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secp256k1.cuh
1451 lines (1231 loc) · 37.1 KB
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secp256k1.cuh
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#ifndef _SECP256K1_CUH
#define _SECP256K1_CUH
#include <cuda.h>
#include <cuda_runtime.h>
#include "ptx.cuh"
#include "bitreverse.h"
__device__ __forceinline__ void copyBigInt(const uint32_t *src, uint32_t *dest);
/**
Prime modulus 2^256 - 2^32 - 977
*/
__constant__ uint32_t _P[8] = {
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFC2F
};
/**
Base point X
*/
__constant__ uint32_t _GX[8] = {
0x79BE667E, 0xF9DCBBAC, 0x55A06295, 0xCE870B07, 0x029BFCDB, 0x2DCE28D9, 0x59F2815B, 0x16F81798
};
/**
Base point Y
*/
__constant__ uint32_t _GY[8] = {
0x483ADA77, 0x26A3C465, 0x5DA4FBFC, 0x0E1108A8, 0xFD17B448, 0xA6855419, 0x9C47D08F, 0xFB10D4B8
};
/**
* Group order
*/
__constant__ uint32_t _N[8] = {
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0xBAAEDCE6, 0xAF48A03B, 0xBFD25E8C, 0xD0364141
};
__constant__ uint32_t _BETA[8] = {
0x7AE96A2B, 0x657C0710, 0x6E64479E, 0xAC3434E9, 0x9CF04975, 0x12F58995, 0xC1396C28, 0x719501EE
};
__constant__ uint32_t _LAMBDA[8] = {
0x5363AD4C, 0xC05C30E0, 0xA5261C02, 0x8812645A, 0x122E22EA, 0x20816678, 0xDF02967C, 0x1B23BD72
};
__device__ int dnKEY_PER_THREAD;
__device__ __forceinline__ void copyBigInt(const uint32_t *src, uint32_t *dest)
{
for(int i = 0; i < 8; i++) {
dest[i] = src[i];
}
}
__device__ bool equal(const uint32_t *a, const uint32_t *b)
{
bool eq = true;
for(int i = 0; i < 8; i++) {
eq &= (a[i] == b[i]);
}
return eq;
}
/**
* Reads an 8-word big integer from device memory
*/
__device__ void readInt(const uint32_t *ara, int idx, uint32_t x[8])
{
int index = ((((blockDim.x * blockIdx.x + threadIdx.x) * dnKEY_PER_THREAD) + idx) * 8);
for (int i = 0; i < 8; i++) {
x[i] = ara[index];
index++;
}
}
/**
* Writes an 8-word big integer to device memory
*/
__device__ void writeInt(uint32_t *ara, int idx, const uint32_t x[8])
{
int index = ((((blockDim.x * blockIdx.x + threadIdx.x) * dnKEY_PER_THREAD) + idx) * 8);
for (int i = 0; i < 8; i++) {
ara[index] = x[i];
index++;
}
}
__device__ void writePoint(uint32_t *arx, uint32_t *ary, int idx, const uint32_t x[8], const uint32_t y[8])
{
int index = ((((blockDim.x * blockIdx.x + threadIdx.x) * dnKEY_PER_THREAD) + idx) * 8);
for (int i = 0; i < 8; i++) {
arx[index] = x[i];
ary[index] = y[i];
index++;
}
}
/**
* Subtraction mod p
*/
__device__ void subModP(const uint32_t a[8], const uint32_t b[8], uint32_t c[8])
{
sub_cc(c[7], a[7], b[7]);
subc_cc(c[6], a[6], b[6]);
subc_cc(c[5], a[5], b[5]);
subc_cc(c[4], a[4], b[4]);
subc_cc(c[3], a[3], b[3]);
subc_cc(c[2], a[2], b[2]);
subc_cc(c[1], a[1], b[1]);
subc_cc(c[0], a[0], b[0]);
uint32_t borrow = 0;
subc(borrow, 0, 0);
if (borrow) {
add_cc(c[7], c[7], _P[7]);
addc_cc(c[6], c[6], _P[6]);
addc_cc(c[5], c[5], _P[5]);
addc_cc(c[4], c[4], _P[4]);
addc_cc(c[3], c[3], _P[3]);
