| /** |
| * EdDSA-Java by str4d |
| * |
| * <p>To the extent possible under law, the person who associated CC0 with EdDSA-Java has waived all |
| * copyright and related or neighboring rights to EdDSA-Java. |
| * |
| * <p>You should have received a copy of the CC0 legalcode along with this work. If not, see |
| * <https://creativecommons.org/publicdomain/zero/1.0/>. |
| */ |
| package org.mariadb.jdbc.plugin.authentication.standard.ed25519.math.ed25519; |
| |
| import org.mariadb.jdbc.plugin.authentication.standard.ed25519.math.ScalarOps; |
| |
| /** |
| * Class for reducing a huge integer modulo the group order q and doing a combined multiply plus add |
| * plus reduce operation. |
| * |
| * <p>$q = 2^{252} + 27742317777372353535851937790883648493$. |
| * |
| * <p>Reviewed/commented by Bloody Rookie (nemproject@gmx.de) |
| */ |
| public class Ed25519ScalarOps implements ScalarOps { |
| |
| /** |
| * Reduction modulo the group order $q$. |
| * |
| * <p>Input: $s[0]+256*s[1]+\dots+256^{63}*s[63] = s$ |
| * |
| * <p>Output: $s[0]+256*s[1]+\dots+256^{31}*s[31] = s \bmod q$ where $q = 2^{252} + |
| * 27742317777372353535851937790883648493$. |
| */ |
| public byte[] reduce(byte[] s) { |
| // s0,..., s22 have 21 bits, s23 has 29 bits |
| long s0 = 0x1FFFFF & Ed25519LittleEndianEncoding.load_3(s, 0); |
| long s1 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(s, 2) >> 5); |
| long s2 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(s, 5) >> 2); |
| long s3 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(s, 7) >> 7); |
| long s4 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(s, 10) >> 4); |
| long s5 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(s, 13) >> 1); |
| long s6 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(s, 15) >> 6); |
| long s7 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(s, 18) >> 3); |
| long s8 = 0x1FFFFF & Ed25519LittleEndianEncoding.load_3(s, 21); |
| long s9 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(s, 23) >> 5); |
| long s10 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(s, 26) >> 2); |
| long s11 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(s, 28) >> 7); |
| long s12 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(s, 31) >> 4); |
| long s13 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(s, 34) >> 1); |
| long s14 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(s, 36) >> 6); |
| long s15 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(s, 39) >> 3); |
| long s16 = 0x1FFFFF & Ed25519LittleEndianEncoding.load_3(s, 42); |
| long s17 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(s, 44) >> 5); |
| long s18 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(s, 47) >> 2); |
| long s19 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(s, 49) >> 7); |
| long s20 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(s, 52) >> 4); |
| long s21 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(s, 55) >> 1); |
| long s22 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(s, 57) >> 6); |
| long s23 = (Ed25519LittleEndianEncoding.load_4(s, 60) >> 3); |
| long carry0; |
| long carry1; |
| long carry2; |
| long carry3; |
| long carry4; |
| long carry5; |
| long carry6; |
| long carry7; |
