Finding short and implementation-friendly addition chains with evolutionary algorithms View Full Text


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Article Info

DATE

2018-06

AUTHORS

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

ABSTRACT

Finding the shortest addition chain for a given exponent is a significant problem in cryptography. In this work, we present a genetic algorithm with a novel encoding 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 exponents of moderate size, but we also investigate values up to 2255-21. For numbers of such size, we were unable to find any results produced by other metaheuristics which could be used for comparison purposes. Therefore, we decided to add three additional strategies to serve as benchmarks. Our results indicate that the proposed approach is a very promising alternative to deal with this problem. We also consider a more practical perspective by taking into account the implementation cost of the chains: we optimize the addition chains with regards to the type of operations as well as the number of instructions required for the implementation. More... »

PAGES

457-481

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
  • 2002-02-08. Resistance Against Differential Power Analysis For Elliptic Curve Cryptosystems in CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS
  • 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
  • 2011-03. Calculating optimal addition chains in COMPUTING
  • 2016. Evolutionary Algorithms for Finding Short Addition Chains: Going the Distance in EVOLUTIONARY COMPUTATION IN COMBINATORIAL OPTIMIZATION
  • 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
  • 2001-07-06. Addition Chain Heuristics in ADVANCES IN CRYPTOLOGY — CRYPTO’ 89 PROCEEDINGS
  • 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
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10732-017-9340-2

    DOI

    http://dx.doi.org/10.1007/s10732-017-9340-2

    DIMENSIONS

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