Abstract
In this paper we present a method for improving the performance of RSA-type exponentiations. The scheme is based on the observation that replacing the exponent d by d′ = d + kΦ(n) has no arithmetic impact but results in significant speed-ups when k is properly chosen. Statistical analysis, verified by extensive simulations, confirms a performance improvement of 9.3% for the square-and-multiply scheme and 4.3% for the signed binary digit algorithm. However, the most attractive feature of our method seems to be the fact that in most cases, existing exponentiation black-boxes can be accelerated by simple external one-time pre-computations without any internal code or hardware modifications.
Chapter PDF
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
I. Bocharova, B. Kudryashov, Fast exponentiation in cryptography, AAECC-11, Lecture Notes in Computer Science 948, Springer Verlag, pp. 146–157, 1995.
A. Booth, A signed binary multiplication technique, Quarterly Journal of Mechanics and Applied Mathematics vol. 4, pp. 236–240, 1951.
A. Chiang, I. Reed, Arithmetic norms and bounds of the arithmetic AN codes, IEEE Trans. on Information Theory, vol. IT-16, pp. 470–476, 1970.
W. Clark, J. Liang, On arithmetic weight for a general radix representation of integers, IEEE Trans. on Information Theory, vol. IT-19, pp. 823–826, 1973.
C. Frougny, Linear numeration systems of order two, Information and Computation, vol. 77, pp. 233–259, 1988.
D. Gollmann, Y. Han, C. Mitchell, Redundant integer representations and fast exponentiation, Designs, Codes and Cryptography, vol. 7, pp. 135–151, 1996.
L. Hui, K. Lam, Fast square-and-multiply exponentiation for RSA, Electronic Letters, vol. 30, pp. 1396–1397, 1994.
D. Knuth, The Art of Computer Programming, Volume 2: Seminumerical Algorithms, Addison-Wesley, Reading, Mass., 1981.
Ç. KoÇ, High-radix and bit re-coding techniques for modular exponentiation, Intern. J. Computer Math., vol. 40, pp. 139–156, 1991.
F. MacWilliams, N. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, p. 309, 1977.
J. Quisquater, C. Couvreur, Fast decipherment algorithm for RSA public-key cryptosystem, Electronic Letters, vol. 18, pp. 905–907, 1982.
J. Sauerbrey, A. Dietel, Resource requirements for the application of addition chains in modulo exponentiation, eurocrypt'92, Lecture Notes in Computer Science 658, Springer Verlag, pp. 174–182, 1992.
N. Takagi, S. Yajima, Modular multiplication hardware algorithms with a redundant representation and their application to RSA cryptosystem, IEEE Trans. on Computers, vol. 41, 1992.
Y. Yacobi, Exponentiating faster with addition chains, eurocrypt'90, Lecture Notes in Computer Science 473, Springer Verlag, pp. 222–229, 1991.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cohen, G., Naccache, D., Lobstein, A., Zémor, G. (1998). How to improve an exponentiation black-box. In: Nyberg, K. (eds) Advances in Cryptology — EUROCRYPT'98. EUROCRYPT 1998. Lecture Notes in Computer Science, vol 1403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054128
Download citation
DOI: https://doi.org/10.1007/BFb0054128
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64518-4
Online ISBN: 978-3-540-69795-4
eBook Packages: Springer Book Archive