Abstract
This paper proposes new techniques of double-size bipartite multiplications with single-size bipartite modular multiplication units. Smartcards are usually equipped with crypto-coprocessors for accelerating the computation of modular multiplications, however, their operand size is limited. Security institutes such as NIST and standards such as EMV have recommended or forced to increase the bit-length of RSA cryptography over years. Therefore, techniques to compute double-size modular multiplications with single-size modular multiplication units has been studied this decade to extend the life expectancy of the low-end devices. We propose new double-size techniques based on multipliers implementing either classical or Montgomery modular multiplications, or even both simultaneously (bipartite modular multiplication), in which case one can potentially compute modular multiplications twice faster.
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
Bajard, J.-C., Didier, L.-S., Kornerup, P.: An RNS Montgomery Modular Multiplication Algorithm. In: Proceedings of ARITH13, pp. 234–239. IEEE Computer Society, Los Alamitos (1997)
Chevallier-Mames, B., Joye, M., Paillier, P.: Faster Double-Size Modular Multiplication From Euclidean Multipliers. In: D.Walter, C., Koç, Ç.K., Paar, C. (eds.) CHES 2003. LNCS, vol. 2779, pp. 214–227. Springer, Heidelberg (2003)
EMVco. EMV Issuer and Application Security Guidelines, Version 1.3 (2005), http://www.emvco.com/specifications.asp?show=4
Fischer, W., Seifert, J.-P.: Increasing the bitlength of crypto-coprocessors. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 71–81. Springer, Heidelberg (2003)
Handschuh, H., Paillier, P.: Smart card crypto-coprocessors for public-key cryptography. In: Schneier, B., Quisquater, J.-J. (eds.) CARDIS 1998. LNCS, vol. 1820, pp. 372–379. Springer, Heidelberg (2000)
Kaihara, M.E., Takagi, N.: Bipartite modular multiplication. In: Rao, J.R., Sunar, B. (eds.) CHES 2005. LNCS, vol. 3659, pp. 201–210. Springer, Heidelberg (2005)
Lenstra, A.K., Verheul, E.R.: Selecting Cryptographic Key Sizes. J. Cryptology 14(4), 255–293 (2001)
Montgomery, P.L.: Modular multiplication without trial division. Mathematics of Computation 44(170), 519–521 (1985)
Menezes, A.J., van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)
National Institute of Standards ant Technology, NIST Special Publication 800-57 DRAFT, Recommendation for KeyManagement Part 1: General (2006), http://csrc.nist.gov/CryptoToolkit/tkkeymgmt.html
Naccache, D., M’Raïhi, D.: Arithmetic co-processors for public-key cryptography: The state of the art. In: CARDIS, pp. 18–20 (1996)
Paillier, P.: Low-cost double-size modular exponentiation or how to stretch your cryptoprocessor. In: Imai, H., Zheng, Y. (eds.) PKC 1999. LNCS, vol. 1560, pp. 223–234. Springer, Heidelberg (1999)
Posch, K.C., Posch, R.: Modulo reduction in Residue Number Systems. IEEE Transactions on Parallel and Distributed Systems 6(5), 449–454 (1995)
Quisquater, J.-J., Couvreur, C.: Fast decipherment algorithm for rsa public-key cryptosystem. Electronics Letters 18(21), 905–907 (1982)
RSA Laboratories, RSA challenges, http://www.rsa.com/rsalabs
Rivest, R.L., Shamir, A., Adelman, L.M.: A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM 21(2), 120–126 (1978)
Yoshino, M., Okeya, K., Vuillaume, C.: Unbridle the Bit-Length of a Crypto-Coprocessor with Montgomery Multiplication. In: Preproceedings of the 13th Annual Workshop on Selected Areas in Cryptography (SAC’06), pp. 184–198 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Yoshino, M., Okeya, K., Vuillaume, C. (2007). Double-Size Bipartite Modular Multiplication. In: Pieprzyk, J., Ghodosi, H., Dawson, E. (eds) Information Security and Privacy. ACISP 2007. Lecture Notes in Computer Science, vol 4586. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73458-1_18
Download citation
DOI: https://doi.org/10.1007/978-3-540-73458-1_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73457-4
Online ISBN: 978-3-540-73458-1
eBook Packages: Computer ScienceComputer Science (R0)