On the uniformity of distribution of the RSA pairs

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Let m = pl be a product of two distinct primes p and l. We show that for almost all exponents e with gcd(e,ρ(m)) = 1 the RSA pairs (cursive Greek chi,cursive Greek chie) are uniformly distributed modulo m when cursive Greek chi runs through • the group of units ℤ*m modulo m (that is, as in the classical RSA scheme); • the set of k-products cursive Greek chi = ai1 ⋯ aik, 1 ≤ i1 < ⋯ < ik, ≤ n, where a1, ⋯ , an ∈ ℤ*m are selected at random (that is, as in the recently introduced RSA scheme with precomputation). These results are based on some new bounds of exponential sums.

Original languageEnglish
Pages (from-to)801-808
Number of pages8
JournalMathematics of Computation
Volume70
Issue number234
DOIs
Publication statusPublished - Apr 2001

Fingerprint

Dive into the research topics of 'On the uniformity of distribution of the RSA pairs'. Together they form a unique fingerprint.

Cite this