Fastest parallel molecular algorithms for the elliptic curve discrete logarithm problem over GF(2n)

Gennaro Iaccarino, Tommaso Mazza

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Cryptography based on Elliptic Curves (ECC) has emerged as an effective alternative to the existing public-key cryp-tosystems (RSA and DSA). Its success was due both to the fact that no fast algorithms were known to break it and that exceptional security levels could be obtained by using short keys. The Elliptic Curve Discrete Logarithm (ECDL) problem is the cornerstone of much of present-day ECCs. It was classified as a computationally intractable problem and, consequently, as a reliable and unbreakable cryptosystem. In a recent work, Li et al. built a molecular computer designed to solve it over GF (2 n). It was based on two DNA-inspired algorithms: a parallel adder and a parallel multiplier, working in O(n) and O(n2) respectively, where n is the input size. In this paper, we first present two faster biological implementations, working in O(log(n)) and O(n · log(n)) respectively (worst case). Then, we propose our model as a reference parallel solution of the ECDL problem and finally we highlight the computational power of such nature-inspired paradigm.

Original languageEnglish
Title of host publicationProceedings of the 2009 Workshop on Bio-inspired Algorithms for Distributed Systems, BADS '09
Pages95-104
Number of pages10
Publication statusPublished - 2009
Event2009 Workshop on Bio-inspired Algorithms for Distributed Systems, BADS '09 - Barcelona, Spain
Duration: Jun 19 2009Jun 19 2009

Other

Other2009 Workshop on Bio-inspired Algorithms for Distributed Systems, BADS '09
Country/TerritorySpain
CityBarcelona
Period6/19/096/19/09

Keywords

  • DNA computing
  • Elliptic curve discrete logarithm
  • Parallel computations

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Hardware and Architecture
  • Software

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