ScMulAdd function Null safety

void ScMulAdd(
  1. Uint8List s,
  2. Uint8List a,
  3. Uint8List b,
  4. Uint8List c
)

The scalars are GF(2^252 + 27742317777372353535851937790883648493). Input: a0+256a1+...+256^31a31 = a b0+256b1+...+256^31b31 = b c0+256c1+...+256^31c31 = c

Output: s0+256s1+...+256^31s31 = (ab+c) mod l where l = 2^252 + 27742317777372353535851937790883648493.

Implementation

/// Input:
///   a[0]+256*a[1]+...+256^31*a[31] = a
///   b[0]+256*b[1]+...+256^31*b[31] = b
///   c[0]+256*c[1]+...+256^31*c[31] = c
///
/// Output:
///   s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
///   where l = 2^252 + 27742317777372353535851937790883648493.
void ScMulAdd(Uint8List s, Uint8List a, Uint8List b, Uint8List c) {
  var a0 = 2097151 & load3(a.sublist(0, a.length));
  var a1 = 2097151 & (load4(a.sublist(2, a.length)) >> 5);
  var a2 = 2097151 & (load3(a.sublist(5, a.length)) >> 2);
  var a3 = 2097151 & (load4(a.sublist(7, a.length)) >> 7);
  var a4 = 2097151 & (load4(a.sublist(10, a.length)) >> 4);
  var a5 = 2097151 & (load3(a.sublist(13, a.length)) >> 1);
  var a6 = 2097151 & (load4(a.sublist(15, a.length)) >> 6);
  var a7 = 2097151 & (load3(a.sublist(18, a.length)) >> 3);
  var a8 = 2097151 & load3(a.sublist(21, a.length));
  var a9 = 2097151 & (load4(a.sublist(23, a.length)) >> 5);
  var a10 = 2097151 & (load3(a.sublist(26, a.length)) >> 2);
  var a11 = (load4(a.sublist(28, a.length)) >> 7);

  var b0 = 2097151 & load3(b.sublist(0, b.length));
  var b1 = 2097151 & (load4(b.sublist(2, b.length)) >> 5);
  var b2 = 2097151 & (load3(b.sublist(5, b.length)) >> 2);
  var b3 = 2097151 & (load4(b.sublist(7, b.length)) >> 7);
  var b4 = 2097151 & (load4(b.sublist(10, b.length)) >> 4);
  var b5 = 2097151 & (load3(b.sublist(13, b.length)) >> 1);
  var b6 = 2097151 & (load4(b.sublist(15, b.length)) >> 6);
  var b7 = 2097151 & (load3(b.sublist(18, b.length)) >> 3);
  var b8 = 2097151 & load3(b.sublist(21, b.length));
  var b9 = 2097151 & (load4(b.sublist(23, b.length)) >> 5);
  var b10 = 2097151 & (load3(b.sublist(26, b.length)) >> 2);
  var b11 = (load4(b.sublist(28, b.length)) >> 7);

  var c0 = 2097151 & load3(c.sublist(0, c.length));
  var c1 = 2097151 & (load4(c.sublist(2, c.length)) >> 5);
  var c2 = 2097151 & (load3(c.sublist(5, c.length)) >> 2);
  var c3 = 2097151 & (load4(c.sublist(7, c.length)) >> 7);
  var c4 = 2097151 & (load4(c.sublist(10, c.length)) >> 4);
  var c5 = 2097151 & (load3(c.sublist(13, c.length)) >> 1);
  var c6 = 2097151 & (load4(c.sublist(15, c.length)) >> 6);
  var c7 = 2097151 & (load3(c.sublist(18, c.length)) >> 3);
  var c8 = 2097151 & load3(c.sublist(21, c.length));
  var c9 = 2097151 & (load4(c.sublist(23, c.length)) >> 5);
  var c10 = 2097151 & (load3(c.sublist(26, c.length)) >> 2);
  var c11 = (load4(c.sublist(28, c.length)) >> 7);

  var carry = List<int>.filled(23, 0);

