Montgomery Exponentiation with no Final Subtractions: Improved Results
作者： Gaël Hachez , Jean-Jacques Quisquater
关键词:
摘要: The Montgomery multiplication is commonly used as the core algorithm for cryptosystems based on modular arithmetic. With advent of new classes attacks (timing attacks, power attacks), implementation should be carefully studied to thwart those attacks. Recently, Colin D. Walter proposed a constant time this [17,18]. In paper, we propose an improved (faster) version implementation. We also provide figures about overhead these versions relatively speed optimised (theoretically and experimentally).
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Paul Barrett, Implementing the Rivest Shamir and Adleman public key encryption algorithm on a standard digital signal processor international cryptology conference. pp. 311- 323 ,(1987) , 10.1007/3-540-47721-7_24
Kouichi Itoh, Masahiko Takenaka, Naoya Torii, Syouji Temma, Yasushi Kurihara, Fast Implementation of Public-Key Cryptography ona DSP TMS320C6201 cryptographic hardware and embedded systems. pp. 61- 72 ,(1999) , 10.1007/3-540-48059-5_7
Colin D. Walter, Montgomery's Multiplication Technique: How to Make It Smaller and Faster cryptographic hardware and embedded systems. pp. 80- 93 ,(1999) , 10.1007/3-540-48059-5_9
Paul C. Kocher, Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems international cryptology conference. ,vol. 1109, pp. 104- 113 ,(1996) , 10.1007/3-540-68697-5_9
Jean-François Dhem, François Koeune, Philippe-Alexandre Leroux, Patrick Mestré, Jean-Jacques Quisquater, Jean-Louis Willems, A Practical Implementation of the Timing Attack smart card research and advanced application conference. ,vol. 1820, pp. 167- 182 ,(1998) , 10.1007/10721064_15
Gaël Hachez, Jean-Jacques Quisquater, Fraņcois Koeune, TIMING ATTACK: WHAT CAN BE ACHIEVED BY A POWERFUL ADVERSARY? ,(2000)
Jean-Jacques Quisquater, Encoding system according to the so-called rsa method, by means of a microcontroller and arrangement implementing this system ,(1991)
Peter L. Montgomery, Modular multiplication without trial division Mathematics of Computation. ,vol. 44, pp. 519- 521 ,(1985) , 10.1090/S0025-5718-1985-0777282-X
Stephen E. Eldridge, A faster modular multiplication algorithm International Journal of Computer Mathematics. ,vol. 40, pp. 63- 68 ,(1991) , 10.1080/00207169108804001
C.D. Walter, Montgomery exponentiation needs no final subtractions Electronics Letters. ,vol. 35, pp. 1831- 1832 ,(1999) , 10.1049/EL:19991230