @see "P1363 5.5.2 p22f, OS2BSP" |
| */ |
| public GF2Polynomial(int length, byte[] os) |
| { |
| int l = length; |
| if (l < 1) |
| { |
| l = 1; |
| } |
| blocks = ((l - 1) >> 5) + 1; |
| value = new int[blocks]; |
| len = l; |
| int i, m; |
| int k = Math.min(((os.length - 1) >> 2) + 1, blocks); |
| for (i = 0; i < k - 1; i++) |
| { |
| m = os.length - (i << 2) - 1; |
| value[i] = (os[m]) & 0x000000ff; |
| value[i] |= (os[m - 1] << 8) & 0x0000ff00; |
| value[i] |= (os[m - 2] << 16) & 0x00ff0000; |
| value[i] |= (os[m - 3] << 24) & 0xff000000; |
| } |
| i = k - 1; |
| m = os.length - (i << 2) - 1; |
| value[i] = os[m] & 0x000000ff; |
| if (m > 0) |
| { |
| value[i] |= (os[m - 1] << 8) & 0x0000ff00; |
| } |
| if (m > 1) |
| { |
| value[i] |= (os[m - 2] << 16) & 0x00ff0000; |
| } |
| if (m > 2) |
| { |
| value[i] |= (os[m - 3] << 24) & 0xff000000; |
| } |
| zeroUnusedBits(); |
| reduceN(); |
| } |
| |
| /** |
| * Creates a new GF2Polynomial by converting the given FlexiBigInt <i>bi</i> |
| * according to 1363 and using the given <i>length</i>. |
| * |
| * @param length the intended length of this polynomial |
| * @param bi the FlexiBigInt to assign to this polynomial |
| * @see "P1363 5.5.1 p22, I2BSP" |
| */ |
| public GF2Polynomial(int length, BigInteger bi) |
| { |
| int l = length; |
| if (l < 1) |
| { |
| l = 1; |
| } |
| blocks = ((l - 1) >> 5) + 1; |
| value = new int[blocks]; |
| len = l; |
| int i; |
| byte[] val = bi.toByteArray(); |
| if (val[0] == 0) |
| { |
| byte[] dummy = new byte[val.length - 1]; |
| System.arraycopy(val, 1, dummy, 0, dummy.length); |
| val = dummy; |
| } |
| int ov = val.length & 0x03; |
| int k = ((val.length - 1) >> 2) + 1; |
| for (i = 0; i < ov; i++) |
| { |
| value[k - 1] |= (val[i] & 0x000000ff) << ((ov - 1 - i) << 3); |
| } |
| int m = 0; |
| for (i = 0; i <= (val.length - 4) >> 2; i++) |
| { |
| m = val.length - 1 - (i << 2); |
| value[i] = (val[m]) & 0x000000ff; |
| value[i] |= ((val[m - 1]) << 8) & 0x0000ff00; |
| value[i] |= ((val[m - 2]) << 16) & 0x00ff0000; |
| value[i] |= ((val[m - 3]) << 24) & 0xff000000; |
| } |
| if ((len & 0x1f) != 0) |
| { |
| value[blocks - 1] &= reverseRightMask[len & 0x1f]; |
| } |
| reduceN(); |
| } |
| |
| /** |
| * Creates a new GF2Polynomial by cloneing the given GF2Polynomial <i>b</i>. |
| * |
| * @param b the GF2Polynomial to clone |
| */ |
| public GF2Polynomial(GF2Polynomial b) |
| { |
| len = b.len; |
| blocks = b.blocks; |
| value = IntUtils.clone(b.value); |
| } |
| |
| /** |
| * @return a copy of this GF2Polynomial |
| */ |
| public Object clone() |
| { |
| return new GF2Polynomial(this); |
| } |
| |
| /** |
| * Returns the length of this GF2Polynomial. The length can be greater than |
| * the degree. To get the degree call reduceN() before calling getLength(). |
| * |
| * @return the length of this GF2Polynomial |
| */ |
| public int getLength() |
| { |
| return len; |
| } |
| |
| /** |
| * Returns the value of this GF2Polynomial in an int[]. |
| * |
| * @return the value of this GF2Polynomial in a new int[], LSB in int[0] |
| */ |
| public int[] toIntegerArray() |
| { |
| int[] result; |
| result = new int[blocks]; |
| System.arraycopy(value, 0, result, 0, blocks); |
| return result; |
| } |
| |
| /** |
| * Returns a string representing this GF2Polynomials value using hexadecimal |
| * or binary radix in MSB-first order. |
| * |
| * @param radix the radix to use (2 or 16, otherwise 2 is used) |
| * @return a String representing this GF2Polynomials value. |
| */ |
| public String toString(int radix) |
| { |
| final char[] HEX_CHARS = {'0', '1', '2', '3', '4', '5', '6', '7', '8', |
| '9', 'a', 'b', 'c', 'd', 'e', 'f'}; |
| final String[] BIN_CHARS = {"0000", "0001", "0010", "0011", "0100", |
| "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", |
| "1101", "1110", "1111"}; |
| String res; |
| int i; |
| res = new String(); |
| if (radix == 16) |
| { |
| for (i = blocks - 1; i >= 0; i--) |
| { |
| res += HEX_CHARS[(value[i] >>> 28) & 0x0f]; |
| res += HEX_CHARS[(value[i] >>> 24) & 0x0f]; |
| res += HEX_CHARS[(value[i] >>> 20) & 0x0f]; |
| res += HEX_CHARS[(value[i] >>> 16) & 0x0f]; |
| res += HEX_CHARS[(value[i] >>> 12) & 0x0f]; |
| res += HEX_CHARS[(value[i] >>> 8) & 0x0f]; |
| res += HEX_CHARS[(value[i] >>> 4) & 0x0f]; |
| res += HEX_CHARS[(value[i]) & 0x0f]; |
| res += " "; |
| } |
| } |
| else |
| { |
| for (i = blocks - 1; i >= 0; i--) |
| { |
| res += BIN_CHARS[(value[i] >>> 28) & 0x0f]; |
| res += BIN_CHARS[(value[i] >>> 24) & 0x0f]; |
| res += BIN_CHARS[(value[i] >>> 20) & 0x0f]; |
| res += BIN_CHARS[(value[i] >>> 16) & 0x0f]; |
| res += BIN_CHARS[(value[i] >>> 12) & 0x0f]; |
| res += BIN_CHARS[(value[i] >>> 8) & 0x0f]; |
| res += BIN_CHARS[(value[i] >>> 4) & 0x0f]; |
| res += BIN_CHARS[(value[i]) & 0x0f]; |
| res += " "; |
| } |
| } |
| return res; |
| } |
| |
| /** |
| * Converts this polynomial to a byte[] (octet string) according to 1363. |
| * |
| * @return a byte[] representing the value of this polynomial |
| * @see "P1363 5.5.2 p22f, BS2OSP" |
| */ |
| public byte[] toByteArray() |
| { |
| int k = ((len - 1) >> 3) + 1; |
| int ov = k & 0x03; |
| int m; |
| byte[] res = new byte[k]; |
| int i; |
| for (i = 0; i < (k >> 2); i++) |
| { |
| m = k - (i << 2) - 1; |
| res[m] = (byte)((value[i] & 0x000000ff)); |
| res[m - 1] = (byte)((value[i] & 0x0000ff00) >>> 8); |