addc_cc(c[2], c[2], _P[2]);
addc_cc(c[1], c[1], _P[1]);
addc(c[0], c[0], _P[0]);
}
}
__device__ uint32_t add(const uint32_t a[8], const uint32_t b[8], uint32_t c[8])
{
add_cc(c[7], a[7], b[7]);
addc_cc(c[6], a[6], b[6]);
addc_cc(c[5], a[5], b[5]);
addc_cc(c[4], a[4], b[4]);
addc_cc(c[3], a[3], b[3]);
addc_cc(c[2], a[2], b[2]);
addc_cc(c[1], a[1], b[1]);
addc_cc(c[0], a[0], b[0]);
uint32_t carry = 0;
addc(carry, 0, 0);
return carry;
}
__device__ uint32_t sub(const uint32_t a[8], const uint32_t b[8], uint32_t c[8])
{
sub_cc(c[7], a[7], b[7]);
subc_cc(c[6], a[6], b[6]);
subc_cc(c[5], a[5], b[5]);
subc_cc(c[4], a[4], b[4]);
subc_cc(c[3], a[3], b[3]);
subc_cc(c[2], a[2], b[2]);
subc_cc(c[1], a[1], b[1]);
subc_cc(c[0], a[0], b[0]);
uint32_t borrow = 0;
subc(borrow, 0, 0);
return (borrow & 0x01);
}
/**
Subtract using two's compliment
*/
__device__ uint32_t sub2c(const uint32_t a[8], const uint32_t b[8], uint32_t c[8])
{
add_cc(c[7], a[7], ~b[7]);
addc_cc(c[6], a[6], ~b[6]);
addc_cc(c[5], a[5], ~b[5]);
addc_cc(c[4], a[4], ~b[4]);
addc_cc(c[3], a[3], ~b[3]);
addc_cc(c[2], a[2], ~b[2]);
addc_cc(c[1], a[1], ~b[1]);
addc_cc(c[0], a[0], ~b[0]);
uint32_t carry = 0;
addc(carry, 0, 0);
add_cc(c[7], c[7], 1);
addc_cc(c[6], c[6], 0);
addc_cc(c[5], c[5], 0);
addc_cc(c[4], c[4], 0);
addc_cc(c[3], c[3], 0);
addc_cc(c[2], c[2], 0);
addc_cc(c[1], c[1], 0);
addc_cc(c[0], c[0], 0);
addc(carry, carry, 0);
return carry;
}
__device__ void divBy2(uint32_t x[8])
{
x[7] = (x[7] >> 1) | (x[6] << 31);
x[6] = (x[6] >> 1) | (x[5] << 31);
x[5] = (x[5] >> 1) | (x[4] << 31);
x[4] = (x[4] >> 1) | (x[3] << 31);
x[3] = (x[3] >> 1) | (x[2] << 31);
x[2] = (x[2] >> 1) | (x[1] << 31);
x[1] = (x[1] >> 1) | (x[0] << 31);
x[0] = (x[0] >> 1);
}
__device__ void addModP(const uint32_t a[8], const uint32_t b[8], uint32_t c[8])
{
add_cc(c[7], a[7], b[7]);
addc_cc(c[6], a[6], b[6]);
addc_cc(c[5], a[5], b[5]);
addc_cc(c[4], a[4], b[4]);
addc_cc(c[3], a[3], b[3]);
addc_cc(c[2], a[2], b[2]);
addc_cc(c[1], a[1], b[1]);
addc_cc(c[0], a[0], b[0]);
uint32_t carry = 0;
addc(carry, 0, 0);
bool gt = false;
for(int i = 0; i < 8; i++) {
if(c[i] > _P[i]) {
gt = true;
break;
} else if(c[i] < _P[i]) {
break;
}
}
if(carry || gt) {
sub_cc(c[7], c[7], _P[7]);
subc_cc(c[6], c[6], _P[6]);
subc_cc(c[5], c[5], _P[5]);
subc_cc(c[4], c[4], _P[4]);
subc_cc(c[3], c[3], _P[3]);
subc_cc(c[2], c[2], _P[2]);
subc_cc(c[1], c[1], _P[1]);
subc(c[0], c[0], _P[0]);
}
}
/**
* Multiplication mod P
*/
__device__ void mulModP(const uint32_t a[8], const uint32_t b[8], uint32_t c[8])
{
uint32_t high[8];
uint32_t t = a[7];
// a[7] * b (low)
for (int i = 7; i >= 0; i--) {
c[i] = t * b[i];
high[i] = 0;
}
// a[7] * b (high)
mad_hi_cc(c[6], t, b[7], c[6]);
madc_hi_cc(c[5], t, b[6], c[5]);
madc_hi_cc(c[4], t, b[5], c[4]);
madc_hi_cc(c[3], t, b[4], c[3]);
madc_hi_cc(c[2], t, b[3], c[2]);
madc_hi_cc(c[1], t, b[2], c[1]);
madc_hi_cc(c[0], t, b[1], c[0]);
madc_hi(high[7], t, b[0], high[7]);
