Function factor_from_order 

pub fn factor_from_order(a: &BigInt, r: u64, n: &BigInt) -> Option<BigInt>

Split n from a known order r of a: if r is even and a^{r/2} is a nontrivial square root of 1 (≢ ±1), then gcd(a^{r/2} ± 1, n) is a proper factor. None when the order is odd or the root is trivial (±1) — the ~50% of the time a fresh a is needed.