Abstract
In this paper, we propose a generalized Takagi-Cryptosystem with a modulus of the form p r q x. We’ve studied for the optimal choice for r, s that gives the best efficiency while maintaining a prescribed security level, and we show that the choice of either p r q r+1,p r-1q r+1, or p r-2q r+2 depending on the value r + s is the optimal. We also present comparison tables for the efficiency of RSA, the multiprime technology, Takagi’s scheme, and our proposed scheme.
Yie’s work was partly supported by Inha Research Fund 2000.
This is a preview of subscription content, log in via an institution to check access.
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
T. Takagi,: Fast RSA-type cryptosystem modulo p k q, Advances in Cryptology-CRYPTO’98 LNCS 1462(1998), pp. 318–326. 284, 286, 287, 290, 294
T. Takagi,: Fast RSA-type cryptosystem using n-adic expansion, Advances in Cryptology-CRYPTO’97 LNCS 1294 (1997), pp. 372–384. 284, 287
D. Boneh, G. Durfee, N. Howgrave-Graham,: Factoring N = p r q for large r, Advances in Cryptology-CRYPTO’99LNCS 1666 (1999), pp. 326–337. 284, 284, 291, 291, 291, 291
D. Coppersmith,: Modifications to the number field sieve, J. of Cryptology, Vol. 6(1993), pp. 169–180. 284
A.K. Lenstra, H.W. Lenstra, Jr.,: Algorithms in Number theory, in Handbook of Theoretical Computer Science (Volume A: Algorithms and Complexity) (1990), pp. 673-715. 284
A.K. Lenstra, E.R. Verheul,: Selecting Cryptographic Key Sizes, http://www.cryptosavvy.com (1999). 283, 285, 285, 292
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lim, S., Kim, S., Yie, I., Lee, H. (2000). A Generalized Takagi-Cryptosystem with a Modulus of the Form prqs . In: Roy, B., Okamoto, E. (eds) Progress in Cryptology —INDOCRYPT 2000. INDOCRYPT 2000. Lecture Notes in Computer Science, vol 1977. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44495-5_25
Download citation
DOI: https://doi.org/10.1007/3-540-44495-5_25
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41452-0
Online ISBN: 978-3-540-44495-4
eBook Packages: Springer Book Archive