Arithmetic operations in the polynomial modular number system

Proceedings - Symposium on Computer Arithmetic

Volumn , Issue , 2005, Pages 206-213

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

^a LIRMM   (France)

^b UNIVERSITY OF CALGARY   (Canada)

Author keywords

Lattice theory; Modular arithmetic; Number system; Table based methods

Indexed keywords

INTEGER PROGRAMMING; MATHEMATICAL OPERATORS; NUMBER THEORY; POLYNOMIALS;

ARITHMETIC OPERATIONS; INTEGER MODULO; POLYNOMIAL ARITHMETIC; POLYNOMIAL MODULAR NUMBER SYSTEMS;

DIGITAL ARITHMETIC;

EID: 27944467947     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (14)

1. J.-C. Bajard, L. Imbert, and T. Plantard. Arithmetic operations in the polynomial modular number system. Research Report 04030, LIRMM - CNRS, 161 rue Ada, 34392 Montpellier cedex 5, France, Sept. 2004. Available electronicaly at http://www.lirmm.fr/~imbert.
2. J.-C. Bajard, L. Imbert, and T. Plantard. Modular number systems: Beyond the Mersenne family. In Selected Areas in Cryptography: 11th International Workshop, SAC 2004, volume 3357 of LNCS, pages 159-169. Springer-Verlag, Jan. 2005.
3. P. Barrett. Implementing the Rivest Shamir and Adleman public key encryption algorithm on a standard digital signal processor. In A. M. Odlyzko, editor, Advances in Cryptology - CRYPTO '86, volume 263 of LNCS, pages 311-326. Springer-Verlag, 1986.
4. 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, pages 335-347. Springer-Verlag, 2004.
5. R. Crandall. Method and apparatus for public key exchange in a cryptographic system. U.S. Patent number 5159632, 1992.
6. W. Diffie and M. E. Hellman. New directions in cryptography. IEEE Transactions on Information Theory, IT-22(6):644-654, November 1976.
7. C. Dwork. Lattices and their applications to cryptography. Lecture notes, Stanford University, 1998.
8. D. Hankerson, A. Menezes, and S. Vanstone. Guide to Elliptic Curve Cryptography. Springer-Verlag, 2004.
9. L. Lovász. An Algorithmic Theory of Numbers, Graphs and Convexity, volume 50 of CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM Publications, 1986.
10. A. Menezes, P. C. Van Oorschot, and S. A. Vanstone. Handbook of applied cryptography. CRC Press, 1997.
11. D. Micciancio and S. Goldwasser. Complexity of Lattice Problems, A Cryptographic Perspective. Kluwer Academic Publishers, 2002.
12. P. L. Montgomery. Modular multiplication without trial division. Mathematics of Computation, 44(170):519-521, Apr. 1985.
13. R. Rivest, A. Shamir, and L. Adleman. A method for obtaining digital signatures and public key cryptosystems. Communications of the ACM, 21(2):120-126, February 1978.
14. J. Solinas. Generalized mersenne numbers. Research Report CORR-99-39, Center for Applied Cryptographic Research, University of Waterloo, Waterloo, ON, Canada, 1999.