| long carry8; |
| long carry9; |
| long carry10; |
| long carry11; |
| long carry12; |
| long carry13; |
| long carry14; |
| long carry15; |
| long carry16; |
| |
| s11 += s23 * 666643; |
| s12 += s23 * 470296; |
| s13 += s23 * 654183; |
| s14 -= s23 * 997805; |
| s15 += s23 * 136657; |
| s16 -= s23 * 683901; |
| // not used again |
| // s23 = 0; |
| |
| s10 += s22 * 666643; |
| s11 += s22 * 470296; |
| s12 += s22 * 654183; |
| s13 -= s22 * 997805; |
| s14 += s22 * 136657; |
| s15 -= s22 * 683901; |
| // not used again |
| // s22 = 0; |
| |
| s9 += s21 * 666643; |
| s10 += s21 * 470296; |
| s11 += s21 * 654183; |
| s12 -= s21 * 997805; |
| s13 += s21 * 136657; |
| s14 -= s21 * 683901; |
| // not used again |
| // s21 = 0; |
| |
| s8 += s20 * 666643; |
| s9 += s20 * 470296; |
| s10 += s20 * 654183; |
| s11 -= s20 * 997805; |
| s12 += s20 * 136657; |
| s13 -= s20 * 683901; |
| // not used again |
| // s20 = 0; |
| |
| s7 += s19 * 666643; |
| s8 += s19 * 470296; |
| s9 += s19 * 654183; |
| s10 -= s19 * 997805; |
| s11 += s19 * 136657; |
| s12 -= s19 * 683901; |
| // not used again |
| // s19 = 0; |
| |
| s6 += s18 * 666643; |
| s7 += s18 * 470296; |
| s8 += s18 * 654183; |
| s9 -= s18 * 997805; |
| s10 += s18 * 136657; |
| s11 -= s18 * 683901; |
| // not used again |
| // s18 = 0; |
| |
| carry6 = (s6 + (1 << 20)) >> 21; |
| s7 += carry6; |
| s6 -= carry6 << 21; |
| carry8 = (s8 + (1 << 20)) >> 21; |
| s9 += carry8; |
| s8 -= carry8 << 21; |
| carry10 = (s10 + (1 << 20)) >> 21; |
| s11 += carry10; |
| s10 -= carry10 << 21; |
| carry12 = (s12 + (1 << 20)) >> 21; |
| s13 += carry12; |
| s12 -= carry12 << 21; |
| carry14 = (s14 + (1 << 20)) >> 21; |
| s15 += carry14; |
| s14 -= carry14 << 21; |
| carry16 = (s16 + (1 << 20)) >> 21; |
| s17 += carry16; |
| s16 -= carry16 << 21; |
| |
| carry7 = (s7 + (1 << 20)) >> 21; |
| s8 += carry7; |
| s7 -= carry7 << 21; |
| carry9 = (s9 + (1 << 20)) >> 21; |
| s10 += carry9; |
| s9 -= carry9 << 21; |
| carry11 = (s11 + (1 << 20)) >> 21; |
| s12 += carry11; |
| s11 -= carry11 << 21; |
| carry13 = (s13 + (1 << 20)) >> 21; |
| s14 += carry13; |
| s13 -= carry13 << 21; |
| carry15 = (s15 + (1 << 20)) >> 21; |
| s16 += carry15; |
| s15 -= carry15 << 21; |
| |
| s5 += s17 * 666643; |
| s6 += s17 * 470296; |
| s7 += s17 * 654183; |
| s8 -= s17 * 997805; |
| s9 += s17 * 136657; |
| s10 -= s17 * 683901; |
| // not used again |
| // s17 = 0; |
| |
| s4 += s16 * 666643; |
| s5 += s16 * 470296; |
| s6 += s16 * 654183; |
| s7 -= s16 * 997805; |
| s8 += s16 * 136657; |
| s9 -= s16 * 683901; |
| // not used again |
| // s16 = 0; |
| |
| s3 += s15 * 666643; |
| s4 += s15 * 470296; |
| s5 += s15 * 654183; |
| s6 -= s15 * 997805; |
| s7 += s15 * 136657; |
| s8 -= s15 * 683901; |
| // not used again |
| // s15 = 0; |
| |
| s2 += s14 * 666643; |
| s3 += s14 * 470296; |
| s4 += s14 * 654183; |
| s5 -= s14 * 997805; |
| s6 += s14 * 136657; |
| s7 -= s14 * 683901; |
| // not used again |
| // s14 = 0; |
| |
| s1 += s13 * 666643; |
| s2 += s13 * 470296; |
| s3 += s13 * 654183; |
| s4 -= s13 * 997805; |
| s5 += s13 * 136657; |
| s6 -= s13 * 683901; |
| // not used again |
| // s13 = 0; |
| |
| s0 += s12 * 666643; |
| s1 += s12 * 470296; |
| s2 += s12 * 654183; |
| s3 -= s12 * 997805; |
