Evolutionary Algorithms for Finding Short Addition Chains: Going the Distance View Full Text


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Chapter Info

DATE

2016

AUTHORS

Stjepan Picek , Carlos A. Coello Coello , Domagoj Jakobovic , Nele Mentens

ABSTRACT

The problem of finding the shortest addition chain for a given exponent is of great relevance in cryptography, but is also very difficult to solve since it is an NP-hard problem. In this paper, we propose a genetic algorithm with a novel representation of solutions and new crossover and mutation operators to minimize the length of the addition chains corresponding to a given exponent. We also develop a repair strategy that significantly enhances the performance of our approach. The results are compared with respect to those generated by other metaheuristics for instances of moderate size, but we also investigate values up to \(2^{127} - 3\). For those instances, we were unable to find any results produced by other metaheuristics for comparison, and three additional strategies were adopted in this case to serve as benchmarks. Our results indicate that the proposed approach is a very promising alternative to deal with this problem. More... »

PAGES

121-137

References to SciGraph publications

  • 2009. Finding Minimal Addition Chains with a Particle Swarm Optimization Algorithm in MICAI 2009: ADVANCES IN ARTIFICIAL INTELLIGENCE
  • 2006-12. Towards Minimal Addition Chains Using Ant Colony Optimisation in JOURNAL OF MATHEMATICAL MODELLING AND ALGORITHMS
  • 2001-08-02. Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms in ADVANCES IN CRYPTOLOGY — CRYPTO 2001
  • 2002. Minimal Addition-Subtraction Chains Using Genetic Algorithms in ADVANCES IN INFORMATION SYSTEMS
  • 2013. A Genetic Algorithm for the Problem of Minimal Brauer Chains in RECENT ADVANCES ON HYBRID INTELLIGENT SYSTEMS
  • 2002-02-08. Resistance Against Differential Power Analysis For Elliptic Curve Cryptosystems in CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS
  • 2004. Finding Minimal Addition Chains Using Ant Colony in INTELLIGENT DATA ENGINEERING AND AUTOMATED LEARNING – IDEAL 2004
  • 2003. Minimal Addition-Subtraction Sequences for Efficient Pre-processing in Large Window-Based Modular Exponentiation Using Genetic Algorithms in INTELLIGENT DATA ENGINEERING AND AUTOMATED LEARNING
  • 2014. Efficient and Secure Algorithms for GLV-Based Scalar Multiplication and Their Implementation on GLV-GLS Curves in TOPICS IN CRYPTOLOGY – CT-RSA 2014
  • 2002-06-21. Minimal Addition Chain for Efficient Modular Exponentiation Using Genetic Algorithms in DEVELOPMENTS IN APPLIED ARTIFICIAL INTELLIGENCE
  • 2005. Finding Optimal Addition Chains Using a Genetic Algorithm Approach in COMPUTATIONAL INTELLIGENCE AND SECURITY
  • 2014. Kummer Strikes Back: New DH Speed Records in ADVANCES IN CRYPTOLOGY – ASIACRYPT 2014
  • 2011-07. Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves in JOURNAL OF CRYPTOLOGY
  • Book

    TITLE

    Evolutionary Computation in Combinatorial Optimization

    ISBN

    978-3-319-30697-1
    978-3-319-30698-8

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-30698-8_9

    DOI

    http://dx.doi.org/10.1007/978-3-319-30698-8_9

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1035105218


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