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Addition chain length minimization with evolutionary programming

Published: 12 July 2011 Publication History

Abstract

This paper presents the use of an evolutionary metaheuristic algorithm called evolutionary programming to minimize the length of addition chains, which is an NP-hard problem. Addition chains are used in modular exponentiation for data encryption and decryption public-key cryptosystems, such as RSA, DSA and others. The algorithm starts with a population of feasible addition chains. After that, the combination of a mutation operator, which allows each individual to generate a feasible offspring, and a replacement process based on stochastic encounters provides a simple approach which is tested on exponents with different features. The proposed algorithm is able to find competitive results with respect to other nature-inspired metaheuristic approaches but with a lower number of evaluations per run.

References

[1]
N. Cruz-Cortés, F. Rodríguez-Henríquez, and C. A. Coello-Coello. An artificial immune system heuristic for generating short addition chains. IEEE Transactions on Evolutionary Computation, 12(1):1--24, February 2008.
[2]
A. León-Javier, N. Cruz-Cortés, M. A. Moreno-Armendáriz, and S. Orantes-Jiménez. Finding minimal addition chains with a particle swarm optimization algorithm. Lecture Notes in Computer Science, 5845/2009:680--691, 2009.
[3]
L. G. Osorio-Hernández, E. Mezura-Montes, N. Cruz-Cortés, and F. Rodríguez-Henríquez. An improved genetic algorithm able to find minimal lenght addition chains for small exponents. In Proceedings of the IEEE Congress on Evolutionary Computation, pages 1422--1429. IEEE Press, 2009.

Cited By

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  • (2022)Evolutionary computation and machine learning in securityProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3520304.3534087(1572-1601)Online publication date: 9-Jul-2022
  • (2021)Evolutionary computation and machine learning in cryptologyProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3449726.3461420(1089-1118)Online publication date: 7-Jul-2021
  • (2020)Evolutionary computation and machine learning in cryptologyProceedings of the 2020 Genetic and Evolutionary Computation Conference Companion10.1145/3377929.3389886(1147-1173)Online publication date: 8-Jul-2020
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Published In

cover image ACM Conferences
GECCO '11: Proceedings of the 13th annual conference companion on Genetic and evolutionary computation
July 2011
1548 pages
ISBN:9781450306904
DOI:10.1145/2001858

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 July 2011

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Author Tags

  1. addition chains
  2. cryptography
  3. evolutionary programming

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Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

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Cited By

View all
  • (2022)Evolutionary computation and machine learning in securityProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3520304.3534087(1572-1601)Online publication date: 9-Jul-2022
  • (2021)Evolutionary computation and machine learning in cryptologyProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3449726.3461420(1089-1118)Online publication date: 7-Jul-2021
  • (2020)Evolutionary computation and machine learning in cryptologyProceedings of the 2020 Genetic and Evolutionary Computation Conference Companion10.1145/3377929.3389886(1147-1173)Online publication date: 8-Jul-2020
  • (2018)Asymmetric Addition Chaining Cryptographic Algorithm (ACCA) for Data Security in CloudAdvances in Big Data and Cloud Computing10.1007/978-981-10-7200-0_30(331-340)Online publication date: 7-Apr-2018
  • (2017)Evolutionary computation and cryptologyProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3067695.3067725(1066-1093)Online publication date: 15-Jul-2017
  • (2016)Evolutionary Computation and CryptologyProceedings of the 2016 on Genetic and Evolutionary Computation Conference Companion10.1145/2908961.2927003(883-909)Online publication date: 20-Jul-2016
  • (2016)A genetic algorithm with a mutation mechanism based on a Gaussian and uniform distribution to minimize addition chains for small exponents2016 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC.2016.7743890(935-940)Online publication date: Jul-2016
  • (2016)Evolutionary Algorithms for Finding Short Addition Chains: Going the DistanceEvolutionary Computation in Combinatorial Optimization10.1007/978-3-319-30698-8_9(121-137)Online publication date: 2016
  • (2013)A Genetic Algorithm for the Problem of Minimal Brauer Chains for Large ExponentsSoft Computing Applications in Optimization, Control, and Recognition10.1007/978-3-642-35323-9_2(27-51)Online publication date: 2013
  • (2013)A Genetic Algorithm for the Problem of Minimal Brauer ChainsRecent Advances on Hybrid Intelligent Systems10.1007/978-3-642-33021-6_37(481-500)Online publication date: 2013

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