| s4 += s12 * 136657; |
| s5 -= s12 * 683901; |
| // set below |
| // s12 = 0; |
| |
| carry0 = (s0 + (1 << 20)) >> 21; |
| s1 += carry0; |
| s0 -= carry0 << 21; |
| carry2 = (s2 + (1 << 20)) >> 21; |
| s3 += carry2; |
| s2 -= carry2 << 21; |
| carry4 = (s4 + (1 << 20)) >> 21; |
| s5 += carry4; |
| s4 -= carry4 << 21; |
| carry6 = (s6 + (1 << 20)) >> 21; |
| s7 += carry6; |
| s6 -= carry6 << 21; |
| carry8 = (s8 + (1 << 20)) >> 21; |
| s9 += carry8; |
| s8 -= carry8 << 21; |
| carry10 = (s10 + (1 << 20)) >> 21; |
| s11 += carry10; |
| s10 -= carry10 << 21; |
| |
| carry1 = (s1 + (1 << 20)) >> 21; |
| s2 += carry1; |
| s1 -= carry1 << 21; |
| carry3 = (s3 + (1 << 20)) >> 21; |
| s4 += carry3; |
| s3 -= carry3 << 21; |
| carry5 = (s5 + (1 << 20)) >> 21; |
| s6 += carry5; |
| s5 -= carry5 << 21; |
| carry7 = (s7 + (1 << 20)) >> 21; |
| s8 += carry7; |
| s7 -= carry7 << 21; |
| carry9 = (s9 + (1 << 20)) >> 21; |
| s10 += carry9; |
| s9 -= carry9 << 21; |
| // carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; |
| carry11 = (s11 + (1 << 20)) >> 21; |
| s12 = carry11; |
| s11 -= carry11 << 21; |
| |
| s0 += s12 * 666643; |
| s1 += s12 * 470296; |
| s2 += s12 * 654183; |
| s3 -= s12 * 997805; |
| s4 += s12 * 136657; |
| s5 -= s12 * 683901; |
| // set below |
| // s12 = 0; |
| |
| carry0 = s0 >> 21; |
| s1 += carry0; |
| s0 -= carry0 << 21; |
| carry1 = s1 >> 21; |
| s2 += carry1; |
| s1 -= carry1 << 21; |
| carry2 = s2 >> 21; |
| s3 += carry2; |
| s2 -= carry2 << 21; |
| carry3 = s3 >> 21; |
| s4 += carry3; |
| s3 -= carry3 << 21; |
| carry4 = s4 >> 21; |
| s5 += carry4; |
| s4 -= carry4 << 21; |
| carry5 = s5 >> 21; |
| s6 += carry5; |
| s5 -= carry5 << 21; |
| carry6 = s6 >> 21; |
| s7 += carry6; |
| s6 -= carry6 << 21; |
| carry7 = s7 >> 21; |
| s8 += carry7; |
| s7 -= carry7 << 21; |
| carry8 = s8 >> 21; |
| s9 += carry8; |
| s8 -= carry8 << 21; |
| carry9 = s9 >> 21; |
| s10 += carry9; |
| s9 -= carry9 << 21; |
| carry10 = s10 >> 21; |
| s11 += carry10; |
| s10 -= carry10 << 21; |
| // carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; |
| carry11 = s11 >> 21; |
| s12 = carry11; |
| s11 -= carry11 << 21; |
| |
| // TODO-CR BR: Is it really needed to do it TWO times? (it doesn't hurt, just a question). |
| s0 += s12 * 666643; |
| s1 += s12 * 470296; |
| s2 += s12 * 654183; |
| s3 -= s12 * 997805; |
| s4 += s12 * 136657; |
| s5 -= s12 * 683901; |
| // not used again |
| // s12 = 0; |
| |
| carry0 = s0 >> 21; |
| s1 += carry0; |
| s0 -= carry0 << 21; |
| carry1 = s1 >> 21; |
| s2 += carry1; |
| s1 -= carry1 << 21; |
| carry2 = s2 >> 21; |
| s3 += carry2; |
| s2 -= carry2 << 21; |
| carry3 = s3 >> 21; |
| s4 += carry3; |
| s3 -= carry3 << 21; |
| carry4 = s4 >> 21; |
| s5 += carry4; |
| s4 -= carry4 << 21; |
| carry5 = s5 >> 21; |
| s6 += carry5; |
| s5 -= carry5 << 21; |
| carry6 = s6 >> 21; |
| s7 += carry6; |
| s6 -= carry6 << 21; |
| carry7 = s7 >> 21; |
| s8 += carry7; |
| s7 -= carry7 << 21; |
| carry8 = s8 >> 21; |
| s9 += carry8; |
| s8 -= carry8 << 21; |
| carry9 = s9 >> 21; |
| s10 += carry9; |
| s9 -= carry9 << 21; |
| carry10 = s10 >> 21; |
| s11 += carry10; |
| s10 -= carry10 << 21; |
| |
| // s0, ..., s11 got 21 bits each. |
| byte[] result = new byte[32]; |
| result[0] = (byte) s0; |