| res[m - 2] = (byte)((value[i] & 0x00ff0000) >>> 16); |
| res[m - 3] = (byte)((value[i] & 0xff000000) >>> 24); |
| } |
| for (i = 0; i < ov; i++) |
| { |
| m = (ov - i - 1) << 3; |
| res[i] = (byte)((value[blocks - 1] & (0x000000ff << m)) >>> m); |
| } |
| return res; |
| } |
| |
| /** |
| * Converts this polynomial to an integer according to 1363. |
| * |
| * @return a FlexiBigInt representing the value of this polynomial |
| * @see "P1363 5.5.1 p22, BS2IP" |
| */ |
| public BigInteger toFlexiBigInt() |
| { |
| if (len == 0 || isZero()) |
| { |
| return new BigInteger(0, new byte[0]); |
| } |
| return new BigInteger(1, toByteArray()); |
| } |
| |
| /** |
| * Sets the LSB to 1 and all other to 0, assigning 'one' to this |
| * GF2Polynomial. |
| */ |
| public void assignOne() |
| { |
| int i; |
| for (i = 1; i < blocks; i++) |
| { |
| value[i] = 0x00; |
| } |
| value[0] = 0x01; |
| } |
| |
| /** |
| * Sets Bit 1 to 1 and all other to 0, assigning 'x' to this GF2Polynomial. |
| */ |
| public void assignX() |
| { |
| int i; |
| for (i = 1; i < blocks; i++) |
| { |
| value[i] = 0x00; |
| } |
| value[0] = 0x02; |
| } |
| |
| /** |
| * Sets all Bits to 1. |
| */ |
| public void assignAll() |
| { |
| int i; |
| for (i = 0; i < blocks; i++) |
| { |
| value[i] = 0xffffffff; |
| } |
| zeroUnusedBits(); |
| } |
| |
| /** |
| * Resets all bits to zero. |
| */ |
| public void assignZero() |
| { |
| int i; |
| for (i = 0; i < blocks; i++) |
| { |
| value[i] = 0x00; |
| } |
| } |
| |
| /** |
| * Fills all len bits of this GF2Polynomial with random values. |
| */ |
| public void randomize() |
| { |
| int i; |
| for (i = 0; i < blocks; i++) |
| { |
| value[i] = rand.nextInt(); |
| } |
| zeroUnusedBits(); |
| } |
| |
| /** |
| * Fills all len bits of this GF2Polynomial with random values using the |
| * specified source of randomness. |
| * |
| * @param rand the source of randomness |
| */ |
| public void randomize(Random rand) |
| { |
| int i; |
| for (i = 0; i < blocks; i++) |
| { |
| value[i] = rand.nextInt(); |
| } |
| zeroUnusedBits(); |
| } |
| |
| /** |
| * Returns true if two GF2Polynomials have the same size and value and thus |
| * are equal. |
| * |
| * @param other the other GF2Polynomial |
| * @return true if this GF2Polynomial equals <i>b</i> (<i>this</i> == |
| * <i>b</i>) |
| */ |
| public boolean equals(Object other) |
| { |
| if (other == null || !(other instanceof GF2Polynomial)) |
| { |
| return false; |
| } |
| |
| GF2Polynomial otherPol = (GF2Polynomial)other; |
| |
| if (len != otherPol.len) |
| { |
| return false; |
| } |
| for (int i = 0; i < blocks; i++) |
| { |
| if (value[i] != otherPol.value[i]) |
| { |
| return false; |
| } |
| } |
| return true; |
| } |
| |
| /** |
| * @return the hash code of this polynomial |
| */ |
| public int hashCode() |
| { |
| return len + Arrays.hashCode(value); |
| } |
| |
| /** |
| * Tests if all bits equal zero. |
| * |
| * @return true if this GF2Polynomial equals 'zero' (<i>this</i> == 0) |
| */ |
| public boolean isZero() |
| { |
| int i; |
| if (len == 0) |
| { |
| return true; |
| } |
| for (i = 0; i < blocks; i++) |
| { |
| if (value[i] != 0) |
| { |
| return false; |
| } |
| } |
| return true; |
| } |
| |
| /** |
| * Tests if all bits are reset to 0 and LSB is set to 1. |
| * |
| * @return true if this GF2Polynomial equals 'one' (<i>this</i> == 1) |
| */ |
| public boolean isOne() |
| { |
| int i; |
| for (i = 1; i < blocks; i++) |
| { |
| if (value[i] != 0) |
| { |
| return false; |
| } |
| } |
| if (value[0] != 0x01) |
| { |
| return false; |
| } |
| return true; |
| } |
| |
| /** |
| * Adds <i>b</i> to this GF2Polynomial and assigns the result to this |
| * GF2Polynomial. <i>b</i> can be of different size. |
| * |
| * @param b GF2Polynomial to add to this GF2Polynomial |
| */ |
| public void addToThis(GF2Polynomial b) |
| { |
| expandN(b.len); |
| xorThisBy(b); |
| } |
| |
| /** |
| * Adds two GF2Polynomials, <i>this</i> and <i>b</i>, and returns the |
| * result. <i>this</i> and <i>b</i> can be of different size. |
| * |
| * @param b a GF2Polynomial |
| * @return a new GF2Polynomial (<i>this</i> + <i>b</i>) |
| */ |
| public GF2Polynomial add(GF2Polynomial b) |
| { |
| return xor(b); |
| } |
| |
| /** |
| * Subtracts <i>b</i> from this GF2Polynomial and assigns the result to |
| * this GF2Polynomial. <i>b</i> can be of different size. |
| * |
| * @param b a GF2Polynomial |
| */ |
| public void subtractFromThis(GF2Polynomial b) |
| { |
| expandN(b.len); |
| xorThisBy(b); |
| } |
| |
| /** |
| * Subtracts two GF2Polynomials, <i>this</i> and <i>b</i>, and returns the |
| * result in a new GF2Polynomial. <i>this</i> and <i>b</i> can be of |
| * different size. |
| * |
| * @param b a GF2Polynomial |
| * @return a new GF2Polynomial (<i>this</i> - <i>b</i>) |
| */ |
| public GF2Polynomial subtract(GF2Polynomial b) |
| { |
| return xor(b); |
| } |
| |
| /** |
| * Toggles the LSB of this GF2Polynomial, increasing its value by 'one'. |
| */ |
| public void increaseThis() |
| { |
| xorBit(0); |
| } |
| |
| /** |
| * Toggles the LSB of this GF2Polynomial, increasing the value by 'one' and |
| * returns the result in a new GF2Polynomial. |
| * |
| * @return <tt>this + 1</tt> |
| */ |
| public GF2Polynomial increase() |
| { |
| GF2Polynomial result = new GF2Polynomial(this); |
| result.increaseThis(); |
