Description
This note discusses the relationship between the two problems of the title. We present probabilistic polynomial-time reductions that show:
1) To factor n, it suffices to be able to compute discrete logarithms modulo n.
2) To compute a discrete logarithm modulo a prime power p^(e), it suffices to know it mod p.
3) To compute a discrete logarithm modulo any n, it suffices to be able to factor and compute discrete logarithms modulo primes.
1) To factor n, it suffices to be able to compute discrete logarithms modulo n.
2) To compute a discrete logarithm modulo a prime power p^(e), it suffices to know it mod p.
3) To compute a discrete logarithm modulo any n, it suffices to be able to factor and compute discrete logarithms modulo primes.
To summarize: solving the discrete logarithm problem for a composite modulus is exactly as hard as factoring and solving it modulo primes.