| result[1] = (byte) (s0 >> 8); |
| result[2] = (byte) ((s0 >> 16) | (s1 << 5)); |
| result[3] = (byte) (s1 >> 3); |
| result[4] = (byte) (s1 >> 11); |
| result[5] = (byte) ((s1 >> 19) | (s2 << 2)); |
| result[6] = (byte) (s2 >> 6); |
| result[7] = (byte) ((s2 >> 14) | (s3 << 7)); |
| result[8] = (byte) (s3 >> 1); |
| result[9] = (byte) (s3 >> 9); |
| result[10] = (byte) ((s3 >> 17) | (s4 << 4)); |
| result[11] = (byte) (s4 >> 4); |
| result[12] = (byte) (s4 >> 12); |
| result[13] = (byte) ((s4 >> 20) | (s5 << 1)); |
| result[14] = (byte) (s5 >> 7); |
| result[15] = (byte) ((s5 >> 15) | (s6 << 6)); |
| result[16] = (byte) (s6 >> 2); |
| result[17] = (byte) (s6 >> 10); |
| result[18] = (byte) ((s6 >> 18) | (s7 << 3)); |
| result[19] = (byte) (s7 >> 5); |
| result[20] = (byte) (s7 >> 13); |
| result[21] = (byte) s8; |
| result[22] = (byte) (s8 >> 8); |
| result[23] = (byte) ((s8 >> 16) | (s9 << 5)); |
| result[24] = (byte) (s9 >> 3); |
| result[25] = (byte) (s9 >> 11); |
| result[26] = (byte) ((s9 >> 19) | (s10 << 2)); |
| result[27] = (byte) (s10 >> 6); |
| result[28] = (byte) ((s10 >> 14) | (s11 << 7)); |
| result[29] = (byte) (s11 >> 1); |
| result[30] = (byte) (s11 >> 9); |
| result[31] = (byte) (s11 >> 17); |
| return result; |
| } |
| |
| /** |
| * $(ab+c) \bmod q$ |
| * |
| * <p>Input: |
| * |
| * <ul> |
| * <li>$a[0]+256*a[1]+\dots+256^{31}*a[31] = a$ |
| * <li>$b[0]+256*b[1]+\dots+256^{31}*b[31] = b$ |
| * <li>$c[0]+256*c[1]+\dots+256^{31}*c[31] = c$ |
| * </ul> |
| * |
| * <p>Output: $result[0]+256*result[1]+\dots+256^{31}*result[31] = (ab+c) \bmod q$ where $q = |
| * 2^{252} + 27742317777372353535851937790883648493$. |
| * |
| * <p>See the comments in {@link #reduce(byte[])} for an explanation of the algorithm. |
| */ |
| public byte[] multiplyAndAdd(byte[] a, byte[] b, byte[] c) { |
| long a0 = 0x1FFFFF & Ed25519LittleEndianEncoding.load_3(a, 0); |
| long a1 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(a, 2) >> 5); |
| long a2 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(a, 5) >> 2); |
| long a3 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(a, 7) >> 7); |
| long a4 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(a, 10) >> 4); |
| long a5 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(a, 13) >> 1); |
| long a6 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(a, 15) >> 6); |
| long a7 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(a, 18) >> 3); |
| long a8 = 0x1FFFFF & Ed25519LittleEndianEncoding.load_3(a, 21); |
| long a9 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(a, 23) >> 5); |
| long a10 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(a, 26) >> 2); |
| long a11 = (Ed25519LittleEndianEncoding.load_4(a, 28) >> 7); |
| long b0 = 0x1FFFFF & Ed25519LittleEndianEncoding.load_3(b, 0); |
| long b1 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(b, 2) >> 5); |
| long b2 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(b, 5) >> 2); |
| long b3 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(b, 7) >> 7); |
| long b4 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(b, 10) >> 4); |
| long b5 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(b, 13) >> 1); |
| long b6 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(b, 15) >> 6); |