| return result; |
| } |
| |
| /** |
| * Multiplies this GF2Polynomial with <i>b</i> and returns the result in a |
| * new GF2Polynomial. This method does not reduce the result in GF(2^N). |
| * This method uses classic multiplication (schoolbook). |
| * |
| * @param b a GF2Polynomial |
| * @return a new GF2Polynomial (<i>this</i> * <i>b</i>) |
| */ |
| public GF2Polynomial multiplyClassic(GF2Polynomial b) |
| { |
| GF2Polynomial result = new GF2Polynomial(Math.max(len, b.len) << 1); |
| GF2Polynomial[] m = new GF2Polynomial[32]; |
| int i, j; |
| m[0] = new GF2Polynomial(this); |
| for (i = 1; i <= 31; i++) |
| { |
| m[i] = m[i - 1].shiftLeft(); |
| } |
| for (i = 0; i < b.blocks; i++) |
| { |
| for (j = 0; j <= 31; j++) |
| { |
| if ((b.value[i] & bitMask[j]) != 0) |
| { |
| result.xorThisBy(m[j]); |
| } |
| } |
| for (j = 0; j <= 31; j++) |
| { |
| m[j].shiftBlocksLeft(); |
| } |
| } |
| return result; |
| } |
| |
| /** |
| * Multiplies this GF2Polynomial with <i>b</i> and returns the result in a |
| * new GF2Polynomial. This method does not reduce the result in GF(2^N). |
| * This method uses Karatzuba multiplication. |
| * |
| * @param b a GF2Polynomial |
| * @return a new GF2Polynomial (<i>this</i> * <i>b</i>) |
| */ |
| public GF2Polynomial multiply(GF2Polynomial b) |
| { |
| int n = Math.max(len, b.len); |
| expandN(n); |
| b.expandN(n); |
| return karaMult(b); |
| } |
| |
| /** |
| * Does the recursion for Karatzuba multiplication. |
| */ |
| private GF2Polynomial karaMult(GF2Polynomial b) |
| { |
| GF2Polynomial result = new GF2Polynomial(len << 1); |
| if (len <= 32) |
| { |
| result.value = mult32(value[0], b.value[0]); |
| return result; |
| } |
| if (len <= 64) |
| { |
| result.value = mult64(value, b.value); |
| return result; |
| } |
| if (len <= 128) |
| { |
| result.value = mult128(value, b.value); |
| return result; |
| } |
| if (len <= 256) |
| { |
| result.value = mult256(value, b.value); |
| return result; |
| } |
| if (len <= 512) |
| { |
| result.value = mult512(value, b.value); |
| return result; |
| } |
| |
| int n = IntegerFunctions.floorLog(len - 1); |
| n = bitMask[n]; |
| |
| GF2Polynomial a0 = lower(((n - 1) >> 5) + 1); |
| GF2Polynomial a1 = upper(((n - 1) >> 5) + 1); |
| GF2Polynomial b0 = b.lower(((n - 1) >> 5) + 1); |
| GF2Polynomial b1 = b.upper(((n - 1) >> 5) + 1); |
| |
| GF2Polynomial c = a1.karaMult(b1); // c = a1*b1 |
| GF2Polynomial e = a0.karaMult(b0); // e = a0*b0 |
| a0.addToThis(a1); // a0 = a0 + a1 |
| b0.addToThis(b1); // b0 = b0 + b1 |
| GF2Polynomial d = a0.karaMult(b0); // d = (a0+a1)*(b0+b1) |
| |
| result.shiftLeftAddThis(c, n << 1); |
| result.shiftLeftAddThis(c, n); |
| result.shiftLeftAddThis(d, n); |
| result.shiftLeftAddThis(e, n); |
| result.addToThis(e); |
| return result; |
| } |
| |
| /** |
| * 16-Integer Version of Karatzuba multiplication. |
| */ |
| private static int[] mult512(int[] a, int[] b) |
| { |
| int[] result = new int[32]; |
| int[] a0 = new int[8]; |
| System.arraycopy(a, 0, a0, 0, Math.min(8, a.length)); |
| int[] a1 = new int[8]; |
| if (a.length > 8) |
| { |
| System.arraycopy(a, 8, a1, 0, Math.min(8, a.length - 8)); |
| } |
| int[] b0 = new int[8]; |
| System.arraycopy(b, 0, b0, 0, Math.min(8, b.length)); |
| int[] b1 = new int[8]; |
| if (b.length > 8) |
| { |
| System.arraycopy(b, 8, b1, 0, Math.min(8, b.length - 8)); |
| } |
| int[] c = mult256(a1, b1); |
| result[31] ^= c[15]; |
| result[30] ^= c[14]; |
| result[29] ^= c[13]; |
| result[28] ^= c[12]; |
| result[27] ^= c[11]; |
| result[26] ^= c[10]; |
| result[25] ^= c[9]; |
| result[24] ^= c[8]; |
| result[23] ^= c[7] ^ c[15]; |
| result[22] ^= c[6] ^ c[14]; |
| result[21] ^= c[5] ^ c[13]; |
| result[20] ^= c[4] ^ c[12]; |
| result[19] ^= c[3] ^ c[11]; |
| result[18] ^= c[2] ^ c[10]; |
| result[17] ^= c[1] ^ c[9]; |
| result[16] ^= c[0] ^ c[8]; |
| result[15] ^= c[7]; |
| result[14] ^= c[6]; |
| result[13] ^= c[5]; |
| result[12] ^= c[4]; |
| result[11] ^= c[3]; |
| result[10] ^= c[2]; |
| result[9] ^= c[1]; |
| result[8] ^= c[0]; |
| a1[0] ^= a0[0]; |
| a1[1] ^= a0[1]; |
| a1[2] ^= a0[2]; |
| a1[3] ^= a0[3]; |
| a1[4] ^= a0[4]; |
| a1[5] ^= a0[5]; |
| a1[6] ^= a0[6]; |
| a1[7] ^= a0[7]; |
| b1[0] ^= b0[0]; |
| b1[1] ^= b0[1]; |
| b1[2] ^= b0[2]; |
| b1[3] ^= b0[3]; |
| b1[4] ^= b0[4]; |
| b1[5] ^= b0[5]; |
| b1[6] ^= b0[6]; |
| b1[7] ^= b0[7]; |
| int[] d = mult256(a1, b1); |
| result[23] ^= d[15]; |
| result[22] ^= d[14]; |
| result[21] ^= d[13]; |
| result[20] ^= d[12]; |
| result[19] ^= d[11]; |
| result[18] ^= d[10]; |
| result[17] ^= d[9]; |
| result[16] ^= d[8]; |
| result[15] ^= d[7]; |
| result[14] ^= d[6]; |
| result[13] ^= d[5]; |
| result[12] ^= d[4]; |
| result[11] ^= d[3]; |
| result[10] ^= d[2]; |
| result[9] ^= d[1]; |
| result[8] ^= d[0]; |
| int[] e = mult256(a0, b0); |
| result[23] ^= e[15]; |
| result[22] ^= e[14]; |
| result[21] ^= e[13]; |
| result[20] ^= e[12]; |
| result[19] ^= e[11]; |
| result[18] ^= e[10]; |
| result[17] ^= e[9]; |
| result[16] ^= e[8]; |
| result[15] ^= e[7] ^ e[15]; |
| result[14] ^= e[6] ^ e[14]; |
| result[13] ^= e[5] ^ e[13]; |
| result[12] ^= e[4] ^ e[12]; |
| result[11] ^= e[3] ^ e[11]; |
| result[10] ^= e[2] ^ e[10]; |
| result[9] ^= e[1] ^ e[9]; |
| result[8] ^= e[0] ^ e[8]; |
| result[7] ^= e[7]; |
| result[6] ^= e[6]; |
| result[5] ^= e[5]; |
| result[4] ^= e[4]; |
| result[3] ^= e[3]; |