  var s0 = c0 + a0 * b0;
  var s1 = c1 + a0 * b1 + a1 * b0;
  var s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
  var s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
  var s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
  var s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
  var s6 =
      c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
  var s7 = c7 +
      a0 * b7 +
      a1 * b6 +
      a2 * b5 +
      a3 * b4 +
      a4 * b3 +
      a5 * b2 +
      a6 * b1 +
      a7 * b0;
  var s8 = c8 +
      a0 * b8 +
      a1 * b7 +
      a2 * b6 +
      a3 * b5 +
      a4 * b4 +
      a5 * b3 +
      a6 * b2 +
      a7 * b1 +
      a8 * b0;
  var s9 = c9 +
      a0 * b9 +
      a1 * b8 +
      a2 * b7 +
      a3 * b6 +
      a4 * b5 +
      a5 * b4 +
      a6 * b3 +
      a7 * b2 +
      a8 * b1 +
      a9 * b0;
  var s10 = c10 +
      a0 * b10 +
      a1 * b9 +
      a2 * b8 +
      a3 * b7 +
      a4 * b6 +
      a5 * b5 +
      a6 * b4 +
      a7 * b3 +
      a8 * b2 +
      a9 * b1 +
      a10 * b0;
  var 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;
  var s12 = a1 * b11 +
      a2 * b10 +
      a3 * b9 +
      a4 * b8 +
      a5 * b7 +
      a6 * b6 +
      a7 * b5 +
      a8 * b4 +
      a9 * b3 +
      a10 * b2 +
      a11 * b1;
  var s13 = a2 * b11 +
      a3 * b10 +
      a4 * b9 +
      a5 * b8 +
      a6 * b7 +
      a7 * b6 +
      a8 * b5 +
      a9 * b4 +
      a10 * b3 +
      a11 * b2;
  var s14 = a3 * b11 +
      a4 * b10 +
      a5 * b9 +
      a6 * b8 +
      a7 * b7 +
      a8 * b6 +
      a9 * b5 +
      a10 * b4 +
      a11 * b3;
  var s15 = a4 * b11 +
      a5 * b10 +
      a6 * b9 +
      a7 * b8 +
      a8 * b7 +
      a9 * b6 +
      a10 * b5 +
      a11 * b4;
  var s16 =
      a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
  var s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
  var s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
  var s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
  var s20 = a9 * b11 + a10 * b10 + a11 * b9;
  var s21 = a10 * b11 + a11 * b10;
  var s22 = a11 * b11;
  var s23 = 0;

  carry[0] = (s0 + (1 << 20)) >> 21;
  s1 += carry[0];
  s0 -= carry[0] << 21;
  carry[2] = (s2 + (1 << 20)) >> 21;
  s3 += carry[2];
  s2 -= carry[2] << 21;
  carry[4] = (s4 + (1 << 20)) >> 21;
  s5 += carry[4];
  s4 -= carry[4] << 21;
  carry[6] = (s6 + (1 << 20)) >> 21;
  s7 += carry[6];
  s6 -= carry[6] << 21;
  carry[8] = (s8 + (1 << 20)) >> 21;
  s9 += carry[8];
  s8 -= carry[8] << 21;
  carry[10] = (s10 + (1 << 20)) >> 21;
  s11 += carry[10];
  s10 -= carry[10] << 21;
  carry[12] = (s12 + (1 << 20)) >> 21;
  s13 += carry[12];
  s12 -= carry[12] << 21;
  carry[14] = (s14 + (1 << 20)) >> 21;
  s15 += carry[14];
  s14 -= carry[14] << 21;
  carry[16] = (s16 + (1 << 20)) >> 21;
  s17 += carry[16];
  s16 -= carry[16] << 21;
  carry[18] = (s18 + (1 << 20)) >> 21;
  s19 += carry[18];
  s18 -= carry[18] << 21;
  carry[20] = (s20 + (1 << 20)) >> 21;
  s21 += carry[20];
  s20 -= carry[20] << 21;
  carry[22] = (s22 + (1 << 20)) >> 21;
  s23 += carry[22];
  s22 -= carry[22] << 21;

