How to calculate modular multplication of array elements to integers in c? - c

Question

Consider the following:
uint8_t message[15] = {
0x32, 0xdc, 0x21, 0x55, 0x3f, 0x87, 0xc8, 0x1e,
0x85, 0x10, 0x43, 0xf9, 0x93, 0x34, 0x1a
};
uint64_t num = 0xa1b2c33412;
I want to multiply the above variable num to the array message[]. The pseudo-code for what I have need, is following:
uint8_t message[15] = {
0x32, 0xdc, 0x21, 0x55, 0x3f, 0x87, 0xc8, 0x1e,
0x85, 0x10, 0x43, 0xf9, 0x93, 0x34, 0x1a
};
uint64_t num = 0xa1b2c33412;
uint64_t p = 0x31ba62ca3037;
uint64_t result = 0x00;
result = moduloMultiplication(message, num, p); // (message * num) (mod p)
I am expecting the following results:
num * msg = num*msg mod p
num * msg = 0x2bf2d18cdf92 (Final result)
Is there any way to multiply the array with value of typeuint64_t?
Any help regarding this will be appreciated...

Answer 1

Assuming the number stored in the 15-byte array is in big-endian order, here is a simple solution:
#include <stdio.h>
#include <stdint.h>
uint64_t moduloMultiplication(const uint8_t message[15], size_t n,
uint64_t num, uint64_t p)
{
uint64_t res = 0;
for (size_t i = 0; i < n; i++) {
// assuming `p < 1ULL << 56`
res = (res * 256 + message[i] * num) % p;
}
return res;
}
int main() {
uint8_t message[15] = {
0x32, 0xdc, 0x21, 0x55, 0x3f, 0x87, 0xc8, 0x1e,
0x85, 0x10, 0x43, 0xf9, 0x93, 0x34, 0x1a
};
uint64_t num = 0xa1b2c33412;
uint64_t p = 0x31ba62ca3037;
// result = (message * num) (mod p)
uint64_t result = moduloMultiplication(message, sizeof message, num, p);
printf("%#"PRIx64"\n", result);
return 0;
}
Output: 0x2bf2d18cdf92
The result differs from that in the question because either the message is incorrect, or your intermediary result is approximate: 201FF4CDCFE8C0000000000000000000000000000 seems incorrect.