| result[2] ^= e[2]; |
| result[1] ^= e[1]; |
| result[0] ^= e[0]; |
| return result; |
| } |
| |
| /** |
| * 8-Integer Version of Karatzuba multiplication. |
| */ |
| private static int[] mult256(int[] a, int[] b) |
| { |
| int[] result = new int[16]; |
| int[] a0 = new int[4]; |
| System.arraycopy(a, 0, a0, 0, Math.min(4, a.length)); |
| int[] a1 = new int[4]; |
| if (a.length > 4) |
| { |
| System.arraycopy(a, 4, a1, 0, Math.min(4, a.length - 4)); |
| } |
| int[] b0 = new int[4]; |
| System.arraycopy(b, 0, b0, 0, Math.min(4, b.length)); |
| int[] b1 = new int[4]; |
| if (b.length > 4) |
| { |
| System.arraycopy(b, 4, b1, 0, Math.min(4, b.length - 4)); |
| } |
| if (a1[3] == 0 && a1[2] == 0 && b1[3] == 0 && b1[2] == 0) |
| { |
| if (a1[1] == 0 && b1[1] == 0) |
| { |
| if (a1[0] != 0 || b1[0] != 0) |
| { // [3]=[2]=[1]=0, [0]!=0 |
| int[] c = mult32(a1[0], b1[0]); |
| result[9] ^= c[1]; |
| result[8] ^= c[0]; |
| result[5] ^= c[1]; |
| result[4] ^= c[0]; |
| } |
| } |
| else |
| { // [3]=[2]=0 [1]!=0, [0]!=0 |
| int[] c = mult64(a1, b1); |
| result[11] ^= c[3]; |
| result[10] ^= c[2]; |
| result[9] ^= c[1]; |
| result[8] ^= c[0]; |
| result[7] ^= c[3]; |
| result[6] ^= c[2]; |
| result[5] ^= c[1]; |
| result[4] ^= c[0]; |
| } |
| } |
| else |
| { // [3]!=0 [2]!=0 [1]!=0, [0]!=0 |
| int[] c = mult128(a1, b1); |
| result[15] ^= c[7]; |
| result[14] ^= c[6]; |
| result[13] ^= c[5]; |
| result[12] ^= c[4]; |
| result[11] ^= c[3] ^ c[7]; |
| result[10] ^= c[2] ^ c[6]; |
| result[9] ^= c[1] ^ c[5]; |
| result[8] ^= c[0] ^ c[4]; |
| result[7] ^= c[3]; |
| result[6] ^= c[2]; |
| result[5] ^= c[1]; |
| result[4] ^= c[0]; |
| } |
| a1[0] ^= a0[0]; |
| a1[1] ^= a0[1]; |
| a1[2] ^= a0[2]; |
| a1[3] ^= a0[3]; |
| b1[0] ^= b0[0]; |
| b1[1] ^= b0[1]; |
| b1[2] ^= b0[2]; |
| b1[3] ^= b0[3]; |
| int[] d = mult128(a1, b1); |
| result[11] ^= d[7]; |
| result[10] ^= d[6]; |
| result[9] ^= d[5]; |
| result[8] ^= d[4]; |
| result[7] ^= d[3]; |
| result[6] ^= d[2]; |
| result[5] ^= d[1]; |
| result[4] ^= d[0]; |
| int[] e = mult128(a0, b0); |
| result[11] ^= e[7]; |
| result[10] ^= e[6]; |
| result[9] ^= e[5]; |
| result[8] ^= e[4]; |
| result[7] ^= e[3] ^ e[7]; |
| result[6] ^= e[2] ^ e[6]; |
| result[5] ^= e[1] ^ e[5]; |
| result[4] ^= e[0] ^ e[4]; |
| result[3] ^= e[3]; |
| result[2] ^= e[2]; |
| result[1] ^= e[1]; |
| result[0] ^= e[0]; |
| return result; |
| } |
| |
| /** |
| * 4-Integer Version of Karatzuba multiplication. |
| */ |
| private static int[] mult128(int[] a, int[] b) |
| { |
| int[] result = new int[8]; |
| int[] a0 = new int[2]; |
| System.arraycopy(a, 0, a0, 0, Math.min(2, a.length)); |
| int[] a1 = new int[2]; |
| if (a.length > 2) |
| { |
| System.arraycopy(a, 2, a1, 0, Math.min(2, a.length - 2)); |
| } |
| int[] b0 = new int[2]; |
| System.arraycopy(b, 0, b0, 0, Math.min(2, b.length)); |
| int[] b1 = new int[2]; |
| if (b.length > 2) |
| { |
| System.arraycopy(b, 2, b1, 0, Math.min(2, b.length - 2)); |
| } |
| if (a1[1] == 0 && b1[1] == 0) |
| { |
| if (a1[0] != 0 || b1[0] != 0) |
| { |
| int[] c = mult32(a1[0], b1[0]); |
| result[5] ^= c[1]; |
| result[4] ^= c[0]; |
| result[3] ^= c[1]; |
| result[2] ^= c[0]; |
| } |
| } |
| else |
| { |
| int[] c = mult64(a1, b1); |
| result[7] ^= c[3]; |
| result[6] ^= c[2]; |
| result[5] ^= c[1] ^ c[3]; |
| result[4] ^= c[0] ^ c[2]; |
| result[3] ^= c[1]; |
| result[2] ^= c[0]; |
| } |
| a1[0] ^= a0[0]; |
| a1[1] ^= a0[1]; |
| b1[0] ^= b0[0]; |
| b1[1] ^= b0[1]; |
| if (a1[1] == 0 && b1[1] == 0) |
| { |
| int[] d = mult32(a1[0], b1[0]); |
| result[3] ^= d[1]; |
| result[2] ^= d[0]; |
| } |
| else |
| { |
| int[] d = mult64(a1, b1); |
| result[5] ^= d[3]; |
| result[4] ^= d[2]; |
| result[3] ^= d[1]; |
| result[2] ^= d[0]; |
| } |
| if (a0[1] == 0 && b0[1] == 0) |
| { |
| int[] e = mult32(a0[0], b0[0]); |
| result[3] ^= e[1]; |
| result[2] ^= e[0]; |
| result[1] ^= e[1]; |
| result[0] ^= e[0]; |
| } |
| else |
| { |
| int[] e = mult64(a0, b0); |
| result[5] ^= e[3]; |
| result[4] ^= e[2]; |
| result[3] ^= e[1] ^ e[3]; |
| result[2] ^= e[0] ^ e[2]; |
| result[1] ^= e[1]; |
| result[0] ^= e[0]; |
| } |
| return result; |
| } |
| |
| /** |
| * 2-Integer Version of Karatzuba multiplication. |
| */ |
| private static int[] mult64(int[] a, int[] b) |
| { |
| int[] result = new int[4]; |
| int a0 = a[0]; |
| int a1 = 0; |
| if (a.length > 1) |
| { |
| a1 = a[1]; |
| } |
| int b0 = b[0]; |
| int b1 = 0; |
| if (b.length > 1) |
| { |
| b1 = b[1]; |
| } |
| if (a1 != 0 || b1 != 0) |
| { |
| int[] c = mult32(a1, b1); |
| result[3] ^= c[1]; |
| result[2] ^= c[0] ^ c[1]; |
| result[1] ^= c[0]; |
| } |
| int[] d = mult32(a0 ^ a1, b0 ^ b1); |
| result[2] ^= d[1]; |
| result[1] ^= d[0]; |
| int[] e = mult32(a0, b0); |
| result[2] ^= e[1]; |
| result[1] ^= e[0] ^ e[1]; |
| result[0] ^= e[0]; |
| return result; |
| } |
| |
| /** |
| * 4-Byte Version of Karatzuba multiplication. Here the actual work is done. |
| */ |
| private static int[] mult32(int a, int b) |
| { |
| int[] result = new int[2]; |
| if (a == 0 || b == 0) |
| { |
| return result; |
| } |
| long b2 = b; |
| b2 &= 0x00000000ffffffffL; |
| int i; |
| long h = 0; |
| for (i = 1; i <= 32; i++) |
| { |
| if ((a & bitMask[i - 1]) != 0) |
| { |
| h ^= b2; |
| } |
| b2 <<= 1; |
| } |
| result[1] = (int)(h >>> 32); |
| result[0] = (int)(h & 0x00000000ffffffffL); |