// a[6] * b (low)
t = a[6];
mad_lo_cc(c[6], t, b[7], c[6]);
madc_lo_cc(c[5], t, b[6], c[5]);
madc_lo_cc(c[4], t, b[5], c[4]);
madc_lo_cc(c[3], t, b[4], c[3]);
madc_lo_cc(c[2], t, b[3], c[2]);
madc_lo_cc(c[1], t, b[2], c[1]);
madc_lo_cc(c[0], t, b[1], c[0]);
madc_lo_cc(high[7], t, b[0], high[7]);
addc(high[6], high[6], 0);
// a[6] * b (high)
mad_hi_cc(c[5], t, b[7], c[5]);
madc_hi_cc(c[4], t, b[6], c[4]);
madc_hi_cc(c[3], t, b[5], c[3]);
madc_hi_cc(c[2], t, b[4], c[2]);
madc_hi_cc(c[1], t, b[3], c[1]);
madc_hi_cc(c[0], t, b[2], c[0]);
madc_hi_cc(high[7], t, b[1], high[7]);
madc_hi(high[6], t, b[0], high[6]);
// a[5] * b (low)
t = a[5];
mad_lo_cc(c[5], t, b[7], c[5]);
madc_lo_cc(c[4], t, b[6], c[4]);
madc_lo_cc(c[3], t, b[5], c[3]);
madc_lo_cc(c[2], t, b[4], c[2]);
madc_lo_cc(c[1], t, b[3], c[1]);
madc_lo_cc(c[0], t, b[2], c[0]);
madc_lo_cc(high[7], t, b[1], high[7]);
madc_lo_cc(high[6], t, b[0], high[6]);
addc(high[5], high[5], 0);
// a[5] * b (high)
mad_hi_cc(c[4], t, b[7], c[4]);
madc_hi_cc(c[3], t, b[6], c[3]);
madc_hi_cc(c[2], t, b[5], c[2]);
madc_hi_cc(c[1], t, b[4], c[1]);
madc_hi_cc(c[0], t, b[3], c[0]);
madc_hi_cc(high[7], t, b[2], high[7]);
madc_hi_cc(high[6], t, b[1], high[6]);
madc_hi(high[5], t, b[0], high[5]);
// a[4] * b (low)
t = a[4];
mad_lo_cc(c[4], t, b[7], c[4]);
madc_lo_cc(c[3], t, b[6], c[3]);
madc_lo_cc(c[2], t, b[5], c[2]);
madc_lo_cc(c[1], t, b[4], c[1]);
madc_lo_cc(c[0], t, b[3], c[0]);
madc_lo_cc(high[7], t, b[2], high[7]);
madc_lo_cc(high[6], t, b[1], high[6]);
madc_lo_cc(high[5], t, b[0], high[5]);
addc(high[4], high[4], 0);
// a[4] * b (high)
mad_hi_cc(c[3], t, b[7], c[3]);
madc_hi_cc(c[2], t, b[6], c[2]);
madc_hi_cc(c[1], t, b[5], c[1]);
madc_hi_cc(c[0], t, b[4], c[0]);
madc_hi_cc(high[7], t, b[3], high[7]);
madc_hi_cc(high[6], t, b[2], high[6]);
madc_hi_cc(high[5], t, b[1], high[5]);
madc_hi(high[4], t, b[0], high[4]);
// a[3] * b (low)
t = a[3];
mad_lo_cc(c[3], t, b[7], c[3]);
madc_lo_cc(c[2], t, b[6], c[2]);
madc_lo_cc(c[1], t, b[5], c[1]);
madc_lo_cc(c[0], t, b[4], c[0]);
madc_lo_cc(high[7], t, b[3], high[7]);
madc_lo_cc(high[6], t, b[2], high[6]);
madc_lo_cc(high[5], t, b[1], high[5]);
madc_lo_cc(high[4], t, b[0], high[4]);
addc(high[3], high[3], 0);
// a[3] * b (high)
mad_hi_cc(c[2], t, b[7], c[2]);
madc_hi_cc(c[1], t, b[6], c[1]);
madc_hi_cc(c[0], t, b[5], c[0]);
madc_hi_cc(high[7], t, b[4], high[7]);
madc_hi_cc(high[6], t, b[3], high[6]);
madc_hi_cc(high[5], t, b[2], high[5]);
madc_hi_cc(high[4], t, b[1], high[4]);
madc_hi(high[3], t, b[0], high[3]);
// a[2] * b (low)
t = a[2];
mad_lo_cc(c[2], t, b[7], c[2]);
madc_lo_cc(c[1], t, b[6], c[1]);
madc_lo_cc(c[0], t, b[5], c[0]);
madc_lo_cc(high[7], t, b[4], high[7]);
madc_lo_cc(high[6], t, b[3], high[6]);
madc_lo_cc(high[5], t, b[2], high[5]);
madc_lo_cc(high[4], t, b[1], high[4]);
madc_lo_cc(high[3], t, b[0], high[3]);
addc(high[2], high[2], 0);
// a[2] * b (high)
mad_hi_cc(c[1], t, b[7], c[1]);