| long b7 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(b, 18) >> 3); |
| long b8 = 0x1FFFFF & Ed25519LittleEndianEncoding.load_3(b, 21); |
| long b9 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(b, 23) >> 5); |
| long b10 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(b, 26) >> 2); |
| long b11 = (Ed25519LittleEndianEncoding.load_4(b, 28) >> 7); |
| long c0 = 0x1FFFFF & Ed25519LittleEndianEncoding.load_3(c, 0); |
| long c1 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(c, 2) >> 5); |
| long c2 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(c, 5) >> 2); |
| long c3 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(c, 7) >> 7); |
| long c4 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(c, 10) >> 4); |
| long c5 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(c, 13) >> 1); |
| long c6 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(c, 15) >> 6); |
| long c7 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(c, 18) >> 3); |
| long c8 = 0x1FFFFF & Ed25519LittleEndianEncoding.load_3(c, 21); |
| long c9 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_4(c, 23) >> 5); |
| long c10 = 0x1FFFFF & (Ed25519LittleEndianEncoding.load_3(c, 26) >> 2); |
| long c11 = (Ed25519LittleEndianEncoding.load_4(c, 28) >> 7); |
| long s0; |
| long s1; |
| long s2; |
| long s3; |
| long s4; |
| long s5; |
| long s6; |
| long s7; |
| long s8; |
| long s9; |
| long s10; |
| long s11; |
| long s12; |
| long s13; |
| long s14; |
| long s15; |
| long s16; |
| long s17; |
| long s18; |
| long s19; |
| long s20; |
| long s21; |
| long s22; |
| long s23; |
| long carry0; |
| long carry1; |
| long carry2; |
| long carry3; |
| long carry4; |
| long carry5; |
| long carry6; |
| long carry7; |
| long carry8; |
| long carry9; |
| long carry10; |
| long carry11; |
| long carry12; |
| long carry13; |
| long carry14; |
| long carry15; |
| long carry16; |
| long carry17; |
| long carry18; |
| long carry19; |
| long carry20; |
| long carry21; |
| long carry22; |
| |
| s0 = c0 + a0 * b0; |
| s1 = c1 + a0 * b1 + a1 * b0; |
| s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0; |
| s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; |
| s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; |
| s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; |
| s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; |
| s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0; |
| s8 = |
| c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 |
| + a8 * b0; |
| s9 = |
| c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 |
| + a9 * b0; |
| s10 = |
| c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 |
| + a8 * b2 + a9 * b1 + a10 * b0; |
| s11 = |
| c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 + a7 * b4 |
| + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; |
| s12 = |
| a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 |
| + a10 * b2 + a11 * b1; |
| s13 = |
| a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 |
| + a11 * b2; |
| s14 = |
| a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3; |
| s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4; |
| s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; |