| return result; |
| } |
| |
| /** |
| * Returns a new GF2Polynomial containing the upper <i>k</i> bytes of this |
| * GF2Polynomial. |
| * |
| * @param k |
| * @return a new GF2Polynomial containing the upper <i>k</i> bytes of this |
| * GF2Polynomial |
| * @see GF2Polynomial#karaMult |
| */ |
| private GF2Polynomial upper(int k) |
| { |
| int j = Math.min(k, blocks - k); |
| GF2Polynomial result = new GF2Polynomial(j << 5); |
| if (blocks >= k) |
| { |
| System.arraycopy(value, k, result.value, 0, j); |
| } |
| return result; |
| } |
| |
| /** |
| * Returns a new GF2Polynomial containing the lower <i>k</i> bytes of this |
| * GF2Polynomial. |
| * |
| * @param k |
| * @return a new GF2Polynomial containing the lower <i>k</i> bytes of this |
| * GF2Polynomial |
| * @see GF2Polynomial#karaMult |
| */ |
| private GF2Polynomial lower(int k) |
| { |
| GF2Polynomial result = new GF2Polynomial(k << 5); |
| System.arraycopy(value, 0, result.value, 0, Math.min(k, blocks)); |
| return result; |
| } |
| |
| /** |
| * Returns the remainder of <i>this</i> divided by <i>g</i> in a new |
| * GF2Polynomial. |
| * |
| * @param g GF2Polynomial != 0 |
| * @return a new GF2Polynomial (<i>this</i> % <i>g</i>) |
| */ |
| public GF2Polynomial remainder(GF2Polynomial g) |
| throws RuntimeException |
| { |
| /* a div b = q / r */ |
| GF2Polynomial a = new GF2Polynomial(this); |
| GF2Polynomial b = new GF2Polynomial(g); |
| GF2Polynomial j; |
| int i; |
| if (b.isZero()) |
| { |
| throw new RuntimeException(); |
| } |
| a.reduceN(); |
| b.reduceN(); |
| if (a.len < b.len) |
| { |
| return a; |
| } |
| i = a.len - b.len; |
| while (i >= 0) |
| { |
| j = b.shiftLeft(i); |
| a.subtractFromThis(j); |
| a.reduceN(); |
| i = a.len - b.len; |
| } |
| return a; |
| } |
| |
| /** |
| * Returns the absolute quotient of <i>this</i> divided by <i>g</i> in a |
| * new GF2Polynomial. |
| * |
| * @param g GF2Polynomial != 0 |
| * @return a new GF2Polynomial |_ <i>this</i> / <i>g</i> _| |
| */ |
| public GF2Polynomial quotient(GF2Polynomial g) |
| throws RuntimeException |
| { |
| /* a div b = q / r */ |
| GF2Polynomial q = new GF2Polynomial(len); |
| GF2Polynomial a = new GF2Polynomial(this); |
| GF2Polynomial b = new GF2Polynomial(g); |
| GF2Polynomial j; |
| int i; |
| if (b.isZero()) |
| { |
| throw new RuntimeException(); |
| } |
| a.reduceN(); |
| b.reduceN(); |
| if (a.len < b.len) |
| { |
| return new GF2Polynomial(0); |
| } |
| i = a.len - b.len; |
| q.expandN(i + 1); |
| |
| while (i >= 0) |
| { |
| j = b.shiftLeft(i); |
| a.subtractFromThis(j); |
| a.reduceN(); |
| q.xorBit(i); |
| i = a.len - b.len; |
| } |
| |
| return q; |
| } |
| |
| /** |
| * Divides <i>this</i> by <i>g</i> and returns the quotient and remainder |
| * in a new GF2Polynomial[2], quotient in [0], remainder in [1]. |
| * |
| * @param g GF2Polynomial != 0 |
| * @return a new GF2Polynomial[2] containing quotient and remainder |
| */ |
| public GF2Polynomial[] divide(GF2Polynomial g) |
| throws RuntimeException |
| { |
| /* a div b = q / r */ |
| GF2Polynomial[] result = new GF2Polynomial[2]; |
| GF2Polynomial q = new GF2Polynomial(len); |
| GF2Polynomial a = new GF2Polynomial(this); |
| GF2Polynomial b = new GF2Polynomial(g); |
| GF2Polynomial j; |
| int i; |
| if (b.isZero()) |
| { |
| throw new RuntimeException(); |
| } |
| a.reduceN(); |
| b.reduceN(); |
| if (a.len < b.len) |
| { |
| result[0] = new GF2Polynomial(0); |
| result[1] = a; |
| return result; |
| } |
| i = a.len - b.len; |
| q.expandN(i + 1); |
| |
| while (i >= 0) |
| { |
| j = b.shiftLeft(i); |
| a.subtractFromThis(j); |
| a.reduceN(); |
| q.xorBit(i); |
| i = a.len - b.len; |
| } |
| |
| result[0] = q; |
| result[1] = a; |
| return result; |
| } |
| |
| /** |
| * Returns the greatest common divisor of <i>this</i> and <i>g</i> in a |
| * new GF2Polynomial. |
| * |
| * @param g GF2Polynomial != 0 |
| * @return a new GF2Polynomial gcd(<i>this</i>,<i>g</i>) |
| * @throws ArithmeticException if <i>this</i> and <i>g</i> both are equal to zero |
| */ |
| public GF2Polynomial gcd(GF2Polynomial g) |
| throws RuntimeException |
| { |
| if (isZero() && g.isZero()) |
| { |
| throw new ArithmeticException("Both operands of gcd equal zero."); |
| } |
| if (isZero()) |
| { |
| return new GF2Polynomial(g); |
| } |
| if (g.isZero()) |
| { |
| return new GF2Polynomial(this); |
| } |
| GF2Polynomial a = new GF2Polynomial(this); |
| GF2Polynomial b = new GF2Polynomial(g); |
| GF2Polynomial c; |
| |
| while (!b.isZero()) |
| { |
| c = a.remainder(b); |
| a = b; |
| b = c; |
| } |
| |
| return a; |
| } |
| |
| /** |
| * Checks if <i>this</i> is irreducible, according to IEEE P1363, A.5.5, |
| * p103.<br> |
| * Note: The algorithm from IEEE P1363, A5.5 can be used to check a |
| * polynomial with coefficients in GF(2^r) for irreducibility. As this class |
| * only represents polynomials with coefficients in GF(2), the algorithm is |
| * adapted to the case r=1. |
| * |
| * @return true if <i>this</i> is irreducible |
| * @see "P1363, A.5.5, p103" |
| */ |
| public boolean isIrreducible() |
| { |
| if (isZero()) |
| { |
| return false; |
| } |
| GF2Polynomial f = new GF2Polynomial(this); |
| int d, i; |
| GF2Polynomial u, g; |
| GF2Polynomial dummy; |
| f.reduceN(); |
| d = f.len - 1; |
| u = new GF2Polynomial(f.len, "X"); |
| |
| for (i = 1; i <= (d >> 1); i++) |
| { |
