Abstract
The performance of public-key cryptosystems is primarily determined by the implementation efficiency of the modular multiplication and exponentiation. As the operands, i.e. the plain text of a message or the cipher (possibly a partially ciphered) text are usually large (1024 bits or more), and in order to improve time requirements of the encryption/decryption operations, it is essential to attempt to minimise the number of modular multiplications performed. In this paper, we exploit the ant colony’s principles to engineer a minimal addition chain that allows one to compute modular exponentiations very efficiently. The obtained results are compared to existing heuristics as well as to genetically evolved addition chains, i.e. using genetic algorithms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Dorigo, M. and Gambardella, L.M. 1997, Ant Colony: a Cooperative Learning Approach to the Travelling Salesman Problem, IEEE Transaction on Evolutionary Computation, Vol. 1, No. 1, pp. 53–66
Downing, P. Leong B. and Sthi, R. 1981, Computing Sequences with Addition Chains, SIAM Journal on Computing, vol. 10, No. 3, pp. 638–646
Feber, J. 1995, Multi-Agent Systems: an Introduction to Distributed Artificial Intelligence, Addison-Wesley
Nedjah, N., Mourelle, L.M. 2002, Efficient Parallel Modular Exponentiation Algorithm, Second International Conference on Information systems, ADVIS′2002, Lecture Notes in Computer Science, Springer-Verlag, vol. 2457, pp. 405–414
Nedjah, N. and Mourelle, L.M., Minimal addition chains using genetic algorithms, Proceedings of the Fifteenth International Conference on Industrial & Engineering Applications of Artificial Intelligence &Expert Systems, Lecture Notes in Computer Science, Springer-Verlag, vol. 2358, pp. 88–98
Rivest, R., Shamir, A. and Adleman, L. 1978, A method for Obtaining Digital Signature and Public-Key Cryptosystems, Communications of the ACM, 21:120–126
Stutzle, T. and Dorigo, M. 1999, ACO Algorithms for the Travelling Salesman Problems, Evolutionary Algorithms in Engineering and Computer Science, John-Wiley
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this paper
Cite this paper
Nedjah, N., Mourelle, L.d. (2006). Towards Very Fast Modular Exponentiations Using Ant Colony. In: Abraham, A., de Baets, B., Köppen, M., Nickolay, B. (eds) Applied Soft Computing Technologies: The Challenge of Complexity. Advances in Soft Computing, vol 34. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31662-0_32
Download citation
DOI: https://doi.org/10.1007/3-540-31662-0_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31649-7
Online ISBN: 978-3-540-31662-6
eBook Packages: EngineeringEngineering (R0)