**Brief approach — goal:** implement modular exponentiation without data-dependent branches or memory accesses. Use bitmasking for conditional moves and a constant-time table lookup for sliding windows.**Constant-time helpers (conceptual C)**c
#include <stdint.h>
/* constant-time conditional select: if (cond) return a else return b
cond must be 0 or 1 */
static inline uint64_t ct_select_u64(uint64_t a, uint64_t b, uint64_t cond) {
uint64_t mask = -(uint64_t)cond; /* all-ones if cond==1, else 0 */
return (a & mask) | (b & ~mask);
}
/* constant-time modular multiply (toy 64-bit example; replace with big-int) */
static inline uint64_t modmul(uint64_t x, uint64_t y, uint64_t m) {
__uint128_t r = (__uint128_t)x * y;
return (uint64_t)(r % m);
}
c
uint64_t modexp_ct(uint64_t base, uint64_t exp, uint64_t mod) {
uint64_t R = 1;
for (int i = 63; i >= 0; --i) {
/* square every loop */
R = modmul(R, R, mod);
/* compute candidate = R * base */
uint64_t candidate = modmul(R, base, mod);
/* choose R = (bit ? candidate : R) in constant time */
uint64_t bit = (exp >> i) & 1;
R = ct_select_u64(candidate, R, bit);
}
return R;
}
