A structural comparison of the computational difficulty of breaking discrete log cryptosystems

Kouichi Sakurai, Hiroki Shizuya

Research output: Contribution to journalArticle

  • 16 Citations

Abstract

The complexity of breaking cryptosystems of which security is based on the discrete logarithm problem is explored. The cryptosystems mainly discussed are the Diffie-Hellman key exchange scheme (DH), the Bellare-Micali noninteractive oblivious transfer scheme (EM), the ElGamal public-key cryptosystem (EG), the Okamoto conference-key sharing scheme (CONF), and the Shamir 3-pass key-transmission scheme (3PASS). The obtained relation among these cryptosystems is that 3 PASS < CONF < EG =£" BM s DH, where <JJdenotes the polynomial-time functionally many-to-one reducibility, i.e., a function version of the <£ -reducibility. We further give some condition in which these algorithms have equivalent difficulty. One of such conditions suggest another advantage of the discrete logarithm associated with ordinary elliptic curves.

LanguageEnglish
Pages29-43
Number of pages15
JournalJournal of Cryptology
Volume11
Issue number1
DOIs
Publication statusPublished - Jan 1 1998

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Cryptosystem
Cryptography
Reducibility
Many to one
Oblivious Transfer
Discrete Logarithm Problem
Discrete Logarithm
Key Exchange
Public-key Cryptosystem
Diffie-Hellman
Elliptic Curves
Polynomial time
Sharing
Polynomials

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Science Applications
  • Applied Mathematics

Cite this

A structural comparison of the computational difficulty of breaking discrete log cryptosystems. / Sakurai, Kouichi; Shizuya, Hiroki.

In: Journal of Cryptology, Vol. 11, No. 1, 01.01.1998, p. 29-43.

Research output: Contribution to journalArticle

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