Abstract
Three modular reduction algorithms for large integers are compared with respect to their performance in portable software: the classical algorithm, Barrett’s algorithm and Montgomery’s algorithm. These algorithms are a time critical step in the implementation of the modular exponentiation operation. For each of these algorithms their application in the modular exponentiation operation is considered. Modular exponentiation constitutes the basis of many well known and widely used public key cryptosystems. A fast and portable modular exponentiation will considerably enhance the speed and applicability of these systems.
Chapter PDF
Similar content being viewed by others
References
P.D. Barrett, “Implementing the Riveat Shamir and Adleman public key encryption algorithm on a standard digital signal processor,” Advances in Cryptology, Proc. Crypto’86, LNCS 263, A.M. Odlyzko, Ed., Springer-Verlag, 1987, pp. 311–323.
S.R. Dussé and B.S. Kaliski, “A cryptographic library for the Motorola DSP56000,” Advances in Cryptology, Proc. Eurocrypt’90, LNCS 473, I.B. Damgård, Ed., Springer-Verlag, 1991, pp. 230–244.
K. Hensel, Theorie der algebraischen Zahlen, Leipzig, 1908.
“American National Standard for Programming Languages—C,” ISO/IEC Standard 9899:1990, International Standards Organization, Geneva, 1990.
D.E. Knuth, The Art of Computer Programming, Vol. 2, Seminumerical Algorithms, 2nd Edition, Addiaon-Wesley, Reading, Mass., 1981.
P.L. Montgomery, “Modular multiplication without trial division,” Mathematics of Computation, Vol. 44, 1985, pp. 519–521.
J.-J. Quisquater, presentation at the rump session of Eurocrypt’90.
M.O. Rabin, “Probabilistic algorithms for testing primality,” J. of Number Theory, Vol. 12, 1980, pp. 128–128.
M. Shand and J. Vuillemin, “Fast Implementations of RSA cryptography,” Proceedings of the 11th IEEE Symposium on Computer Arithmetic, IEEE Computer Society Press, Los Alamitos, CA, 1993, pp. 252–259.
CD. Walter, “Faster modular multiplication by operand scaling,” Advances in Cryptology, Proc. Crypto’91, LNCS 576, J. Feigenbaum, Ed., Springer-Verlag, 1992, pp. 313–323.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bosselaers, A., Govaerts, R., Vandewalle, J. (1994). Comparison of three modular reduction functions. In: Stinson, D.R. (eds) Advances in Cryptology — CRYPTO’ 93. CRYPTO 1993. Lecture Notes in Computer Science, vol 773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48329-2_16
Download citation
DOI: https://doi.org/10.1007/3-540-48329-2_16
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57766-9
Online ISBN: 978-3-540-48329-8
eBook Packages: Springer Book Archive