madc_hi_cc(c[0], t, b[6], c[0]);
madc_hi_cc(high[7], t, b[5], high[7]);
madc_hi_cc(high[6], t, b[4], high[6]);
madc_hi_cc(high[5], t, b[3], high[5]);
madc_hi_cc(high[4], t, b[2], high[4]);
madc_hi_cc(high[3], t, b[1], high[3]);
madc_hi(high[2], t, b[0], high[2]);
// a[1] * b (low)
t = a[1];
mad_lo_cc(c[1], t, b[7], c[1]);
madc_lo_cc(c[0], t, b[6], c[0]);
madc_lo_cc(high[7], t, b[5], high[7]);
madc_lo_cc(high[6], t, b[4], high[6]);
madc_lo_cc(high[5], t, b[3], high[5]);
madc_lo_cc(high[4], t, b[2], high[4]);
madc_lo_cc(high[3], t, b[1], high[3]);
madc_lo_cc(high[2], t, b[0], high[2]);
addc(high[1], high[1], 0);
// a[1] * b (high)
mad_hi_cc(c[0], t, b[7], c[0]);
madc_hi_cc(high[7], t, b[6], high[7]);
madc_hi_cc(high[6], t, b[5], high[6]);
madc_hi_cc(high[5], t, b[4], high[5]);
madc_hi_cc(high[4], t, b[3], high[4]);
madc_hi_cc(high[3], t, b[2], high[3]);
madc_hi_cc(high[2], t, b[1], high[2]);
madc_hi(high[1], t, b[0], high[1]);
// a[0] * b (low)
t = a[0];
mad_lo_cc(c[0], t, b[7], c[0]);
madc_lo_cc(high[7], t, b[6], high[7]);
madc_lo_cc(high[6], t, b[5], high[6]);
madc_lo_cc(high[5], t, b[4], high[5]);
madc_lo_cc(high[4], t, b[3], high[4]);
madc_lo_cc(high[3], t, b[2], high[3]);
madc_lo_cc(high[2], t, b[1], high[2]);
madc_lo_cc(high[1], t, b[0], high[1]);
addc(high[0], high[0], 0);
// a[0] * b (high)
mad_hi_cc(high[7], t, b[7], high[7]);
madc_hi_cc(high[6], t, b[6], high[6]);
madc_hi_cc(high[5], t, b[5], high[5]);
madc_hi_cc(high[4], t, b[4], high[4]);
madc_hi_cc(high[3], t, b[3], high[3]);
madc_hi_cc(high[2], t, b[2], high[2]);
madc_hi_cc(high[1], t, b[1], high[1]);
madc_hi(high[0], t, b[0], high[0]);
// At this point we have 16 32-bit words representing a 512-bit value
// high[0 ... 7] and c[0 ... 7]
const uint32_t s = 977;
// Store high[6] and high[7] since they will be overwritten
uint32_t high7 = high[7];
uint32_t high6 = high[6];
// Take high 256 bits, multiply by 2^32, add to low 256 bits
// That is, take high[0 ... 7], shift it left 1 word and add it to c[0 ... 7]
add_cc(c[6], high[7], c[6]);
addc_cc(c[5], high[6], c[5]);
addc_cc(c[4], high[5], c[4]);
addc_cc(c[3], high[4], c[3]);
addc_cc(c[2], high[3], c[2]);
addc_cc(c[1], high[2], c[1]);
addc_cc(c[0], high[1], c[0]);
addc_cc(high[7], high[0], 0);
addc(high[6], 0, 0);
// Take high 256 bits, multiply by 977, add to low 256 bits
// That is, take high[0 ... 5], high6, high7, multiply by 977 and add to c[0 ... 7]
mad_lo_cc(c[7], high7, s, c[7]);
madc_lo_cc(c[6], high6, s, c[6]);
madc_lo_cc(c[5], high[5], s, c[5]);
madc_lo_cc(c[4], high[4], s, c[4]);
madc_lo_cc(c[3], high[3], s, c[3]);
madc_lo_cc(c[2], high[2], s, c[2]);
madc_lo_cc(c[1], high[1], s, c[1]);
madc_lo_cc(c[0], high[0], s, c[0]);
addc_cc(high[7], high[7], 0);
addc(high[6], high[6], 0);
mad_hi_cc(c[6], high7, s, c[6]);
madc_hi_cc(c[5], high6, s, c[5]);
madc_hi_cc(c[4], high[5], s, c[4]);
madc_hi_cc(c[3], high[4], s, c[3]);
madc_hi_cc(c[2], high[3], s, c[2]);
madc_hi_cc(c[1], high[2], s, c[1]);