| s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; |
| s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; |
| s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; |
| s20 = a9 * b11 + a10 * b10 + a11 * b9; |
| s21 = a10 * b11 + a11 * b10; |
| s22 = a11 * b11; |
| // set below |
| // s23 = 0; |
| |
| carry0 = (s0 + (1 << 20)) >> 21; |
| s1 += carry0; |
| s0 -= carry0 << 21; |
| carry2 = (s2 + (1 << 20)) >> 21; |
| s3 += carry2; |
| s2 -= carry2 << 21; |
| carry4 = (s4 + (1 << 20)) >> 21; |
| s5 += carry4; |
| s4 -= carry4 << 21; |
| carry6 = (s6 + (1 << 20)) >> 21; |
| s7 += carry6; |
| s6 -= carry6 << 21; |
| carry8 = (s8 + (1 << 20)) >> 21; |
| s9 += carry8; |
| s8 -= carry8 << 21; |
| carry10 = (s10 + (1 << 20)) >> 21; |
| s11 += carry10; |
| s10 -= carry10 << 21; |
| carry12 = (s12 + (1 << 20)) >> 21; |
| s13 += carry12; |
| s12 -= carry12 << 21; |
| carry14 = (s14 + (1 << 20)) >> 21; |
| s15 += carry14; |
| s14 -= carry14 << 21; |
| carry16 = (s16 + (1 << 20)) >> 21; |
| s17 += carry16; |
| s16 -= carry16 << 21; |
| carry18 = (s18 + (1 << 20)) >> 21; |
| s19 += carry18; |
| s18 -= carry18 << 21; |
| carry20 = (s20 + (1 << 20)) >> 21; |
| s21 += carry20; |
| s20 -= carry20 << 21; |
| // carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21; |
| carry22 = (s22 + (1 << 20)) >> 21; |
| s23 = carry22; |
| s22 -= carry22 << 21; |
| |
| carry1 = (s1 + (1 << 20)) >> 21; |
| s2 += carry1; |
| s1 -= carry1 << 21; |
| carry3 = (s3 + (1 << 20)) >> 21; |
| s4 += carry3; |
| s3 -= carry3 << 21; |
| carry5 = (s5 + (1 << 20)) >> 21; |
| s6 += carry5; |
| s5 -= carry5 << 21; |
| carry7 = (s7 + (1 << 20)) >> 21; |
| s8 += carry7; |
| s7 -= carry7 << 21; |
| carry9 = (s9 + (1 << 20)) >> 21; |
| s10 += carry9; |
| s9 -= carry9 << 21; |
| carry11 = (s11 + (1 << 20)) >> 21; |
| s12 += carry11; |
| s11 -= carry11 << 21; |
| carry13 = (s13 + (1 << 20)) >> 21; |
| s14 += carry13; |
| s13 -= carry13 << 21; |
| carry15 = (s15 + (1 << 20)) >> 21; |
| s16 += carry15; |
| s15 -= carry15 << 21; |
| carry17 = (s17 + (1 << 20)) >> 21; |
| s18 += carry17; |
| s17 -= carry17 << 21; |
| carry19 = (s19 + (1 << 20)) >> 21; |
| s20 += carry19; |
| s19 -= carry19 << 21; |
| carry21 = (s21 + (1 << 20)) >> 21; |
| s22 += carry21; |
| s21 -= carry21 << 21; |
| |
| s11 += s23 * 666643; |
| s12 += s23 * 470296; |
| s13 += s23 * 654183; |
| s14 -= s23 * 997805; |
| s15 += s23 * 136657; |
| s16 -= s23 * 683901; |
| // not used again |
| // s23 = 0; |
| |
| s10 += s22 * 666643; |
| s11 += s22 * 470296; |
| s12 += s22 * 654183; |
| s13 -= s22 * 997805; |
| s14 += s22 * 136657; |
| s15 -= s22 * 683901; |
| // not used again |
| // s22 = 0; |
| |
| s9 += s21 * 666643; |
| s10 += s21 * 470296; |
| s11 += s21 * 654183; |
| s12 -= s21 * 997805; |
| s13 += s21 * 136657; |
| s14 -= s21 * 683901; |
| // not used again |
| // s21 = 0; |
| |
| s8 += s20 * 666643; |
| s9 += s20 * 470296; |
| s10 += s20 * 654183; |
| s11 -= s20 * 997805; |
| s12 += s20 * 136657; |
| s13 -= s20 * 683901; |
| // not used again |
| // s20 = 0; |
| |
| s7 += s19 * 666643; |
| s8 += s19 * 470296; |
| s9 += s19 * 654183; |
| s10 -= s19 * 997805; |
| s11 += s19 * 136657; |
| s12 -= s19 * 683901; |
| // not used again |
| // s19 = 0; |
| |
| s6 += s18 * 666643; |
