Modular number systems: Beyond the mersenne family

Lecture Notes in Computer Science

Volumn 3357, Issue , 2005, Pages 159-169

  Bajard, Jean Claude ^a   Imbert, Laurent ^a,b   Plantard, Thomas ^a  

^a LIRMM   (France)

^b UNIVERSITY OF CALGARY   (Canada)

Author keywords

Elliptic curve cryptography; Generalized Mersenne numbers; Montgomery multiplication

Indexed keywords

CRYPTOGRAPHY; MATHEMATICAL OPERATORS;

ELLIPTIC CURVE CRYPTOGRAPHY; GENERALIZED MERSENNE NUMBERS; MODULAR MULTIPLICATION; MONTGOMERY MULTIPLICATION;

NUMBER THEORY;

EID: 24144452461     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (8)

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2. J. Chung and A. Hasan. More generalized mersenne numbers. In M. Matsui and R. Zuccherato, editors, Selected Areas in Cryptography - SAC 2003, volume 3006 of LNCS, Ottawa, Canada, August 2003. Springer-Verlag, (to appear).
3. R. Crandall. Method and apparatus for public key exchange in a cryptographic system. U.S. Patent number 5159632, 1992.
4. D. Hankerson, A. Menezes, and S. Vanstone. Guide to Elliptic Curve Cryptography. Springer-Verlag, 2004.
5. Ç. K. Koç, T. Acar, and B. S. Kaliski Jr. Analyzing and comparing montgomery multiplication algorithms. IEEE Micro, 16(3):26-33, June 1996.
6. A. J. Menezes, P. C. Van Oorschot, and S. A. Vanstone. Handbook of applied cryptography. CRC Press, 2000 N.W. Corporate Blvd., Boca Raton, FL 33431-9868, USA, 1997.
7. P. L. Montgomery. Modular multiplication without trial division. Mathematics of Computation, 44(170):519-521, April 1985.
8. J. Solinas. Generalized mersenne numbers. Research Report CORR-99-39, Center for Applied Cryptographic Research, University of Waterloo, Waterloo, ON, Canada, 1999.