4.3 Article

Finding short and implementation-friendly addition chains with evolutionary algorithms

期刊

JOURNAL OF HEURISTICS
卷 24, 期 3, 页码 457-481

出版社

SPRINGER
DOI: 10.1007/s10732-017-9340-2

关键词

Addition chains; Genetic algorithms; Cryptography; Optimization; Implementation

资金

  1. Croatian Science Foundation [IP-2014-09-4882]
  2. CONACyT Project [221551]
  3. Research Council KU Leuven [C16/15/058]
  4. IOF project EDA-DSE [HB/13/020]

向作者/读者索取更多资源

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 . 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.

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