VSH and multiplicative modular relations between small primes with polynomial exponents

Ian F. Blake, Florian Luca, Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We study the frequency of the positive integers n that are products of two primes of the same order of magnitude and such that the congruence Π i = 1 k p i f i (n) ≡ 1 (mod n) holds with some fixed nonzero polynomials f 1 (X), ..., f k (X) Z [ X ], where p i denotes the i th prime. The question is motivated by collision finding in the so-called Very Smooth Hash function, introduced by Contini et al. (Lecture notes in computer science, vol. 4004. Springer, Berlin, pp 165-182, 2006).

Original languageEnglish
Pages (from-to)181-188
Number of pages8
JournalApplicable Algebra in Engineering, Communications and Computing
Volume25
Issue number3
DOIs
Publication statusPublished - Jun 2014

Keywords

  • Hash function
  • Multiplicative relations
  • Polynomials
  • Primes

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