Ed25519ScalarOps.java
/**
* 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 static org.mariadb.jdbc.plugin.authentication.standard.ed25519.math.ed25519.Ed25519LittleEndianEncoding.load_3;
import static org.mariadb.jdbc.plugin.authentication.standard.ed25519.math.ed25519.Ed25519LittleEndianEncoding.load_4;
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 & load_3(s, 0);
long s1 = 0x1FFFFF & (load_4(s, 2) >> 5);
long s2 = 0x1FFFFF & (load_3(s, 5) >> 2);
long s3 = 0x1FFFFF & (load_4(s, 7) >> 7);
long s4 = 0x1FFFFF & (load_4(s, 10) >> 4);
long s5 = 0x1FFFFF & (load_3(s, 13) >> 1);
long s6 = 0x1FFFFF & (load_4(s, 15) >> 6);
long s7 = 0x1FFFFF & (load_3(s, 18) >> 3);
long s8 = 0x1FFFFF & load_3(s, 21);
long s9 = 0x1FFFFF & (load_4(s, 23) >> 5);
long s10 = 0x1FFFFF & (load_3(s, 26) >> 2);
long s11 = 0x1FFFFF & (load_4(s, 28) >> 7);
long s12 = 0x1FFFFF & (load_4(s, 31) >> 4);
long s13 = 0x1FFFFF & (load_3(s, 34) >> 1);
long s14 = 0x1FFFFF & (load_4(s, 36) >> 6);
long s15 = 0x1FFFFF & (load_3(s, 39) >> 3);
long s16 = 0x1FFFFF & load_3(s, 42);
long s17 = 0x1FFFFF & (load_4(s, 44) >> 5);
long s18 = 0x1FFFFF & (load_3(s, 47) >> 2);
long s19 = 0x1FFFFF & (load_4(s, 49) >> 7);
long s20 = 0x1FFFFF & (load_4(s, 52) >> 4);
long s21 = 0x1FFFFF & (load_3(s, 55) >> 1);
long s22 = 0x1FFFFF & (load_4(s, 57) >> 6);
long s23 = (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;
/**
* Lots of magic numbers :) To understand what's going on below, note that
*
* <p>(1) q = 2^252 + q0 where q0 = 27742317777372353535851937790883648493. (2) s11 is the
* coefficient of 2^(11*21), s23 is the coefficient of 2^(^23*21) and 2^252 = 2^((23-11) * 21)).
* (3) 2^252 congruent -q0 modulo q. (4) -q0 = 666643 * 2^0 + 470296 * 2^21 + 654183 * 2^(2*21)
* - 997805 * 2^(3*21) + 136657 * 2^(4*21) - 683901 * 2^(5*21)
*
* <p>Thus s23 * 2^(23*11) = s23 * 2^(12*21) * 2^(11*21) = s3 * 2^252 * 2^(11*21) congruent s23
* * (666643 * 2^0 + 470296 * 2^21 + 654183 * 2^(2*21) - 997805 * 2^(3*21) + 136657 * 2^(4*21) -
* 683901 * 2^(5*21)) * 2^(11*21) modulo q = s23 * (666643 * 2^(11*21) + 470296 * 2^(12*21) +
* 654183 * 2^(13*21) - 997805 * 2^(14*21) + 136657 * 2^(15*21) - 683901 * 2^(16*21)).
*
* <p>The same procedure is then applied for s22,...,s18.
*/
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;
/** Time to reduce the coefficient in order not to get an overflow. */
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;
/** Continue with above procedure. */
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;
/** Reduce coefficients again. */
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 & load_3(a, 0);
long a1 = 0x1FFFFF & (load_4(a, 2) >> 5);
long a2 = 0x1FFFFF & (load_3(a, 5) >> 2);
long a3 = 0x1FFFFF & (load_4(a, 7) >> 7);
long a4 = 0x1FFFFF & (load_4(a, 10) >> 4);
long a5 = 0x1FFFFF & (load_3(a, 13) >> 1);
long a6 = 0x1FFFFF & (load_4(a, 15) >> 6);
long a7 = 0x1FFFFF & (load_3(a, 18) >> 3);
long a8 = 0x1FFFFF & load_3(a, 21);
long a9 = 0x1FFFFF & (load_4(a, 23) >> 5);
long a10 = 0x1FFFFF & (load_3(a, 26) >> 2);
long a11 = (load_4(a, 28) >> 7);
long b0 = 0x1FFFFF & load_3(b, 0);
long b1 = 0x1FFFFF & (load_4(b, 2) >> 5);
long b2 = 0x1FFFFF & (load_3(b, 5) >> 2);
long b3 = 0x1FFFFF & (load_4(b, 7) >> 7);
long b4 = 0x1FFFFF & (load_4(b, 10) >> 4);
long b5 = 0x1FFFFF & (load_3(b, 13) >> 1);
long b6 = 0x1FFFFF & (load_4(b, 15) >> 6);
long b7 = 0x1FFFFF & (load_3(b, 18) >> 3);
long b8 = 0x1FFFFF & load_3(b, 21);
long b9 = 0x1FFFFF & (load_4(b, 23) >> 5);
long b10 = 0x1FFFFF & (load_3(b, 26) >> 2);
long b11 = (load_4(b, 28) >> 7);
long c0 = 0x1FFFFF & load_3(c, 0);
long c1 = 0x1FFFFF & (load_4(c, 2) >> 5);
long c2 = 0x1FFFFF & (load_3(c, 5) >> 2);
long c3 = 0x1FFFFF & (load_4(c, 7) >> 7);
long c4 = 0x1FFFFF & (load_4(c, 10) >> 4);
long c5 = 0x1FFFFF & (load_3(c, 13) >> 1);
long c6 = 0x1FFFFF & (load_4(c, 15) >> 6);
long c7 = 0x1FFFFF & (load_3(c, 18) >> 3);
long c8 = 0x1FFFFF & load_3(c, 21);
long c9 = 0x1FFFFF & (load_4(c, 23) >> 5);
long c10 = 0x1FFFFF & (load_3(c, 26) >> 2);
long c11 = (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;
}
}