Short exponent diffie-hellman problems

Takeshi Koshiba, Kaoru Kurosawa

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

In this paper, we study short exponent Diffie-Hellman problems, where significantly many lower bits are zeros in the exponent. We first prove that the decisional version of this problem is as hard as two well known hard problems, the standard decisional Diffie-Hellman problem (DDH) and the short exponent discrete logarithm problem. It implies that we can improve the efficiency of ElGamal scheme and Cramer-Shoup scheme under the two widely accepted assumptions. We next derive a similar result for the computational version of this problem.

Original languageEnglish
Pages (from-to)173-186
Number of pages14
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2947
Publication statusPublished - 2004
Externally publishedYes

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Diffie-Hellman
Exponent
Discrete Logarithm Problem
Imply
Zero

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

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abstract = "In this paper, we study short exponent Diffie-Hellman problems, where significantly many lower bits are zeros in the exponent. We first prove that the decisional version of this problem is as hard as two well known hard problems, the standard decisional Diffie-Hellman problem (DDH) and the short exponent discrete logarithm problem. It implies that we can improve the efficiency of ElGamal scheme and Cramer-Shoup scheme under the two widely accepted assumptions. We next derive a similar result for the computational version of this problem.",
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AB - In this paper, we study short exponent Diffie-Hellman problems, where significantly many lower bits are zeros in the exponent. We first prove that the decisional version of this problem is as hard as two well known hard problems, the standard decisional Diffie-Hellman problem (DDH) and the short exponent discrete logarithm problem. It implies that we can improve the efficiency of ElGamal scheme and Cramer-Shoup scheme under the two widely accepted assumptions. We next derive a similar result for the computational version of this problem.

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