| s7 += s18 * 470296; |
| s8 += s18 * 654183; |
| s9 -= s18 * 997805; |
| s10 += s18 * 136657; |
| s11 -= s18 * 683901; |
| // not used again |
| // s18 = 0; |
| |
| carry6 = (s6 + (1 << 20)) >> 21; |
| s7 += carry6; |
| s6 -= carry6 << 21; |
| carry8 = (s8 + (1 << 20)) >> 21; |
| s9 += carry8; |
| s8 -= carry8 << 21; |
| carry10 = (s10 + (1 << 20)) >> 21; |
| s11 += carry10; |
| s10 -= carry10 << 21; |
| carry12 = (s12 + (1 << 20)) >> 21; |
| s13 += carry12; |
| s12 -= carry12 << 21; |
| carry14 = (s14 + (1 << 20)) >> 21; |
| s15 += carry14; |
| s14 -= carry14 << 21; |
| carry16 = (s16 + (1 << 20)) >> 21; |
| s17 += carry16; |
| s16 -= carry16 << 21; |
| |
| carry7 = (s7 + (1 << 20)) >> 21; |
| s8 += carry7; |
| s7 -= carry7 << 21; |
| carry9 = (s9 + (1 << 20)) >> 21; |
| s10 += carry9; |
| s9 -= carry9 << 21; |
| carry11 = (s11 + (1 << 20)) >> 21; |
| s12 += carry11; |
| s11 -= carry11 << 21; |
| carry13 = (s13 + (1 << 20)) >> 21; |
| s14 += carry13; |
| s13 -= carry13 << 21; |
| carry15 = (s15 + (1 << 20)) >> 21; |
| s16 += carry15; |
| s15 -= carry15 << 21; |
| |
| s5 += s17 * 666643; |
| s6 += s17 * 470296; |
| s7 += s17 * 654183; |
| s8 -= s17 * 997805; |
| s9 += s17 * 136657; |
| s10 -= s17 * 683901; |
| // not used again |
| // s17 = 0; |
| |
| s4 += s16 * 666643; |
| s5 += s16 * 470296; |
| s6 += s16 * 654183; |
| s7 -= s16 * 997805; |
| s8 += s16 * 136657; |
| s9 -= s16 * 683901; |
| // not used again |
| // s16 = 0; |
| |
| s3 += s15 * 666643; |
| s4 += s15 * 470296; |
| s5 += s15 * 654183; |
| s6 -= s15 * 997805; |
| s7 += s15 * 136657; |
| s8 -= s15 * 683901; |
| // not used again |
| // s15 = 0; |
| |
| s2 += s14 * 666643; |
| s3 += s14 * 470296; |
| s4 += s14 * 654183; |
| s5 -= s14 * 997805; |
| s6 += s14 * 136657; |
| s7 -= s14 * 683901; |
| // not used again |
| // s14 = 0; |
| |
| s1 += s13 * 666643; |
| s2 += s13 * 470296; |
| s3 += s13 * 654183; |
| s4 -= s13 * 997805; |
| s5 += s13 * 136657; |
| s6 -= s13 * 683901; |
| // not used again |
| // s13 = 0; |
| |
| s0 += s12 * 666643; |
| s1 += s12 * 470296; |
| s2 += s12 * 654183; |
| s3 -= s12 * 997805; |
| s4 += s12 * 136657; |
| s5 -= s12 * 683901; |
| // set below |
| // s12 = 0; |
| |
| carry0 = (s0 + (1 << 20)) >> 21; |
| s1 += carry0; |
| s0 -= carry0 << 21; |
| carry2 = (s2 + (1 << 20)) >> 21; |
| s3 += carry2; |
| s2 -= carry2 << 21; |
| carry4 = (s4 + (1 << 20)) >> 21; |
| s5 += carry4; |
| s4 -= carry4 << 21; |
| carry6 = (s6 + (1 << 20)) >> 21; |
| s7 += carry6; |
| s6 -= carry6 << 21; |
| carry8 = (s8 + (1 << 20)) >> 21; |
| s9 += carry8; |
| s8 -= carry8 << 21; |
| carry10 = (s10 + (1 << 20)) >> 21; |
| s11 += carry10; |
| s10 -= carry10 << 21; |
| |
| carry1 = (s1 + (1 << 20)) >> 21; |
| s2 += carry1; |
| s1 -= carry1 << 21; |
| carry3 = (s3 + (1 << 20)) >> 21; |
| s4 += carry3; |
| s3 -= carry3 << 21; |
| carry5 = (s5 + (1 << 20)) >> 21; |
| s6 += carry5; |
| s5 -= carry5 << 21; |
| carry7 = (s7 + (1 << 20)) >> 21; |
| s8 += carry7; |
| s7 -= carry7 << 21; |
| carry9 = (s9 + (1 << 20)) >> 21; |
| s10 += carry9; |
| s9 -= carry9 << 21; |
| // carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; |
| carry11 = (s11 + (1 << 20)) >> 21; |
| s12 = carry11; |
| s11 -= carry11 << 21; |
| |
| s0 += s12 * 666643; |
