diff --git a/mpy-modules/curve25519/arithmetic.c b/mpy-modules/curve25519/arithmetic.c index cac13af..8fa15e3 100644 --- a/mpy-modules/curve25519/arithmetic.c +++ b/mpy-modules/curve25519/arithmetic.c @@ -1,4 +1,5 @@ -#include "py/dynruntime.h" +#include "stdint.h" +#include "ec.h" uint32_t add_zxy(uint32_t *z, uint32_t *x, uint32_t *y) { @@ -179,7 +180,7 @@ void mul_add_zx0y0(uint32_t *z, uint32_t x, uint32_t y) { void pu_add_shift(uint32_t *t, uint32_t u) { // computes t = (t + (2^255 -19) * u) >> 32 __asm__ volatile ( - "MOV r3, 19\n" + "MOV r3, %2\n" "UMULL r5, r6, r3, %1\n" "MOV r2, 0\n" "LSRS %1, %1, 1\n" @@ -224,7 +225,7 @@ void pu_add_shift(uint32_t *t, uint32_t u) { "STMIA r2!, {r4}\n" "STMIA r2, {r5}\n" // ms-word = 0 //"SUBS %0, %0, 32\n" - : : "r" (t), "r" (u) : "r2", "r3", "r4", "r5", "r6" + : : "r" (t), "r" (u) , "r" (DIFF_P) : "r2", "r3", "r4", "r5", "r6" ); } @@ -238,7 +239,7 @@ void mont_mul_zxy_mod_p(uint32_t *z, uint32_t *x, uint32_t *y, uint32_t *p) { for (int i=0; i<9; i++) a[i] = 0; for (int i=0; i<8; i++) { - u = (a[0] + x[i] * y[0]) * 678152731; + u = (a[0] + x[i] * y[0]) * MINUS_IM; mul_add_zxy(a, y, x[i]); // A <- A + xi y pu_add_shift(a, u); // A <- (A + u m) / b } @@ -256,7 +257,7 @@ void mont_mul_zxy0_mod_p(uint32_t *z, uint32_t *x, uint32_t y, uint32_t *p) { for (int i=0; i<9; i++) a[i] = 0; for (int i=0; i<8; i++) { - u = (a[0] + x[i] * y) * 678152731; + u = (a[0] + x[i] * y) * MINUS_IM; mul_add_zx0y0(a, y, x[i]); // A <- A + xi y pu_add_shift(a, u); // A <- (A + u m) / b } diff --git a/mpy-modules/curve25519/arithmetic.h b/mpy-modules/curve25519/arithmetic.h index 022d019..b7e4301 100644 --- a/mpy-modules/curve25519/arithmetic.h +++ b/mpy-modules/curve25519/arithmetic.h @@ -1,11 +1,8 @@ #ifndef __arithmetic__ #define __arithmetic__ -void shift_right(uint32_t *x); void add_zxy_mod_p(uint32_t *z, uint32_t *x, uint32_t *y, uint32_t *p); void sub_zxy_mod_p(uint32_t *z, uint32_t *x, uint32_t *y, uint32_t *p); -void mul_zxy(uint32_t *z, uint32_t *x, uint32_t y); -void mul_zx0y0(uint32_t *z, uint32_t x, uint32_t y); void mont_mul_zxy_mod_p(uint32_t *z, uint32_t *x, uint32_t *y, uint32_t *p); void mont_mul_zxy0_mod_p(uint32_t *z, uint32_t *x, uint32_t y, uint32_t *p); diff --git a/mpy-modules/curve25519/ec.c b/mpy-modules/curve25519/ec.c index 0a3cd41..78e593f 100644 --- a/mpy-modules/curve25519/ec.c +++ b/mpy-modules/curve25519/ec.c @@ -8,13 +8,7 @@ const uint32_t pR2 = 0x5a4; const uint32_t R = 38; const uint32_t