madc_hi_cc(c[0], high[1], s, c[0]);
madc_hi_cc(high[7], high[0], s, high[7]);
addc(high[6], high[6], 0);
// Repeat the same steps, but this time we only need to handle high[6] and high[7]
high7 = high[7];
high6 = high[6];
// Take the high 64 bits, multiply by 2^32 and add to the low 256 bits
add_cc(c[6], high[7], c[6]);
addc_cc(c[5], high[6], c[5]);
addc_cc(c[4], c[4], 0);
addc_cc(c[3], c[3], 0);
addc_cc(c[2], c[2], 0);
addc_cc(c[1], c[1], 0);
addc_cc(c[0], c[0], 0);
addc(high[7], 0, 0);
// Take the high 64 bits, multiply by 977 and add to the low 256 bits
mad_lo_cc(c[7], high7, s, c[7]);
madc_lo_cc(c[6], high6, s, c[6]);
addc_cc(c[5], c[5], 0);
addc_cc(c[4], c[4], 0);
addc_cc(c[3], c[3], 0);
addc_cc(c[2], c[2], 0);
addc_cc(c[1], c[1], 0);
addc_cc(c[0], c[0], 0);
addc(high[7], high[7], 0);
mad_hi_cc(c[6], high7, s, c[6]);
madc_hi_cc(c[5], high6, s, c[5]);
addc_cc(c[4], c[4], 0);
addc_cc(c[3], c[3], 0);
addc_cc(c[2], c[2], 0);
addc_cc(c[1], c[1], 0);
addc_cc(c[0], c[0], 0);
addc(high[7], high[7], 0);
bool overflow = high[7] != 0;
uint32_t borrow = sub(c, _P, c);
if(overflow) {
if(!borrow) {
sub(c, _P, c);
}
} else {
if(borrow) {
add(c, _P, c);
}
}
}
/**
* Square mod P
* b = a * a
*/
__device__ void squareModP(const uint32_t a[8], uint32_t b[8])
{
mulModP(a, a, b);
}
/**
* Square mod P
* x = x * x
*/
__device__ void squareModP(uint32_t x[8])
{
uint32_t tmp[8];
squareModP(x, tmp);
copyBigInt(tmp, x);
}
/**
* Multiply mod P
* c = a * c
*/
__device__ void mulModP(const uint32_t a[8], uint32_t c[8])
{
uint32_t tmp[8];
mulModP(a, c, tmp);
copyBigInt(tmp, c);
}
/**
* Multiplicative inverse mod P using Fermat's method of x^(p-2) mod p
*/
__device__ void invModP(uint32_t value[8])
{
uint32_t x[8];
copyBigInt(value, x);
uint32_t y[8] = { 0, 0, 0, 0, 0, 0, 0, 1 };
// 0xd - 1101
mulModP(x, y);
squareModP(x);
//mulModP(x, y);
squareModP(x);
mulModP(x, y);
squareModP(x);
mulModP(x, y);
squareModP(x);
// 0x2 - 0010
//mulModP(x, y);
squareModP(x);
mulModP(x, y);
squareModP(x);
//mulModP(x, y);
squareModP(x);
//mulModP(x, y);
squareModP(x);
// 0xc = 0x1100
//mulModP(x, y);
squareModP(x);
//mulModP(x, y);
squareModP(x);
mulModP(x, y);
squareModP(x);
mulModP(x, y);
squareModP(x);
// 0xfffff
for(int i = 0; i < 20; i++) {
mulModP(x, y);
squareModP(x);
}
// 0xe - 1110
//mulModP(x, y);
squareModP(x);
mulModP(x, y);
squareModP(x);
mulModP(x, y);
squareModP(x);
mulModP(x, y);
squareModP(x);
// 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffff
for(int i = 0; i < 219; i++) {
mulModP(x, y);
squareModP(x);
}
mulModP(x, y);
copyBigInt(y, value);
}
__device__ void invModP(const uint32_t *value, uint32_t *inverse)
{
copyBigInt(value, inverse);
invModP(inverse);
}
__device__ void negModP(const uint32_t *value, uint32_t *negative)
{
sub_cc(negative[0], _P[0], value[0]);
subc_cc(negative[1], _P[1], value[1]);
subc_cc(negative[2], _P[2], value[2]);
subc_cc(negative[3], _P[3], value[3]);
subc_cc(negative[4], _P[4], value[4]);