| s1 += s12 * 470296; |
| s2 += s12 * 654183; |
| s3 -= s12 * 997805; |
| s4 += s12 * 136657; |
| s5 -= s12 * 683901; |
| // set below |
| // s12 = 0; |
| |
| carry0 = s0 >> 21; |
| s1 += carry0; |
| s0 -= carry0 << 21; |
| carry1 = s1 >> 21; |
| s2 += carry1; |
| s1 -= carry1 << 21; |
| carry2 = s2 >> 21; |
| s3 += carry2; |
| s2 -= carry2 << 21; |
| carry3 = s3 >> 21; |
| s4 += carry3; |
| s3 -= carry3 << 21; |
| carry4 = s4 >> 21; |
| s5 += carry4; |
| s4 -= carry4 << 21; |
| carry5 = s5 >> 21; |
| s6 += carry5; |
| s5 -= carry5 << 21; |
| carry6 = s6 >> 21; |
| s7 += carry6; |
| s6 -= carry6 << 21; |
| carry7 = s7 >> 21; |
| s8 += carry7; |
| s7 -= carry7 << 21; |
| carry8 = s8 >> 21; |
| s9 += carry8; |
| s8 -= carry8 << 21; |
| carry9 = s9 >> 21; |
| s10 += carry9; |
| s9 -= carry9 << 21; |
| carry10 = s10 >> 21; |
| s11 += carry10; |
| s10 -= carry10 << 21; |
| // carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; |
| carry11 = s11 >> 21; |
| s12 = carry11; |
| s11 -= carry11 << 21; |
| |
| s0 += s12 * 666643; |
| s1 += s12 * 470296; |
| s2 += s12 * 654183; |
| s3 -= s12 * 997805; |
| s4 += s12 * 136657; |
| s5 -= s12 * 683901; |
| // not used again |
| // s12 = 0; |
| |
| carry0 = s0 >> 21; |
| s1 += carry0; |
| s0 -= carry0 << 21; |
| carry1 = s1 >> 21; |
| s2 += carry1; |
| s1 -= carry1 << 21; |
| carry2 = s2 >> 21; |
| s3 += carry2; |
| s2 -= carry2 << 21; |
| carry3 = s3 >> 21; |
| s4 += carry3; |
| s3 -= carry3 << 21; |
| carry4 = s4 >> 21; |
| s5 += carry4; |
| s4 -= carry4 << 21; |
| carry5 = s5 >> 21; |
| s6 += carry5; |
| s5 -= carry5 << 21; |
| carry6 = s6 >> 21; |
| s7 += carry6; |
| s6 -= carry6 << 21; |
| carry7 = s7 >> 21; |
| s8 += carry7; |
| s7 -= carry7 << 21; |
| carry8 = s8 >> 21; |
| s9 += carry8; |
| s8 -= carry8 << 21; |
| carry9 = s9 >> 21; |
| s10 += carry9; |
| s9 -= carry9 << 21; |
| carry10 = s10 >> 21; |
| s11 += carry10; |
| s10 -= carry10 << 21; |
| |
| byte[] result = new byte[32]; |
| result[0] = (byte) s0; |
| result[1] = (byte) (s0 >> 8); |
| result[2] = (byte) ((s0 >> 16) | (s1 << 5)); |
| result[3] = (byte) (s1 >> 3); |
| result[4] = (byte) (s1 >> 11); |
| result[5] = (byte) ((s1 >> 19) | (s2 << 2)); |
| result[6] = (byte) (s2 >> 6); |
| result[7] = (byte) ((s2 >> 14) | (s3 << 7)); |
| result[8] = (byte) (s3 >> 1); |
| result[9] = (byte) (s3 >> 9); |
| result[10] = (byte) ((s3 >> 17) | (s4 << 4)); |
| result[11] = (byte) (s4 >> 4); |
| result[12] = (byte) (s4 >> 12); |
| result[13] = (byte) ((s4 >> 20) | (s5 << 1)); |
| result[14] = (byte) (s5 >> 7); |
| result[15] = (byte) ((s5 >> 15) | (s6 << 6)); |
| result[16] = (byte) (s6 >> 2); |
| result[17] = (byte) (s6 >> 10); |
| result[18] = (byte) ((s6 >> 18) | (s7 << 3)); |
| result[19] = (byte) (s7 >> 5); |
| result[20] = (byte) (s7 >> 13); |
| result[21] = (byte) s8; |
| result[22] = (byte) (s8 >> 8); |
| result[23] = (byte) ((s8 >> 16) | (s9 << 5)); |
| result[24] = (byte) (s9 >> 3); |
| result[25] = (byte) (s9 >> 11); |
| result[26] = (byte) ((s9 >> 19) | (s10 << 2)); |
| result[27] = (byte) (s10 >> 6); |
| result[28] = (byte) ((s10 >> 14) | (s11 << 7)); |
| result[29] = (byte) (s11 >> 1); |
| result[30] = (byte) (s11 >> 9); |
| result[31] = (byte) (s11 >> 17); |
| return result; |
| } |
| } |