  carry[1] = (s1 + (1 << 20)) >> 21;
  s2 += carry[1];
  s1 -= carry[1] << 21;
  carry[3] = (s3 + (1 << 20)) >> 21;
  s4 += carry[3];
  s3 -= carry[3] << 21;
  carry[5] = (s5 + (1 << 20)) >> 21;
  s6 += carry[5];
  s5 -= carry[5] << 21;
  carry[7] = (s7 + (1 << 20)) >> 21;
  s8 += carry[7];
  s7 -= carry[7] << 21;
  carry[9] = (s9 + (1 << 20)) >> 21;
  s10 += carry[9];
  s9 -= carry[9] << 21;
  carry[11] = (s11 + (1 << 20)) >> 21;
  s12 += carry[11];
  s11 -= carry[11] << 21;
  carry[13] = (s13 + (1 << 20)) >> 21;
  s14 += carry[13];
  s13 -= carry[13] << 21;
  carry[15] = (s15 + (1 << 20)) >> 21;
  s16 += carry[15];
  s15 -= carry[15] << 21;
  carry[17] = (s17 + (1 << 20)) >> 21;
  s18 += carry[17];
  s17 -= carry[17] << 21;
  carry[19] = (s19 + (1 << 20)) >> 21;
  s20 += carry[19];
  s19 -= carry[19] << 21;
  carry[21] = (s21 + (1 << 20)) >> 21;
  s22 += carry[21];
  s21 -= carry[21] << 21;

  s11 += s23 * 666643;
  s12 += s23 * 470296;
  s13 += s23 * 654183;
  s14 -= s23 * 997805;
  s15 += s23 * 136657;
  s16 -= s23 * 683901;
  s23 = 0;

  s10 += s22 * 666643;
  s11 += s22 * 470296;
  s12 += s22 * 654183;
  s13 -= s22 * 997805;
  s14 += s22 * 136657;
  s15 -= s22 * 683901;
  s22 = 0;

  s9 += s21 * 666643;
  s10 += s21 * 470296;
  s11 += s21 * 654183;
  s12 -= s21 * 997805;
  s13 += s21 * 136657;
  s14 -= s21 * 683901;
  s21 = 0;

  s8 += s20 * 666643;
  s9 += s20 * 470296;
  s10 += s20 * 654183;
  s11 -= s20 * 997805;
  s12 += s20 * 136657;
  s13 -= s20 * 683901;
  s20 = 0;

  s7 += s19 * 666643;
  s8 += s19 * 470296;
  s9 += s19 * 654183;
  s10 -= s19 * 997805;
  s11 += s19 * 136657;
  s12 -= s19 * 683901;
  s19 = 0;

  s6 += s18 * 666643;
  s7 += s18 * 470296;
  s8 += s18 * 654183;
  s9 -= s18 * 997805;
  s10 += s18 * 136657;
  s11 -= s18 * 683901;
  s18 = 0;

  carry[6] = (s6 + (1 << 20)) >> 21;
  s7 += carry[6];
  s6 -= carry[6] << 21;
  carry[8] = (s8 + (1 << 20)) >> 21;
  s9 += carry[8];
  s8 -= carry[8] << 21;
  carry[10] = (s10 + (1 << 20)) >> 21;
  s11 += carry[10];
  s10 -= carry[10] << 21;
  carry[12] = (s12 + (1 << 20)) >> 21;
  s13 += carry[12];
  s12 -= carry[12] << 21;
  carry[14] = (s14 + (1 << 20)) >> 21;
  s15 += carry[14];
  s14 -= carry[14] << 21;
  carry[16] = (s16 + (1 << 20)) >> 21;
  s17 += carry[16];
  s16 -= carry[16] << 21;

