Abstract
In most currently used public-key cryptographic systems, including those based on the difficulty to either factorize large numbers like the RSA [RSA78] or to extract a discrete logarithm of a large number [Elg85,DH76,US 94], the most time consuming part is modular exponentiation. The base of this computation is modular multiplication. We demonstrate the ability to implement very efficiently public-key cryptographic algorithms on nearly standard processors. Furthermore, as our study is also oriented to smart cards, we focus on algorithms minimizing the RAM needed for the computations as well as the ROM code.
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References
Barrett, P.: Communications authentication and security using public key encryption - A design for implementation -. Master’s thesis, Oxford University (September 1984)
Barrett, P.: Implementing the Rivest Shamir and Adleman public key encryption algorithm on a standard digital signal processor. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 311–323. Springer, Heidelberg (1987)
Brickell, E.F.: A fast modular multiplication algorithm with application to two key cryptography. In: Chaum, D., Rivest, R.L., Sherman, A.T. (eds.) Advances in cryptology Proc. of CRYPTO 1982, pp. 51–60. Plenum Press, New York (1983)
Benaloh, J., Dai, W.: Fast modular reduction. Rump Session of CRYPTO 1995, Santa Barbara, California (August 1995)
Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE transactions on information theory 22, 644–654 (1976)
Dhem, J.-F.: Modified version of the Barrett algorithm. Technical report (July 1994)
Dhem, J.F.: Design of an efficient public-key cryptographic library for RISC-based smart cards. Ph.D. thesis, Université catholique de Louvain - UCL Crypto Group - Laboratoire de microélectronique (DICE) (May 1998)
Dhem, J.-F., Joye, M., Quisquater, J.-J.: Normalisation in diminished- radix modulus transformation. Electronics letters 33, 1931 (1997)
Dhem, J.-F., Veithen, D., Quisquater, J.-J.: SCALPS: Smart Card for Limited Payment Systems. IEEE Micro, pp. 42–51 (June 1996)
de Waleffe, D., Quisquater, J.-J.: CORSAIR: a smart card for public key cryptosystems. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 502–513. Springer, Heidelberg (1991)
Elgamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE transactions on information theory 31, 469–472 (1985)
Ferreira, R., Malzahn, R., Marissen, P., Quisquater, J.-J., Wille, T.: FAME: A 3rd generation coprocessor for optimising public key crypto-systems in smart card applications. In: Hartel, P.H., Paradinas, P., Quisquater, J.-J. (eds.) Proc. CARDIS 1996, Smart Card Research and Advanced Applications, Stichting Mathematisch centrum, CWI, Amsterdam, The Netherlands, September 16–18, pp. 59–72 (1996)
Knuth, D.E.: The art of computer programming. In: Seminumerical Algorithms of Computer science and information processing, 3rd edn., vol. 2. Addison-Wesley, Reading (1997)
Posch, K.C., Posch, R.: Approaching encryption at ISDN speed using partial parallel modulus multiplication. In: Microprocessing and microprogramming, vol. 29, pp. 177–184. North-Holland, Amsterdam (1990)
Quisquater, J.-J., de Waleffe, D., Bournas, J.-P.: CORSAIR: A chip with fast RSA capability. In: Chaum, D. (ed.) Proc. Smart Card 2000, pp. 199–205. Elsevier Science Publishers, Amsterdam (1991)
Quisquater, J.-J.: Procédé de codage selon la méthode dite RSA, par un microcontrôleur et dispositifs utilisant ce procédé. Demande de brevet français. No de dépôt 90 02274, February 23 (1990)
Quisquater, J.-J.: Encoding system according to the so-called RSA method, by means of a microcontroller and arrangement implementing this system. U.S. Patent # 5,166,978, November 24 (1992)
Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. In: Proc. Communications of the ACM, vol. 21, pp. 120–126. ACM, New York (1978)
Sedlak, H.: The RSA cryptography processor. In: Price, W.L., Chaum, D. (eds.) EUROCRYPT 1987. LNCS, vol. 304, pp. 95–105. Springer, Heidelberg (1988)
US DEPARTMENT OF COMMERCE - National Institute of Standards and Technology. FIPS PUB 186: Digital Signature Standard (DSS), May 19 (1994)
Walter, C.D.: Faster modular multiplication by operand scaling. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 313–323. Springer, Heidelberg (1992)
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Dhem, J.F., Quisquater, J.J. (2000). Recent Results on Modular Multiplications for Smart Cards. In: Quisquater, JJ., Schneier, B. (eds) Smart Card Research and Applications. CARDIS 1998. Lecture Notes in Computer Science, vol 1820. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10721064_31
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DOI: https://doi.org/10.1007/10721064_31
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