On small gaps between the elements of multiplicative subgroups of finite fields

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We establish new results about the frequency of small gaps between the elements of multiplicative subgroups of finite fields. As an application, we give some rigorous support to uniqueness assumptions of Boneh et al. (Why textbook ElGamal and RSA encryption are insecure, 2000) for solutions to additive and multiplicative subgroup rounding problems. These problems arise during attacks on some careless use of the ElGamal encryption.

Original languageEnglish
Pages (from-to)63-71
Number of pages9
JournalDesigns, Codes and Cryptography
Volume80
Issue number1
DOIs
Publication statusPublished - 1 Jul 2016
Externally publishedYes

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Keywords

  • Additive subgroup rounding problem
  • Finite fields
  • Multiplicative subgroup rounding problem
  • Multiplicative subgroups

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