  carry[7] = (s7 + (1 << 20)) >> 21;
  s8 += carry[7];
  s7 -= carry[7] << 21;
  carry[9] = (s9 + (1 << 20)) >> 21;
  s10 += carry[9];
  s9 -= carry[9] << 21;
  carry[11] = (s11 + (1 << 20)) >> 21;
  s12 += carry[11];
  s11 -= carry[11] << 21;
  carry[13] = (s13 + (1 << 20)) >> 21;
  s14 += carry[13];
  s13 -= carry[13] << 21;
  carry[15] = (s15 + (1 << 20)) >> 21;
  s16 += carry[15];
  s15 -= carry[15] << 21;

  s5 += s17 * 666643;
  s6 += s17 * 470296;
  s7 += s17 * 654183;
  s8 -= s17 * 997805;
  s9 += s17 * 136657;
  s10 -= s17 * 683901;
  s17 = 0;

  s4 += s16 * 666643;
  s5 += s16 * 470296;
  s6 += s16 * 654183;
  s7 -= s16 * 997805;
  s8 += s16 * 136657;
  s9 -= s16 * 683901;
  s16 = 0;

  s3 += s15 * 666643;
  s4 += s15 * 470296;
  s5 += s15 * 654183;
  s6 -= s15 * 997805;
  s7 += s15 * 136657;
  s8 -= s15 * 683901;
  s15 = 0;

  s2 += s14 * 666643;
  s3 += s14 * 470296;
  s4 += s14 * 654183;
  s5 -= s14 * 997805;
  s6 += s14 * 136657;
  s7 -= s14 * 683901;
  s14 = 0;

  s1 += s13 * 666643;
  s2 += s13 * 470296;
  s3 += s13 * 654183;
  s4 -= s13 * 997805;
  s5 += s13 * 136657;
  s6 -= s13 * 683901;
  s13 = 0;

  s0 += s12 * 666643;
  s1 += s12 * 470296;
  s2 += s12 * 654183;
  s3 -= s12 * 997805;
  s4 += s12 * 136657;
  s5 -= s12 * 683901;
  s12 = 0;

  carry[0] = (s0 + (1 << 20)) >> 21;
  s1 += carry[0];
  s0 -= carry[0] << 21;
  carry[2] = (s2 + (1 << 20)) >> 21;
  s3 += carry[2];
  s2 -= carry[2] << 21;
  carry[4] = (s4 + (1 << 20)) >> 21;
  s5 += carry[4];
  s4 -= carry[4] << 21;
  carry[6] = (s6 + (1 << 20)) >> 21;
  s7 += carry[6];
  s6 -= carry[6] << 21;
  carry[8] = (s8 + (1 << 20)) >> 21;
  s9 += carry[8];
  s8 -= carry[8] << 21;
  carry[10] = (s10 + (1 << 20)) >> 21;
  s11 += carry[10];
  s10 -= carry[10] << 21;

  carry[1] = (s1 + (1 << 20)) >> 21;
  s2 += carry[1];
  s1 -= carry[1] << 21;
  carry[3] = (s3 + (1 << 20)) >> 21;
  s4 += carry[3];
  s3 -= carry[3] << 21;
  carry[5] = (s5 + (1 << 20)) >> 21;
  s6 += carry[5];
  s5 -= carry[5] << 21;
  carry[7] = (s7 + (1 << 20)) >> 21;
  s8 += carry[7];
  s7 -= carry[7] << 21;
  carry[9] = (s9 + (1 << 20)) >> 21;
  s10 += carry[9];
  s9 -= carry[9] << 21;
  carry[11] = (s11 + (1 << 20)) >> 21;
  s12 += carry[11];
  s11 -= carry[11] << 21;

  s0 += s12 * 666643;
  s1 += s12 * 470296;
  s2 += s12 * 654183;
  s3 -= s12 * 997805;
  s4 += s12 * 136657;
  s5 -= s12 * 683901;
  s12 = 0;

