Function rsa_private_exponent 

pub fn rsa_private_exponent(
    e: &BigInt,
    p: &BigInt,
    q: &BigInt,
) -> Option<BigInt>

Derive the RSA private exponent d = e⁻¹ mod φ(N) from the public exponent and the two primes (φ = (p−1)(q−1)), or None if e is not coprime to φ. The “if you can factor, you can break RSA” direction: the factorization hands over the private key.