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

Igor E. Shparlinski

doi:10.1007/s10623-015-0063-9

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

Igor E. Shparlinski^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 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 language	English
Pages (from-to)	63-71
Number of pages	9
Journal	Designs, Codes and Cryptography
Volume	80
Issue number	1
DOIs	https://doi.org/10.1007/s10623-015-0063-9
Publication status	Published - 1 Jul 2016
Externally published	Yes

Keywords

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

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10.1007/s10623-015-0063-9

Cite this

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KW - Multiplicative subgroup rounding problem

KW - Multiplicative subgroups

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

Abstract

Keywords

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