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In this article we present applications of smooth numbers to the unconditional derandomization of some well-known integer factoring algorithms. We begin with Pollard's p − 1 algorithm, which finds in random polynomial time the prime divisors p of an integer n such that p − 1 is smooth. We show that these prime factors can be recovered in deterministic… (More)

The discrete logarithm problem modulo a composite—abbreviate it as DLPC—is the following: given a (possibly) composite integer n ≥ 1 and elements $${a, b \in \mathbb{Z}_n^*}$$ , determine an $${x \in \mathbb{N}}$$ satisfying a x = b if one exists. The question whether integer factoring can be reduced in deterministic polynomial time to the DLPC remains… (More)

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