| u.squareThisPreCalc(); |
| u = u.remainder(f); |
| dummy = u.add(new GF2Polynomial(32, "X")); |
| if (!dummy.isZero()) |
| { |
| g = f.gcd(dummy); |
| if (!g.isOne()) |
| { |
| return false; |
| } |
| } |
| else |
| { |
| return false; |
| } |
| } |
| |
| return true; |
| } |
| |
| /** |
| * Reduces this GF2Polynomial using the trinomial x^<i>m</i> + x^<i>tc</i> + |
| * 1. |
| * |
| * @param m the degree of the used field |
| * @param tc degree of the middle x in the trinomial |
| */ |
| void reduceTrinomial(int m, int tc) |
| { |
| int i; |
| int p0, p1; |
| int q0, q1; |
| long t; |
| p0 = m >>> 5; // block which contains 2^m |
| q0 = 32 - (m & 0x1f); // (32-index) of 2^m within block p0 |
| p1 = (m - tc) >>> 5; // block which contains 2^tc |
| q1 = 32 - ((m - tc) & 0x1f); // (32-index) of 2^tc within block q1 |
| int max = ((m << 1) - 2) >>> 5; // block which contains 2^(2m-2) |
| int min = p0; // block which contains 2^m |
| for (i = max; i > min; i--) |
| { // for i = maxBlock to minBlock |
| // reduce coefficients contained in t |
| // t = block[i] |
| t = value[i] & 0x00000000ffffffffL; |
| // block[i-p0-1] ^= t << q0 |
| value[i - p0 - 1] ^= (int)(t << q0); |
| // block[i-p0] ^= t >>> (32-q0) |
| value[i - p0] ^= t >>> (32 - q0); |
| // block[i-p1-1] ^= << q1 |
| value[i - p1 - 1] ^= (int)(t << q1); |
| // block[i-p1] ^= t >>> (32-q1) |
| value[i - p1] ^= t >>> (32 - q1); |
| value[i] = 0x00; |
| } |
| // reduce last coefficients in block containing 2^m |
| t = value[min] & 0x00000000ffffffffL & (0xffffffffL << (m & 0x1f)); // t |
| // contains the last coefficients > m |
| value[0] ^= t >>> (32 - q0); |
| if (min - p1 - 1 >= 0) |
| { |
| value[min - p1 - 1] ^= (int)(t << q1); |
| } |
| value[min - p1] ^= t >>> (32 - q1); |
| |
| value[min] &= reverseRightMask[m & 0x1f]; |
| blocks = ((m - 1) >>> 5) + 1; |
| len = m; |
| } |
| |
| /** |
| * Reduces this GF2Polynomial using the pentanomial x^<i>m</i> + x^<i>pc[2]</i> + |
| * x^<i>pc[1]</i> + x^<i>pc[0]</i> + 1. |
| * |
| * @param m the degree of the used field |
| * @param pc degrees of the middle x's in the pentanomial |
| */ |
| void reducePentanomial(int m, int[] pc) |
| { |
| int i; |
| int p0, p1, p2, p3; |
| int q0, q1, q2, q3; |
| long t; |
| p0 = m >>> 5; |
| q0 = 32 - (m & 0x1f); |
| p1 = (m - pc[0]) >>> 5; |
| q1 = 32 - ((m - pc[0]) & 0x1f); |
| p2 = (m - pc[1]) >>> 5; |
| q2 = 32 - ((m - pc[1]) & 0x1f); |
| p3 = (m - pc[2]) >>> 5; |
| q3 = 32 - ((m - pc[2]) & 0x1f); |
| int max = ((m << 1) - 2) >>> 5; |
| int min = p0; |
| for (i = max; i > min; i--) |
| { |
| t = value[i] & 0x00000000ffffffffL; |
| value[i - p0 - 1] ^= (int)(t << q0); |
| value[i - p0] ^= t >>> (32 - q0); |
| value[i - p1 - 1] ^= (int)(t << q1); |
| value[i - p1] ^= t >>> (32 - q1); |
| value[i - p2 - 1] ^= (int)(t << q2); |
| value[i - p2] ^= t >>> (32 - q2); |
| value[i - p3 - 1] ^= (int)(t << q3); |
| value[i - p3] ^= t >>> (32 - q3); |
| value[i] = 0; |
| } |
| t = value[min] & 0x00000000ffffffffL & (0xffffffffL << (m & 0x1f)); |
| value[0] ^= t >>> (32 - q0); |
| if (min - p1 - 1 >= 0) |
| { |
| value[min - p1 - 1] ^= (int)(t << q1); |
| } |
| value[min - p1] ^= t >>> (32 - q1); |
| if (min - p2 - 1 >= 0) |
| { |
| value[min - p2 - 1] ^= (int)(t << q2); |
| } |
| value[min - p2] ^= t >>> (32 - q2); |
| if (min - p3 - 1 >= 0) |
| { |
| value[min - p3 - 1] ^= (int)(t << q3); |
| } |
| value[min - p3] ^= t >>> (32 - q3); |
| value[min] &= reverseRightMask[m & 0x1f]; |
| |
| blocks = ((m - 1) >>> 5) + 1; |
| len = m; |
| } |
| |
| /** |
| * Reduces len by finding the most significant bit set to one and reducing |
| * len and blocks. |
| */ |
| public void reduceN() |
| { |
| int i, j, h; |
| i = blocks - 1; |
| while ((value[i] == 0) && (i > 0)) |
| { |
| i--; |
| } |
| h = value[i]; |
| j = 0; |
| while (h != 0) |
| { |
| h >>>= 1; |
| j++; |
| } |
| len = (i << 5) + j; |
| blocks = i + 1; |
| } |
| |
| /** |
| * Expands len and int[] value to <i>i</i>. This is useful before adding |
| * two GF2Polynomials of different size. |
| * |
| * @param i the intended length |
| */ |
| public void expandN(int i) |
| { |
| int k; |
| int[] bs; |
| if (len >= i) |
| { |
| return; |
| } |
| len = i; |
| k = ((i - 1) >>> 5) + 1; |
| if (blocks >= k) |
| { |
| return; |
| } |
| if (value.length >= k) |
| { |
| int j; |
| for (j = blocks; j < k; j++) |
| { |
| value[j] = 0; |
| } |
| blocks = k; |
| return; |
| } |
| bs = new int[k]; |
| System.arraycopy(value, 0, bs, 0, blocks); |
| blocks = k; |
| value = null; |
| value = bs; |
| } |
| |
| /** |
| * Squares this GF2Polynomial and expands it accordingly. This method does |
| * not reduce the result in GF(2^N). There exists a faster method for |
| * squaring in GF(2^N). |
| * |
| * @see GF2nPolynomialElement#square |
| */ |
| public void squareThisBitwise() |
| { |
| int i, h, j, k; |
| if (isZero()) |
| { |
| return; |
| } |
| int[] result = new int[blocks << 1]; |
| for (i = blocks - 1; i >= 0; i--) |
| { |
| h = value[i]; |
| j = 0x00000001; |
| for (k = 0; k < 16; k++) |
| { |
| if ((h & 0x01) != 0) |
| { |
| result[i << 1] |= j; |
| } |
| if ((h & 0x00010000) != 0) |
| { |
| result[(i << 1) + 1] |= j; |
| } |
| j <<= 2; |
| h >>>= 1; |
| } |
| } |
| value = null; |
| value = result; |
| blocks = result.length; |
| len = (len << 1) - 1; |
| } |
| |
| /** |