subc_cc(negative[5], _P[5], value[5]);
subc_cc(negative[6], _P[6], value[6]);
subc(negative[7], _P[7], value[7]);
}
__device__ __forceinline__ void beginBatchAdd(const uint32_t *px, uint32_t *xPtr, uint32_t *chain, int i, uint32_t inverse[8])
{
uint32_t x[8];
readInt(xPtr, i, x);
// x = Gx - x
subModP(px, x, x);
// Keep a chain of multiples of the diff, i.e. c[0] = diff0, c[1] = diff0 * diff1,
// c[2] = diff2 * diff1 * diff0, etc
mulModP(x, inverse);
//memcpy(chain + (i * 8 * sizeof(uint32_t)), inverse, 8 * sizeof(uint32_t));
int index = (i * 8);
for (int j = 0; j < 8; j++) {
chain[index] = inverse[j];
index++;
}
//writeInt(chain, i, inverse);
}
__device__ __forceinline__ void beginBatchAddWithDouble(const uint32_t *px, const uint32_t *py, uint32_t *xPtr, uint32_t *chain, int i, uint32_t inverse[8])
{
uint32_t x[8];
readInt(xPtr, i, x);
if(equal(px, x)) {
addModP(py, py, x);
} else {
// x = Gx - x
subModP(px, x, x);
}
// Keep a chain of multiples of the diff, i.e. c[0] = diff0, c[1] = diff0 * diff1,
// c[2] = diff2 * diff1 * diff0, etc
mulModP(x, inverse);
writeInt(chain, i, inverse);
}
__device__ void completeBatchAddWithDouble(const uint32_t *px, const uint32_t *py, uint32_t *xPtr, uint32_t *yPtr, int i, uint32_t *chain, uint32_t *inverse, uint32_t newX[8], uint32_t newY[8])
{
uint32_t s[8];
uint32_t x[8];
uint32_t y[8];
readInt(xPtr, i, x);
readInt(yPtr, i, y);
if(i >= 1) {
uint32_t c[8];
readInt(chain, i - 1, c);
mulModP(inverse, c, s);
uint32_t diff[8];
if(equal(px, x)) {
addModP(py, py, diff);
} else {
subModP(px, x, diff);
}
mulModP(diff, inverse);
} else {
copyBigInt(inverse, s);
}
if(equal(px, x)) {
// currently s = 1 / 2y
uint32_t x2[8];
uint32_t tx2[8];
// 3x^2
mulModP(x, x, x2);
addModP(x2, x2, tx2);
addModP(x2, tx2, tx2);
// s = 3x^2 * 1/2y
mulModP(tx2, s);
// s^2
uint32_t s2[8];
mulModP(s, s, s2);
// Rx = s^2 - 2px
subModP(s2, x, newX);
subModP(newX, x, newX);
// Ry = s(px - rx) - py
uint32_t k[8];
subModP(px, newX, k);
mulModP(s, k, newY);
subModP(newY, py, newY);
} else {
uint32_t rise[8];
subModP(py, y, rise);
mulModP(rise, s);
// Rx = s^2 - Gx - Qx
uint32_t s2[8];
mulModP(s, s, s2);
subModP(s2, px, newX);
subModP(newX, x, newX);
// Ry = s(px - rx) - py
uint32_t k[8];
subModP(px, newX, k);
mulModP(s, k, newY);
subModP(newY, py, newY);
}
}
__device__ void completeBatchAdd(const uint32_t *px, const uint32_t *py, uint32_t *xPtr, uint32_t *yPtr, int i, uint32_t *chain, uint32_t *inverse, uint32_t newX[8], uint32_t newY[8])
{
uint32_t s[8];
uint32_t x[8];
readInt(xPtr, i, x);
if(i >= 1) {
uint32_t c[8];
//readInt(chain, i - 1, c);
int index = ((i - 1) * 8);
for (int j = 0; j < 8; j++) {
c[j] = chain[index];
index++;
}
//memcpy(c, chain + ((i-1) * 8 * sizeof(uint32_t)), 8 * sizeof(uint32_t));
mulModP(inverse, c, s);
uint32_t diff[8];
subModP(px, x, diff);
mulModP(diff, inverse);
} else {
copyBigInt(inverse, s);
}
uint32_t y[8];
readInt(yPtr, i, y);
uint32_t rise[8];
