How to generate random integers with known factorization

Authors:
Eric Bach
Affiliations:
-
Venue:
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Year:
1983

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Abstract

Recent work in public-key cryptography has led to the need to generate large random numbers with known factorization. This paper describes a probabilistic algorithm that produces a random k-bit integer in factored form. Each such number is equally likely to appear. The expected running time is, up to a constant factor, that required for k prime tests on k-bit integers. Thus, under reasonable assumptions about the speed of primality testing, it is a polynomial time process.