| * Squares this GF2Polynomial by using precomputed values of squaringTable. |
| * This method does not reduce the result in GF(2^N). |
| */ |
| public void squareThisPreCalc() |
| { |
| int i; |
| if (isZero()) |
| { |
| return; |
| } |
| if (value.length >= (blocks << 1)) |
| { |
| for (i = blocks - 1; i >= 0; i--) |
| { |
| value[(i << 1) + 1] = GF2Polynomial.squaringTable[(value[i] & 0x00ff0000) >>> 16] |
| | (GF2Polynomial.squaringTable[(value[i] & 0xff000000) >>> 24] << 16); |
| value[i << 1] = GF2Polynomial.squaringTable[value[i] & 0x000000ff] |
| | (GF2Polynomial.squaringTable[(value[i] & 0x0000ff00) >>> 8] << 16); |
| } |
| blocks <<= 1; |
| len = (len << 1) - 1; |
| } |
| else |
| { |
| int[] result = new int[blocks << 1]; |
| for (i = 0; i < blocks; i++) |
| { |
| result[i << 1] = GF2Polynomial.squaringTable[value[i] & 0x000000ff] |
| | (GF2Polynomial.squaringTable[(value[i] & 0x0000ff00) >>> 8] << 16); |
| result[(i << 1) + 1] = GF2Polynomial.squaringTable[(value[i] & 0x00ff0000) >>> 16] |
| | (GF2Polynomial.squaringTable[(value[i] & 0xff000000) >>> 24] << 16); |
| } |
| value = null; |
| value = result; |
| blocks <<= 1; |
| len = (len << 1) - 1; |
| } |
| } |
| |
| /** |
| * Does a vector-multiplication modulo 2 and returns the result as boolean. |
| * |
| * @param b GF2Polynomial |
| * @return this x <i>b</i> as boolean (1->true, 0->false) |
| */ |
| public boolean vectorMult(GF2Polynomial b) |
| throws RuntimeException |
| { |
| int i; |
| int h; |
| boolean result = false; |
| if (len != b.len) |
| { |
| throw new RuntimeException(); |
| } |
| for (i = 0; i < blocks; i++) |
| { |
| h = value[i] & b.value[i]; |
| result ^= parity[h & 0x000000ff]; |
| result ^= parity[(h >>> 8) & 0x000000ff]; |
| result ^= parity[(h >>> 16) & 0x000000ff]; |
| result ^= parity[(h >>> 24) & 0x000000ff]; |
| } |
| return result; |
| } |
| |
| /** |
| * Returns the bitwise exclusive-or of <i>this</i> and <i>b</i> in a new |
| * GF2Polynomial. <i>this</i> and <i>b</i> can be of different size. |
| * |
| * @param b GF2Polynomial |
| * @return a new GF2Polynomial (<i>this</i> ^ <i>b</i>) |
| */ |
| public GF2Polynomial xor(GF2Polynomial b) |
| { |
| int i; |
| GF2Polynomial result; |
| int k = Math.min(blocks, b.blocks); |
| if (len >= b.len) |
| { |
| result = new GF2Polynomial(this); |
| for (i = 0; i < k; i++) |
| { |
| result.value[i] ^= b.value[i]; |
| } |
| } |
| else |
| { |
| result = new GF2Polynomial(b); |
| for (i = 0; i < k; i++) |
| { |
| result.value[i] ^= value[i]; |
| } |
| } |
| // If we xor'ed some bits too many by proceeding blockwise, |
| // restore them to zero: |
| result.zeroUnusedBits(); |
| return result; |
| } |
| |
| /** |
| * Computes the bitwise exclusive-or of this GF2Polynomial and <i>b</i> and |
| * stores the result in this GF2Polynomial. <i>b</i> can be of different |
| * size. |
| * |
| * @param b GF2Polynomial |
| */ |
| public void xorThisBy(GF2Polynomial b) |
| { |
| int i; |
| for (i = 0; i < Math.min(blocks, b.blocks); i++) |
| { |
| value[i] ^= b.value[i]; |
| } |
| // If we xor'ed some bits too many by proceeding blockwise, |
| // restore them to zero: |
| zeroUnusedBits(); |
| } |
| |
| /** |
| * If {@link #len} is not a multiple of the block size (32), some extra bits |
| * of the last block might have been modified during a blockwise operation. |
| * This method compensates for that by restoring these "extra" bits to zero. |
| */ |
| private void zeroUnusedBits() |
| { |
| if ((len & 0x1f) != 0) |
| { |
| value[blocks - 1] &= reverseRightMask[len & 0x1f]; |
| } |
| } |
| |
| /** |
| * Sets the bit at position <i>i</i>. |
| * |
| * @param i int |
| * @throws RuntimeException if (<i>i</i> < 0) || (<i>i</i> > (len - 1)) |
| */ |
| public void setBit(int i) |
| throws RuntimeException |
| { |
| if (i < 0 || i > (len - 1)) |
| { |
| throw new RuntimeException(); |
| } |
| value[i >>> 5] |= bitMask[i & 0x1f]; |
| return; |
| } |
| |
| /** |
| * Returns the bit at position <i>i</i>. |
| * |
| * @param i int |
| * @return the bit at position <i>i</i> if <i>i</i> is a valid position, 0 |
| * otherwise. |
| */ |
| public int getBit(int i) |
| { |
| if (i < 0) |
| { |
| throw new RuntimeException(); |
| } |
| if (i > (len - 1)) |
| { |
| return 0; |
| } |
| return ((value[i >>> 5] & bitMask[i & 0x1f]) != 0) ? 1 : 0; |
| } |
| |
| /** |
| * Resets the bit at position <i>i</i>. |
| * |
| * @param i int |
| * @throws RuntimeException if (<i>i</i> < 0) || (<i>i</i> > (len - 1)) |
| */ |
| public void resetBit(int i) |
| throws RuntimeException |
| { |
| if (i < 0) |
| { |
| throw new RuntimeException(); |
| } |
| if (i > (len - 1)) |
| { |
| return; |
| } |
| value[i >>> 5] &= ~bitMask[i & 0x1f]; |
| } |
| |
| /** |
| * Xors the bit at position <i>i</i>. |
| * |
| * @param i int |
| * @throws RuntimeException if (<i>i</i> < 0) || (<i>i</i> > (len - 1)) |
| */ |
| public void xorBit(int i) |
| throws RuntimeException |
| { |
| if (i < 0 || i > (len - 1)) |
| { |
| throw new RuntimeException(); |
| } |
| value[i >>> 5] ^= bitMask[i & 0x1f]; |
| } |
| |
| /** |
| * Tests the bit at position <i>i</i>. |
| * |
| * @param i the position of the bit to be tested |
| * @return true if the bit at position <i>i</i> is set (a(<i>i</i>) == |
| * 1). False if (<i>i</i> < 0) || (<i>i</i> > (len - 1)) |
| */ |
| public boolean testBit(int i) |
| { |
| if (i < 0) |
| { |
