More on security of public-key cryptosystems based on chebyshev polynomials

Kai Y. Cheong, Takeshi Koshiba

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


Recently, a public-key cryptosystem based on Chebyshev polynomials has been proposed, but it has been later analyzed and shown insecure. This paper addresses some unanswered questions about the cryptosystem. We deal with the issue of computational precision. This is important for two reasons. Firstly, the cryptosystem is defined on real numbers, but any practical data communication channel can only transmit a limited number of digits. Any real number can only be specified to some precision level, and we study the effect of that. Secondly, we show that the precision issue is related to its security. In particular, the algorithm previously proposed to break the cryptosystem may not work in some situations. Moreover, we introduce another method to break the cryptosystem with general precision settings. We extend the method to show that a certain class of cryptosystems is insecure. Our method is based on the known techniques on the shortest vector problem in lattice and linear congruences.

Original languageEnglish
Pages (from-to)795-799
Number of pages5
JournalIEEE Transactions on Circuits and Systems II: Express Briefs
Issue number9
Publication statusPublished - 2007 Sept
Externally publishedYes


  • Chaos-based cryptography
  • Chebyshev polynomials
  • key agreement
  • public-key cryptography

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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