Cryptology ePrint Archive: Report 2008/437

Divisibility, Smoothness and Cryptographic Applications

David Naccache and Igor Shparlinski

Abstract: This paper deals with products of moderate-size primes, familiarly known as {\sl smooth numbers}. Smooth numbers play an crucial role in information theory, signal processing and cryptography.

We present various properties of smooth numbers relating to their enumeration, distribution and occurrence in various integer sequences. We then turn our attention to cryptographic applications in which smooth numbers play a pivotal role.

Category / Keywords: foundations / divisibility, public-key cryptography, prime numbers

Date: received 11 Oct 2008, last revised 17 Oct 2008

Contact author: david naccache at ens fr

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Version: 20081020:184202 (All versions of this report)

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