| throw new RuntimeException(); |
| } |
| if (i > (len - 1)) |
| { |
| return false; |
| } |
| return (value[i >>> 5] & bitMask[i & 0x1f]) != 0; |
| } |
| |
| /** |
| * Returns this GF2Polynomial shift-left by 1 in a new GF2Polynomial. |
| * |
| * @return a new GF2Polynomial (this << 1) |
| */ |
| public GF2Polynomial shiftLeft() |
| { |
| GF2Polynomial result = new GF2Polynomial(len + 1, value); |
| int i; |
| for (i = result.blocks - 1; i >= 1; i--) |
| { |
| result.value[i] <<= 1; |
| result.value[i] |= result.value[i - 1] >>> 31; |
| } |
| result.value[0] <<= 1; |
| return result; |
| } |
| |
| /** |
| * Shifts-left this by one and enlarges the size of value if necesary. |
| */ |
| public void shiftLeftThis() |
| { |
| /** @todo This is untested. */ |
| int i; |
| if ((len & 0x1f) == 0) |
| { // check if blocks increases |
| len += 1; |
| blocks += 1; |
| if (blocks > value.length) |
| { // enlarge value |
| int[] bs = new int[blocks]; |
| System.arraycopy(value, 0, bs, 0, value.length); |
| value = null; |
| value = bs; |
| } |
| for (i = blocks - 1; i >= 1; i--) |
| { |
| value[i] |= value[i - 1] >>> 31; |
| value[i - 1] <<= 1; |
| } |
| } |
| else |
| { |
| len += 1; |
| for (i = blocks - 1; i >= 1; i--) |
| { |
| value[i] <<= 1; |
| value[i] |= value[i - 1] >>> 31; |
| } |
| value[0] <<= 1; |
| } |
| } |
| |
| /** |
| * Returns this GF2Polynomial shift-left by <i>k</i> in a new |
| * GF2Polynomial. |
| * |
| * @param k int |
| * @return a new GF2Polynomial (this << <i>k</i>) |
| */ |
| public GF2Polynomial shiftLeft(int k) |
| { |
| // Variant 2, requiring a modified shiftBlocksLeft(k) |
| // In case of modification, consider a rename to doShiftBlocksLeft() |
| // with an explicit note that this method assumes that the polynomial |
| // has already been resized. Or consider doing things inline. |
| // Construct the resulting polynomial of appropriate length: |
| GF2Polynomial result = new GF2Polynomial(len + k, value); |
| // Shift left as many multiples of the block size as possible: |
| if (k >= 32) |
| { |
| result.doShiftBlocksLeft(k >>> 5); |
| } |
| // Shift left by the remaining (<32) amount: |
| final int remaining = k & 0x1f; |
| if (remaining != 0) |
| { |
| for (int i = result.blocks - 1; i >= 1; i--) |
| { |
| result.value[i] <<= remaining; |
| result.value[i] |= result.value[i - 1] >>> (32 - remaining); |
| } |
| result.value[0] <<= remaining; |
| } |
| return result; |
| } |
| |
| /** |
| * Shifts left b and adds the result to Its a fast version of |
| * <tt>this = add(b.shl(k));</tt> |
| * |
| * @param b GF2Polynomial to shift and add to this |
| * @param k the amount to shift |
| * @see GF2nPolynomialElement#invertEEA |
| */ |
| public void shiftLeftAddThis(GF2Polynomial b, int k) |
| { |
| if (k == 0) |
| { |
| addToThis(b); |
| return; |
| } |
| int i; |
| expandN(b.len + k); |
| int d = k >>> 5; |
| for (i = b.blocks - 1; i >= 0; i--) |
| { |
| if ((i + d + 1 < blocks) && ((k & 0x1f) != 0)) |
| { |
| value[i + d + 1] ^= b.value[i] >>> (32 - (k & 0x1f)); |
| } |
| value[i + d] ^= b.value[i] << (k & 0x1f); |
| } |
| } |
| |
| /** |
| * Shifts-left this GF2Polynomial's value blockwise 1 block resulting in a |
| * shift-left by 32. |
| * |
| * @see GF2Polynomial#multiply |
| */ |
| void shiftBlocksLeft() |
| { |
| blocks += 1; |
| len += 32; |
| if (blocks <= value.length) |
| { |
| int i; |
| for (i = blocks - 1; i >= 1; i--) |
| { |
| value[i] = value[i - 1]; |
| } |
| value[0] = 0x00; |
| } |
| else |
| { |
| int[] result = new int[blocks]; |
| System.arraycopy(value, 0, result, 1, blocks - 1); |
| value = null; |
| value = result; |
| } |
| } |
| |
| /** |
| * Shifts left this GF2Polynomial's value blockwise <i>b</i> blocks |
| * resulting in a shift-left by b*32. This method assumes that {@link #len} |
| * and {@link #blocks} have already been updated to reflect the final state. |
| * |
| * @param b shift amount (in blocks) |
| */ |
| private void doShiftBlocksLeft(int b) |
| { |
| if (blocks <= value.length) |
| { |
| int i; |
| for (i = blocks - 1; i >= b; i--) |
| { |
| value[i] = value[i - b]; |
| } |
| for (i = 0; i < b; i++) |
| { |
| value[i] = 0x00; |
| } |
| } |
| else |
| { |
| int[] result = new int[blocks]; |
| System.arraycopy(value, 0, result, b, blocks - b); |
| value = null; |
| value = result; |
| } |
| } |
| |
| /** |
| * Returns this GF2Polynomial shift-right by 1 in a new GF2Polynomial. |
| * |
| * @return a new GF2Polynomial (this << 1) |
| */ |
| public GF2Polynomial shiftRight() |
| { |
| GF2Polynomial result = new GF2Polynomial(len - 1); |
| int i; |
| System.arraycopy(value, 0, result.value, 0, result.blocks); |
| for (i = 0; i <= result.blocks - 2; i++) |
| { |
| result.value[i] >>>= 1; |
| result.value[i] |= result.value[i + 1] << 31; |
| } |
| result.value[result.blocks - 1] >>>= 1; |
| if (result.blocks < blocks) |
| { |
| result.value[result.blocks - 1] |= value[result.blocks] << 31; |
| } |
| return result; |
| } |
| |
| /** |
| * Shifts-right this GF2Polynomial by 1. |
| */ |
| public void shiftRightThis() |
| { |
| int i; |
| len -= 1; |
| blocks = ((len - 1) >>> 5) + 1; |
| for (i = 0; i <= blocks - 2; i++) |
| { |
| value[i] >>>= 1; |
| value[i] |= value[i + 1] << 31; |
| } |
| value[blocks - 1] >>>= 1; |
| if ((len & 0x1f) == 0) |
| { |
| value[blocks - 1] |= value[blocks] << 31; |
| } |
| } |
| |
| } |