subModP(py, y, rise);
mulModP(rise, s);
// Rx = s^2 - Gx - Qx
uint32_t s2[8];
mulModP(s, s, s2);
subModP(s2, px, newX);
subModP(newX, x, newX);
// Ry = s(px - rx) - py
uint32_t k[8];
subModP(px, newX, k);
mulModP(s, k, newY);
subModP(newY, py, newY);
}
__device__ __forceinline__ void doBatchInverse(uint32_t inverse[8])
{
invModP(inverse);
}
////////////////////////////////////////////////////////////////////////////////////////////////////////////
__device__ void dec_fe_mul_inner(const uint32_t *a, const uint32_t *b, uint32_t *r) {
uint64_t c = (uint64_t)a[0] * b[0];
uint32_t t0 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[0] * b[1] +
(uint64_t)a[1] * b[0];
uint32_t t1 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[0] * b[2] +
(uint64_t)a[1] * b[1] +
(uint64_t)a[2] * b[0];
uint32_t t2 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[0] * b[3] +
(uint64_t)a[1] * b[2] +
(uint64_t)a[2] * b[1] +
(uint64_t)a[3] * b[0];
uint32_t t3 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[0] * b[4] +
(uint64_t)a[1] * b[3] +
(uint64_t)a[2] * b[2] +
(uint64_t)a[3] * b[1] +
(uint64_t)a[4] * b[0];
uint32_t t4 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[0] * b[5] +
(uint64_t)a[1] * b[4] +
(uint64_t)a[2] * b[3] +
(uint64_t)a[3] * b[2] +
(uint64_t)a[4] * b[1] +
(uint64_t)a[5] * b[0];
uint32_t t5 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[0] * b[6] +
(uint64_t)a[1] * b[5] +
(uint64_t)a[2] * b[4] +
(uint64_t)a[3] * b[3] +
(uint64_t)a[4] * b[2] +
(uint64_t)a[5] * b[1] +
(uint64_t)a[6] * b[0];
uint32_t t6 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[0] * b[7] +
(uint64_t)a[1] * b[6] +
(uint64_t)a[2] * b[5] +
(uint64_t)a[3] * b[4] +
(uint64_t)a[4] * b[3] +
(uint64_t)a[5] * b[2] +
(uint64_t)a[6] * b[1] +
(uint64_t)a[7] * b[0];
uint32_t t7 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[0] * b[8] +
(uint64_t)a[1] * b[7] +
(uint64_t)a[2] * b[6] +
(uint64_t)a[3] * b[5] +
(uint64_t)a[4] * b[4] +
(uint64_t)a[5] * b[3] +
(uint64_t)a[6] * b[2] +
(uint64_t)a[7] * b[1] +
(uint64_t)a[8] * b[0];
uint32_t t8 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[0] * b[9] +
(uint64_t)a[1] * b[8] +
(uint64_t)a[2] * b[7] +
(uint64_t)a[3] * b[6] +
(uint64_t)a[4] * b[5] +
(uint64_t)a[5] * b[4] +
(uint64_t)a[6] * b[3] +
(uint64_t)a[7] * b[2] +
(uint64_t)a[8] * b[1] +
(uint64_t)a[9] * b[0];
uint32_t t9 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[1] * b[9] +
(uint64_t)a[2] * b[8] +
(uint64_t)a[3] * b[7] +
(uint64_t)a[4] * b[6] +
(uint64_t)a[5] * b[5] +
(uint64_t)a[6] * b[4] +
(uint64_t)a[7] * b[3] +
(uint64_t)a[8] * b[2] +
(uint64_t)a[9] * b[1];
uint32_t t10 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[2] * b[9] +
(uint64_t)a[3] * b[8] +
(uint64_t)a[4] * b[7] +
(uint64_t)a[5] * b[6] +
(uint64_t)a[6] * b[5] +
(uint64_t)a[7] * b[4] +
(uint64_t)a[8] * b[3] +
(uint64_t)a[9] * b[2];
uint32_t t11 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[3] * b[9] +