sqrt_minus_486664R[8] = {0x4038adb9, 0xa83f001e, 0xc1bcaf57, 0x688c332e, 0xa9fa8eee, 0xcb6e1095, 0xa7ab4e9e, 0x1baf4abd}; -struct curve { - uint32_t a24; - uint32_t p[8]; - uint32_t pR2; -}; - -struct curve Curve; +uint32_t Curve_p[8]; void random_z(uint32_t *z) { // TODO: a true random source should be provided @@ -24,24 +18,22 @@ void random_z(uint32_t *z) { void ini_curve() { - Curve.a24 = a24R; - Curve.pR2 = pR2; for (int i=0; i<8; i++) { - Curve.p[i] = p[7-i]; + Curve_p[i] = p[7-i]; } } void to_Montgomery(uint32_t *x) { uint32_t s[8]; - mont_mul_zxy0_mod_p(s, x, Curve.pR2, Curve.p); + mont_mul_zxy0_mod_p(s, x, pR2, Curve_p); for (uint32_t i=0;i<8;i++) x[i] = s[i]; } void from_Montgomery(uint32_t *x) { uint32_t s[8]; - mont_mul_zxy0_mod_p(s, x, 1, Curve.p); + mont_mul_zxy0_mod_p(s, x, 1, Curve_p); for (uint32_t i=0;i<8;i++) x[i] = s[i]; } @@ -59,75 +51,75 @@ void mod_inverse(uint32_t *z_inv, uint32_t *z) { uint32_t t1[8]; uint32_t i; - mont_mul_zxy_mod_p(z2, z, z, Curve.p); // 2 - mont_mul_zxy_mod_p(t1, z2, z2, Curve.p); // 4 - mont_mul_zxy_mod_p(t0, t1, t1, Curve.p); // 8 - mont_mul_zxy_mod_p(z9, t0, z, Curve.p); // 9 - mont_mul_zxy_mod_p(z11, z9, z2, Curve.p); // 11 - mont_mul_zxy_mod_p(t0, z11, z11, Curve.p); // 22 - mont_mul_zxy_mod_p(z2_5_0, t0, z9, Curve.p); // 31 = 2^5 - 2^0 + mont_mul_zxy_mod_p(z2, z, z, Curve_p); // 2 + mont_mul_zxy_mod_p(t1, z2, z2, Curve_p); // 4 + mont_mul_zxy_mod_p(t0, t1, t1, Curve_p); // 8 + mont_mul_zxy_mod_p(z9, t0, z, Curve_p); // 9 + mont_mul_zxy_mod_p(z11, z9, z2, Curve_p); // 11 + mont_mul_zxy_mod_p(t0, z11, z11, Curve_p); // 22 + mont_mul_zxy_mod_p(z2_5_0, t0, z9, Curve_p); // 31 = 2^5 - 2^0 - mont_mul_zxy_mod_p(t0, z2_5_0, z2_5_0, Curve.p); // 2^6 - 2^1 - mont_mul_zxy_mod_p(t1, t0, t0, Curve.p); // 2^7 - 2^2 - mont_mul_zxy_mod_p(t0, t1, t1, Curve.p); // 2^8 - 2^3 - mont_mul_zxy_mod_p(t1, t0, t0, Curve.p); // 2^9 - 2^4 - mont_mul_zxy_mod_p(t0, t1, t1, Curve.p); // 2^10 - 2^5 - mont_mul_zxy_mod_p(z2_10_0, t0, z2_5_0, Curve.p); // 2^10 - 2^0 + mont_mul_zxy_mod_p(t0, z2_5_0, z2_5_0, Curve_p); // 2^6 - 2^1 + mont_mul_zxy_mod_p(t1, t0, t0, Curve_p); // 2^7 - 2^2 + mont_mul_zxy_mod_p(t0, t1, t1, Curve_p); // 2^8 - 2^3 + mont_mul_zxy_mod_p(t1, t0, t0, Curve_p); // 2^9 - 2^4 + mont_mul_zxy_mod_p(t0, t1, t1, Curve_p); // 2^10 - 2^5 + mont_mul_zxy_mod_p(z2_10_0, t0, z2_5_0, Curve_p); // 2^10 - 2^0 - mont_mul_zxy_mod_p(t0, z2_10_0, z2_10_0, Curve.p); // 2^11 - 2^1 - mont_mul_zxy_mod_p(t1, t0, t0, Curve.p); // 2^12 - 2^2 + mont_mul_zxy_mod_p(t0, z2_10_0, z2_10_0, Curve_p); // 2^11 - 2^1 + mont_mul_zxy_mod_p(t1, t0, t0, Curve_p); // 2^12 - 2^2 for (i = 2; i < 10; i += 2) { - mont_mul_zxy_mod_p(t0, t1, t1, Curve.p); - mont_mul_zxy_mod_p(t1, t0, t0, Curve.p); + mont_mul_zxy_mod_p(t0, t1, t1, Curve_p); + mont_mul_zxy_mod_p(t1, t0, t0, Curve_p); } // 2^20 - 2^10 - mont_mul_zxy_mod_p(z2_20_0, t1, z2_10_0, Curve.p); // 2^20 - 2^0 + mont_mul_zxy_mod_p(z2_20_0, t1, z2_10_0, Curve_p); // 2^20 - 2^0 - mont_mul_zxy_mod_p(t0, z2_20_0, z2_20_0, Curve.p); // 2^21 - 2^1 - mont_mul_zxy_mod_p(t1, t0, t0, Curve.p); // 2^22 - 2^2 + mont_mul_zxy_mod_p(t0, z2_20_0, z2_20_0, Curve_p); // 2^21 - 2^1 + mont_mul_zxy_mod_p(t1, t0, t0, Curve_p); // 2^22 - 2^2 for (i = 2; i < 20; i += 2) { - mont_mul_zxy_mod_p(t0, t1, t1, Curve.p); - mont_mul_zxy_mod_p(t1, t0, t0, Curve.p); + mont_mul_zxy_mod_p(t0, t1, t1, Curve_p); + mont_mul_zxy_mod_p(t1, t0, t0, Curve_p); } // 2^40 - 2^20 - mont_mul_zxy_mod_p(t0, t1, z2_20_0, Curve.p); // 2^40 - 2^0 + mont_mul_zxy_mod_p(t0, t1, z2_20_0, Curve_p); // 2^40 - 2^0 - mont_mul_zxy_mod_p(t1, t0, t0, Curve.p); // 2^41 - 2^1 - mont_mul_zxy_mod_p(t0, t1, t1, Curve.p); // 2^42 - 2^2 + mont_mul_zxy_mod_p(t1, t0, t0, Curve_p); // 2^41 - 2^1 + mont_mul_zxy_mod_p(t0, t1, t1, Curve_p); // 2^42 - 2^2 for (i = 2; i < 10; i += 2) { - mont_mul_zxy_mod_p(t1, t0, t0, Curve.p); - mont_mul_zxy_mod_p(t0, t1, t1, Curve.p); + mont_mul_zxy_mod_p(t1, t0, t0, Curve_p); + mont_mul_zxy_mod_p(t0, t1, t1, Curve_p); } // 2^50 - 2^10 - mont_mul_zxy_mod_p(z2_50_0, t0, z2_10_0, Curve.p); // 2^50 - 2^0 + mont_mul_zxy_mod_p(z2_50_0, t0, z2_10_0, Curve_p); // 2^50 - 2^0 - mont_mul_zxy_mod_p(t0, z2_50_0, z2_50_0, Curve.p); // 2^51 - 2^1 - mont_mul_zxy_mod_p(t1, t0, t0, Curve.p); // 2^42 - 2^2 + mont_mul_zxy_mod_p(t0, z2_50_0, z2_50_0, Curve_p); // 2^51 - 2^1 + mont_mul_zxy_mod_p(t1, t0, t0, Curve_p); // 2^42 - 2^2 for (i = 2; i < 50; i += 2) { - mont_mul_zxy_mod_p(t0, t1, t1, Curve.p); - mont_mul_zxy_mod_p(t1, t0, t0, Curve.p); + mont_mul_zxy_mod_p(t0, t1, t1, Curve_p); + mont_mul_zxy_mod_p(t1, t0, t0, Curve_p); } // 2^100 - 2^50 - mont_mul_zxy_mod_p(z2_100_0, t1, z2_50_0, Curve.p); // 2^100 - 2^0 + mont_mul_zxy_mod_p(z2_100_0, t1, z2_50_0, Curve_p); // 2^100 - 2^0 - mont_mul_zxy_mod_p(t1, z2_100_0, z2_100_0, Curve.p); // 2^101 - 2^1 - mont_mul_zxy_mod_p(t0, t1, t1, Curve.p); // 2^102 - 2^2 + mont_mul_zxy_mod_p(t1, z2_100_0, z2_100_0, Curve_p); // 2^101 - 2^1 + mont_mul_zxy_mod_p(t0, t1, t1, Curve_p); // 2^102 - 2^2 for (i = 2; i < 100; i += 2) { - mont_mul_zxy_mod_p(t1, t0, t0, Curve.p); - mont_mul_zxy_mod_p(t0, t1, t1, Curve.p); + mont_mul_zxy_mod_p(t1, t0, t0, Curve_p); + mont_mul_zxy_mod_p(t0, t1, t1, Curve_p); } // 2^200 - 2^100 - mont_mul_zxy_mod_p(t1, t0, z2_100_0, Curve.p); // 2^200 - 2^0 + mont_mul_zxy_mod_p(t1, t0, z2_100_0, Curve_p); // 2^200 - 2^0 - mont_mul_zxy_mod_p(t0, t1, t1, Curve.p); // 2^201 - 2^1 - mont_mul_zxy_mod_p(t1, t0, t0, Curve.p); // 2^102 - 2^2 + mont_mul_zxy_mod_p(t0, t1, t1, Curve_p); // 2^201 - 2^1 + mont_mul_zxy_mod_p(t1, t0, t0, Curve_p); // 2^102 - 2^2 for (i = 2; i < 50; i += 2) { - mont_mul_zxy_mod_p(t0, t1, t1, Curve.p); - mont_mul_zxy_mod_p(t1, t0, t0, Curve.p); + mont_mul_zxy_mod_p(t0, t1, t1, Curve_p); + mont_mul_zxy_mod_p(t1, t0, t0, Curve_p); } // 2^250 - 2^50 - mont_mul_zxy_mod_p(t0, t1, z2_50_0, Curve.p); // 2^250 - 2^0 + mont_mul_zxy_mod_p(t0, t1, z2_50_0, Curve_p); // 2^250 - 2^0 - mont_mul_zxy_mod_p(t1, t0, t0, Curve.p); // 2^251 - 2^1 - mont_mul_zxy_mod_p(t0, t1, t1, Curve.p); // 2^252 - 2^2 - mont_mul_zxy_mod_p(t1, t0, t0, Curve.p); // 2^253 - 2^3 - mont_mul_zxy_mod_p(t0, t1, t1, Curve.p); // 2^254 - 2^4 - mont_mul_zxy_mod_p(t1, t0, t0, Curve.p); // 2^255 - 2^5 - mont_mul_zxy_mod_p(z_inv, t1, z11, Curve.p); // 2^255 - 21 + mont_mul_zxy_mod_p(t1, t0, t0, Curve_p); // 2^251 - 2^1 + mont_mul_zxy_mod_p(t0, t1, t1, Curve_p); // 2^252 - 2^2 + mont_mul_zxy_mod_p(t1, t0, t0, Curve_p); // 2^253 - 2^3 + mont_mul_zxy_mod_p(t0, t1, t1, Curve_p); // 2^254 - 2^4 + mont_mul_zxy_mod_p(t1, t0, t0, Curve_p); // 2^255 - 2^5 + mont_mul_zxy_mod_p(z_inv, t1, z11, Curve_p); // 2^255 - 21 } void recover_y(uint32_t *x, uint32_t *y, uint32_t *z, uint32_t *xp, uint32_t *yp, uint32_t *xq, uint32_t *zq, uint32_t *xpq, uint32_t *zpq) { @@ -135,26 +127,26 @@ void recover_y(uint32_t *x, uint32_t *y, uint32_t *z, uint32_t *xp, uint32_t *yp uint32_t AR = 18493156; uint32_t v1[8], v2[8], v3[8], v4[8], s[8], t[8]; - mont_mul_zxy_mod_p(v1, xp, zq, Curve.p); - add_zxy_mod_p(v2, xq, v1, Curve.p); - sub_zxy_mod_p(v3, xq, v1, Curve.p); - mont_mul_zxy_mod_p(t, v3, v3, Curve.p); - mont_mul_zxy_mod_p(v3, t, xpq, Curve.p); - mont_mul_zxy0_mod_p(v1, zq, AR, Curve.p); - add_zxy_mod_p(v1, v1, v1, Curve.p); - add_zxy_mod_p(v2, v2, v1, Curve.p); - mont_mul_zxy_mod_p(v4, xp, xq, Curve.p); - add_zxy_mod_p(v4, v4, zq, Curve.p); - mont_mul_zxy_mod_p(s, v2, v4, Curve.p); - mont_mul_zxy_mod_p(t, v1, zq, Curve.p); - sub_zxy_mod_p(s, s, t, Curve.p); - mont_mul_zxy_mod_p(v2, s, zpq, Curve.p); - sub_zxy_mod_p(y, v2, v3, Curve.p); - add_zxy_mod_p(v1, yp, yp, Curve.p); - mont_mul_zxy_mod_p(s, v1, zq, Curve.p); - mont_mul_zxy_mod_p(v1, s, zpq, Curve.p); - mont_mul_zxy_mod_p(x, v1, xq, Curve.p); - mont_mul_zxy_mod_p(z, v1, zq, Curve.p); + mont_mul_zxy_mod_p(v1, xp, zq, Curve_p); + add_zxy_mod_p(v2, xq, v1, Curve_p); + sub_zxy_mod_p(v3, xq, v1, Curve_p); + mont_mul_zxy_mod_p(t, v3, v3, Curve_p); + mont_mul_zxy_mod_p(v3, t, xpq, Curve_p); + mont_mul_zxy0_mod_p(v1, zq, AR, Curve_p); + add_zxy_mod_p(v1, v1, v1, Curve_p); + add_zxy_mod_p(v2, v2, v1, Curve_p); + mont_mul_zxy_mod_p(v4, xp, xq, Curve_p); + add_zxy_mod_p(v4, v4, zq, Curve_p); + mont_mul_zxy_mod_p(s, v2, v4, Curve_p); + mont_mul_zxy_mod_p(t, v1, zq, Curve_p); + sub_zxy_mod_p(s, s, t, Curve_p); + mont_mul_zxy_mod_p(v2, s, zpq, Curve_p); + sub_zxy_mod_p(y, v2, v3, Curve_p); + add_zxy_mod_p(v1, yp, yp, Curve_p); + mont_mul_zxy_mod_p(s, v1, zq, Curve_p); + mont_mul_zxy_mod_p(v1, s, zpq, Curve_p); + mont_mul_zxy_mod_p(x, v1, xq, Curve_p); + mont_mul_zxy_mod_p(z, v1, zq, Curve_p); } @@ -164,16 +156,16 @@ void montgomery2edward(uint32_t *x, uint32_t *y, uint32_t *u, uint32_t *v) { for (uint32_t i=1; i<8; i++) t[i] = 0; t[0] = R; // 1*R - add_zxy_mod_p(s, u, t, Curve.p); // s = u+1 - mont_mul_zxy_mod_p(w, s, v, Curve.p); + add_zxy_mod_p(s, u, t, Curve_p); // s = u+1 + mont_mul_zxy_mod_p(w, s, v, Curve_p); mod_inverse(w, w); // w = (u+1)^(-1) * v^(-1) - sub_zxy_mod_p(y, u, t, Curve.p); // y = u-1 - mont_mul_zxy_mod_p(x, y, w, Curve.p); // x = (u-1)/((u+1) * v) - mont_mul_zxy_mod_p(y, x, v, Curve.p); + sub_zxy_mod_p(y, u, t, Curve_p); // y = u-1 + mont_mul_zxy_mod_p(x, y, w, Curve_p); // x = (u-1)/((u+1) * v) + mont_mul_zxy_mod_p(y, x, v, Curve_p); for (uint32_t i=0; i<8; i++) t[i] = sqrt_minus_486664R[7-i]; - mont_mul_zxy_mod_p(x, t, w, Curve.p); - mont_mul_zxy_mod_p(t, x, s, Curve.p); - mont_mul_zxy_mod_p(x, t, u, Curve.p); + mont_mul_zxy_mod_p(x, t, w, Curve_p); + mont_mul_zxy_mod_p(t, x, s, Curve_p); + mont_mul_zxy_mod_p(x, t, u, Curve_p); } @@ -214,7 +206,7 @@ void X25519(uint32_t *q, uint32_t *r, uint8_t *k, uint32_t *u, uint32_t *v, uint } to_Montgomery(A); for (uint32_t i=0; i<8; i++) x1[i] = A[i]; - mont_mul_zxy_mod_p(x3, A, z3, Curve.p); + mont_mul_zxy_mod_p(x3, A, z3, Curve_p); swap = 0; kw = k[31]; @@ -227,24 +219,24 @@ void X25519(uint32_t *q, uint32_t *r, uint8_t *k, uint32_t *u, uint32_t *v, uint cswap(swap, &z2, &z3); swap = kt; - add_zxy_mod_p(A, x2, z2, Curve.p); - mont_mul_zxy_mod_p(AA, A, A, Curve.p); - sub_zxy_mod_p(B, x2, z2, Curve.p); - mont_mul_zxy_mod_p(BB, B, B, Curve.p); - sub_zxy_mod_p(E, AA, BB, Curve.p); - add_zxy_mod_p(C, x3, z3, Curve.p); - sub_zxy_mod_p(D, x3, z3, Curve.p); - mont_mul_zxy_mod_p(DA, D, A, Curve.p); - mont_mul_zxy_mod_p(CB, C, B, Curve.p); - add_zxy_mod_p(A, DA, CB, Curve.p); - mont_mul_zxy_mod_p(x3, A, A, Curve.p); - sub_zxy_mod_p(A, DA, CB, Curve.p); - mont_mul_zxy_mod_p(B, A, A, Curve.p); - mont_mul_zxy_mod_p(z3, x1, B, Curve.p); - mont_mul_zxy_mod_p(x2, AA, BB, Curve.p); - mont_mul_zxy0_mod_p(A, E, Curve.a24, Curve.p); - add_zxy_mod_p(AA, AA, A, Curve.p); - mont_mul_zxy_mod_p(z2, E, AA, Curve.p); + add_zxy_mod_p(A, x2, z2, Curve_p); + mont_mul_zxy_mod_p(AA, A, A, Curve_p); + sub_zxy_mod_p(B, x2, z2, Curve_p); + mont_mul_zxy_mod_p(BB, B, B, Curve_p); + sub_zxy_mod_p(E, AA, BB, Curve_p); + add_zxy_mod_p(C, x3, z3, Curve_p); + sub_zxy_mod_p(D, x3, z3, Curve_p); + mont_mul_zxy_mod_p(DA, D, A, Curve_p); + mont_mul_zxy_mod_p(CB, C, B, Curve_p); + add_zxy_mod_p(A, DA, CB, Curve_p); + mont_mul_zxy_mod_p(x3, A, A, Curve_p); + sub_zxy_mod_p(A, DA, CB, Curve_p); + mont_mul_zxy_mod_p(B, A, A, Curve_p); + mont_mul_zxy_mod_p(z3, x1, B, Curve_p); + mont_mul_zxy_mod_p(x2, AA, BB, Curve_p); + mont_mul_zxy0_mod_p(A, E, a24R, Curve_p); + add_zxy_mod_p(AA, AA, A, Curve_p); + mont_mul_zxy_mod_p(z2, E, AA, Curve_p); } // conditional swap cswap(swap, &x2, &x3); @@ -259,8 +251,8 @@ void X25519(uint32_t *q, uint32_t *r, uint8_t *k, uint32_t *u, uint32_t *v, uint to_Montgomery(BB); recover_y(A, B, C, AA, BB, x2, z2, x3, z3); mod_inverse(C, C); - mont_mul_zxy_mod_p(q, A, C, Curve.p); - mont_mul_zxy_mod_p(r, B, C, Curve.p); + mont_mul_zxy_mod_p(q, A, C, Curve_p); + mont_mul_zxy_mod_p(r, B, C, Curve_p); if (toEdward) { for (uint32_t i=0; i<8; i++) { A[i] = q[i]; @@ -274,7 +266,7 @@ void X25519(uint32_t *q, uint32_t *r, uint8_t *k, uint32_t *u, uint32_t *v, uint // compute x-only // compute z2^(-1) = z2^{p-2} mod_inverse(A, z2); - mont_mul_zxy_mod_p(q, x2, A, Curve.p); + mont_mul_zxy_mod_p(q, x2, A, Curve_p); from_Montgomery(q); } } diff --git a/mpy-modules/curve25519/ec.h b/mpy-modules/curve25519/ec.h index f5865df..ff9fb42 100644 --- a/mpy-modules/curve25519/ec.h +++ b/mpy-modules/curve25519/ec.h @@ -1,6 +1,8 @@ #ifndef __ec__ #define __ec__ +#define DIFF_P 19 +#define MINUS_IM 678152731 // -m^(-1) mod b is 678152731 for curve25519 void X25519(uint32_t *q, uint32_t *r, uint8_t *k, uint32_t *u, uint32_t *v, uint8_t toEdward); #endif