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ec_mulmuladd.cairo
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ec_mulmuladd.cairo
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//*************************************************************************************/
///* Copyright (C) 2022 - Renaud Dubois - This file is part of Cairo_musig2 project */
///* License: This software is licensed under a dual BSD and GPL v2 license. */
///* See LICENSE file at the root folder of the project. */
///* FILE: multipoint.cairo */
///* */
///* */
///* DESCRIPTION: optimization of dual base multiplication */
///* the algorithm combines the so called Shamir's trick with Windowing method */
//*************************************************************************************/
from starkware.cairo.common.cairo_secp.bigint import BigInt3
from src.secp256r1.ec import EcPoint, ec_add, ec_mul, ec_double
//Structure storing all aP+b.Q for (a,b) in [0..3]x[0..3]
struct Window {
G: EcPoint,
Q: EcPoint,
W3: EcPoint,
W4: EcPoint,
W5: EcPoint,
W6: EcPoint,
W7: EcPoint,
W8: EcPoint,
W9: EcPoint,
W10: EcPoint,
W11: EcPoint,
W12: EcPoint,
W13: EcPoint,
W14: EcPoint,
W15: EcPoint,
}
//https://crypto.stackexchange.com/questions/99975/strauss-shamir-trick-on-ec-multiplication-by-scalar,
//* Internal call for recursion of point multiplication via Shamir's trick+Windowed method */
func ec_mulmuladd_W_inner{range_check_ptr}(
R: EcPoint, Prec:Window,
scalar_u: felt, scalar_v: felt, m: felt,
computed_u: felt, computed_v: felt,
) -> (res: EcPoint, updated_u: felt, updated_v: felt) {
alloc_locals;
let mm2 = m-2;
if (m == -1) {
return (res=R, updated_u=computed_u, updated_v=computed_v);
}
//still have to make the last addition over 1 bit (initial length was odd)
if(m == 0){
let u0 = scalar_u - 2*computed_u;
let v0 = scalar_v - 2*computed_v;
let (double_point) = ec_double(R);
if (u0 == 0 and v0 == 0) {
return (res=double_point, updated_u=2*computed_u + 0, updated_v=2*computed_v + 0);
}
if (u0 == 1 and v0 == 0) {
let (res) = ec_add(double_point,Prec.G);
return (res=res, updated_u=2*computed_u + 1, updated_v=2*computed_v + 0);
}
if (u0 == 0 and v0 == 1) {
let (res)=ec_add(double_point,Prec.Q);
return (res=res, updated_u=2*computed_u + 0, updated_v=2*computed_v + 1);
}
assert u0 = 1;
assert v0 = 1;
let (res)=ec_add(double_point, Prec.W3);
return (res=res, updated_u=2*computed_u + 1, updated_v=2*computed_v + 1);
}
let (double_point) = ec_double(R);
let (quadruple_point) = ec_double(double_point);
// Extract bits
local dibit;
%{ ids.dibit = ((ids.scalar_u >> ids.m) & 1) + 2 * ((ids.scalar_v >> ids.m) & 1) %}
// 2 * v1 + u1
let dibit_1 = dibit;
local dibit;
local m = m - 1;
%{ ids.dibit = ((ids.scalar_u >> ids.m) & 1) + 2 * ((ids.scalar_v >> ids.m) & 1) %}
// 2 * v0 + u0
let dibit_0 = dibit;