(uint64_t)a[4] * b[8] +
(uint64_t)a[5] * b[7] +
(uint64_t)a[6] * b[6] +
(uint64_t)a[7] * b[5] +
(uint64_t)a[8] * b[4] +
(uint64_t)a[9] * b[3];
uint32_t t12 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[4] * b[9] +
(uint64_t)a[5] * b[8] +
(uint64_t)a[6] * b[7] +
(uint64_t)a[7] * b[6] +
(uint64_t)a[8] * b[5] +
(uint64_t)a[9] * b[4];
uint32_t t13 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[5] * b[9] +
(uint64_t)a[6] * b[8] +
(uint64_t)a[7] * b[7] +
(uint64_t)a[8] * b[6] +
(uint64_t)a[9] * b[5];
uint32_t t14 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[6] * b[9] +
(uint64_t)a[7] * b[8] +
(uint64_t)a[8] * b[7] +
(uint64_t)a[9] * b[6];
uint32_t t15 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[7] * b[9] +
(uint64_t)a[8] * b[8] +
(uint64_t)a[9] * b[7];
uint32_t t16 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[8] * b[9] +
(uint64_t)a[9] * b[8];
uint32_t t17 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[9] * b[9];
uint32_t t18 = c & 0x3FFFFFFUL; c = c >> 26;
uint32_t t19 = c;
c = t0 + (uint64_t)t10 * 0x3D10UL;
t0 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t1 + (uint64_t)t10 * 0x400UL + (uint64_t)t11 * 0x3D10UL;
t1 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t2 + (uint64_t)t11 * 0x400UL + (uint64_t)t12 * 0x3D10UL;
t2 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t3 + (uint64_t)t12 * 0x400UL + (uint64_t)t13 * 0x3D10UL;
r[3] = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t4 + (uint64_t)t13 * 0x400UL + (uint64_t)t14 * 0x3D10UL;
r[4] = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t5 + (uint64_t)t14 * 0x400UL + (uint64_t)t15 * 0x3D10UL;
r[5] = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t6 + (uint64_t)t15 * 0x400UL + (uint64_t)t16 * 0x3D10UL;
r[6] = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t7 + (uint64_t)t16 * 0x400UL + (uint64_t)t17 * 0x3D10UL;
r[7] = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t8 + (uint64_t)t17 * 0x400UL + (uint64_t)t18 * 0x3D10UL;
r[8] = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t9 + (uint64_t)t18 * 0x400UL + (uint64_t)t19 * 0x1000003D10UL;
r[9] = c & 0x03FFFFFUL; c = c >> 22;
uint64_t d = t0 + c * 0x3D1UL;
r[0] = d & 0x3FFFFFFUL; d = d >> 26;
d = d + t1 + c * 0x40;
r[1] = d & 0x3FFFFFFUL; d = d >> 26;
r[2] = t2 + d;
}
__device__ void dec_fe_mul(ec_fe_t *r, const ec_fe_t *a, const ec_fe_t *b) {
dec_fe_mul_inner(a->n, b->n, r->n);
}
__device__ void dec_fe_sqr_inner(const uint32_t *a, uint32_t *r) {
uint64_t c = (uint64_t)a[0] * a[0];
uint32_t t0 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[0] * 2) * a[1];
uint32_t t1 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[0] * 2) * a[2] +
(uint64_t)a[1] * a[1];
uint32_t t2 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[0] * 2) * a[3] +
(uint64_t)(a[1] * 2) * a[2];
uint32_t t3 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[0] * 2) * a[4] +
(uint64_t)(a[1] * 2) * a[3] +
(uint64_t)a[2] * a[2];