  carry[0] = s0 >> 21;
  s1 += carry[0];
  s0 -= carry[0] << 21;
  carry[1] = s1 >> 21;
  s2 += carry[1];
  s1 -= carry[1] << 21;
  carry[2] = s2 >> 21;
  s3 += carry[2];
  s2 -= carry[2] << 21;
  carry[3] = s3 >> 21;
  s4 += carry[3];
  s3 -= carry[3] << 21;
  carry[4] = s4 >> 21;
  s5 += carry[4];
  s4 -= carry[4] << 21;
  carry[5] = s5 >> 21;
  s6 += carry[5];
  s5 -= carry[5] << 21;
  carry[6] = s6 >> 21;
  s7 += carry[6];
  s6 -= carry[6] << 21;
  carry[7] = s7 >> 21;
  s8 += carry[7];
  s7 -= carry[7] << 21;
  carry[8] = s8 >> 21;
  s9 += carry[8];
  s8 -= carry[8] << 21;
  carry[9] = s9 >> 21;
  s10 += carry[9];
  s9 -= carry[9] << 21;
  carry[10] = s10 >> 21;
  s11 += carry[10];
  s10 -= carry[10] << 21;
  carry[11] = s11 >> 21;
  s12 += carry[11];
  s11 -= carry[11] << 21;

  s0 += s12 * 666643;
  s1 += s12 * 470296;
  s2 += s12 * 654183;
  s3 -= s12 * 997805;
  s4 += s12 * 136657;
  s5 -= s12 * 683901;
  s12 = 0;

  carry[0] = s0 >> 21;
  s1 += carry[0];
  s0 -= carry[0] << 21;
  carry[1] = s1 >> 21;
  s2 += carry[1];
  s1 -= carry[1] << 21;
  carry[2] = s2 >> 21;
  s3 += carry[2];
  s2 -= carry[2] << 21;
  carry[3] = s3 >> 21;
  s4 += carry[3];
  s3 -= carry[3] << 21;
  carry[4] = s4 >> 21;
  s5 += carry[4];
  s4 -= carry[4] << 21;
  carry[5] = s5 >> 21;
  s6 += carry[5];
  s5 -= carry[5] << 21;
  carry[6] = s6 >> 21;
  s7 += carry[6];
  s6 -= carry[6] << 21;
  carry[7] = s7 >> 21;
  s8 += carry[7];
  s7 -= carry[7] << 21;
  carry[8] = s8 >> 21;
  s9 += carry[8];
  s8 -= carry[8] << 21;
  carry[9] = s9 >> 21;
  s10 += carry[9];
  s9 -= carry[9] << 21;
  carry[10] = s10 >> 21;
  s11 += carry[10];
  s10 -= carry[10] << 21;

  s[0] = s0 >> 0;
  s[1] = s0 >> 8;
  s[2] = (s0 >> 16) | (s1 << 5);
  s[3] = s1 >> 3;
  s[4] = s1 >> 11;
  s[5] = (s1 >> 19) | (s2 << 2);
  s[6] = s2 >> 6;
  s[7] = (s2 >> 14) | (s3 << 7);
  s[8] = s3 >> 1;
  s[9] = s3 >> 9;
  s[10] = (s3 >> 17) | (s4 << 4);
  s[11] = s4 >> 4;
  s[12] = s4 >> 12;
  s[13] = (s4 >> 20) | (s5 << 1);
  s[14] = s5 >> 7;
  s[15] = (s5 >> 15) | (s6 << 6);
  s[16] = s6 >> 2;
  s[17] = s6 >> 10;
  s[18] = (s6 >> 18) | (s7 << 3);
  s[19] = s7 >> 5;
  s[20] = s7 >> 13;
  s[21] = s8 >> 0;
  s[22] = s8 >> 8;
  s[23] = (s8 >> 16) | (s9 << 5);
  s[24] = s9 >> 3;
  s[25] = s9 >> 11;
  s[26] = (s9 >> 19) | (s10 << 2);
  s[27] = s10 >> 6;
  s[28] = (s10 >> 14) | (s11 << 7);
  s[29] = s11 >> 1;
  s[30] = s11 >> 9;
  s[31] = s11 >> 17;
}