if (dibit_0 == 0) {
if (dibit_1 == 0) {
return ec_mulmuladd_W_inner(quadruple_point, Prec, scalar_u, scalar_v, mm2, 4*computed_u, 4*computed_v);
}
if (dibit_1 == 1) {
let (ecTemp) = ec_add(quadruple_point,Prec.W4);
return ec_mulmuladd_W_inner(ecTemp, Prec, scalar_u, scalar_v, mm2, 4*computed_u + 2, 4*computed_v);
}
if (dibit_1 == 2) {
let (ecTemp) = ec_add(quadruple_point,Prec.W8);
return ec_mulmuladd_W_inner(ecTemp, Prec, scalar_u, scalar_v, mm2, 4*computed_u, 4*computed_v + 2);
}
assert dibit_1 = 3;
let (ecTemp) = ec_add(quadruple_point,Prec.W12);
return ec_mulmuladd_W_inner(ecTemp, Prec, scalar_u, scalar_v, mm2, 4*computed_u + 2, 4*computed_v + 2);
}
if (dibit_0 == 1) {
if (dibit_1 == 0) {
let (ecTemp) = ec_add(quadruple_point,Prec.G);
return ec_mulmuladd_W_inner(ecTemp, Prec, scalar_u, scalar_v, mm2, 4*computed_u + 1, 4*computed_v);
}
if (dibit_1 == 1) {
let (ecTemp) = ec_add(quadruple_point,Prec.W5);
return ec_mulmuladd_W_inner(ecTemp, Prec, scalar_u, scalar_v, mm2, 4*computed_u + 3, 4*computed_v);
}
if (dibit_1 == 2) {
let (ecTemp) = ec_add(quadruple_point,Prec.W9);
return ec_mulmuladd_W_inner(ecTemp, Prec, scalar_u, scalar_v, mm2, 4*computed_u + 1, 4*computed_v + 2);
}
assert dibit_1 = 3;
let (ecTemp) = ec_add(quadruple_point,Prec.W13);
return ec_mulmuladd_W_inner(ecTemp, Prec, scalar_u, scalar_v, mm2, 4*computed_u + 3, 4*computed_v + 2);
}
if (dibit_0 == 2) {
if (dibit_1 == 0) {
let (ecTemp) = ec_add(quadruple_point,Prec.Q);
return ec_mulmuladd_W_inner(ecTemp, Prec, scalar_u, scalar_v, mm2, 4*computed_u, 4*computed_v + 1);
}
if (dibit_1 == 1) {
let (ecTemp) = ec_add(quadruple_point,Prec.W6);
return ec_mulmuladd_W_inner(ecTemp, Prec, scalar_u, scalar_v, mm2, 4*computed_u + 2, 4*computed_v + 1);
}
if (dibit_1 == 2) {
let (ecTemp) = ec_add(quadruple_point,Prec.W10);
return ec_mulmuladd_W_inner(ecTemp, Prec, scalar_u, scalar_v, mm2, 4*computed_u, 4*computed_v + 3);
}
assert dibit_1 = 3;
let (ecTemp) = ec_add(quadruple_point,Prec.W14);
return ec_mulmuladd_W_inner(ecTemp, Prec, scalar_u, scalar_v, mm2, 4*computed_u + 2, 4*computed_v + 3);
}
assert dibit_0 = 3;
if (dibit_1 == 0) {
let (ecTemp) = ec_add(quadruple_point,Prec.W3);
return ec_mulmuladd_W_inner(ecTemp, Prec, scalar_u, scalar_v, mm2, 4*computed_u + 1, 4*computed_v + 1);
}
if (dibit_1 == 1) {
let (ecTemp) = ec_add(quadruple_point,Prec.W7);
return ec_mulmuladd_W_inner(ecTemp, Prec, scalar_u, scalar_v, mm2, 4*computed_u + 3, 4*computed_v + 1);
}
if (dibit_1 == 2) {
let (ecTemp) = ec_add(quadruple_point,Prec.W11);
return ec_mulmuladd_W_inner(ecTemp, Prec, scalar_u, scalar_v, mm2, 4*computed_u + 1, 4*computed_v + 3);
}
assert dibit_1 = 3;
let (ecTemp) = ec_add(quadruple_point,Prec.W15);
return ec_mulmuladd_W_inner(ecTemp, Prec, scalar_u, scalar_v, mm2, 4*computed_u + 3 , 4*computed_v + 3);
}