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Computación y Sistemas
versión On-line ISSN 2007-9737versión impresa ISSN 1405-5546
Comp. y Sist. vol.12 no.3 Ciudad de México ene./mar. 2009
Artículos
Searching Prime Numbers with Short Binary Signed Representation
Búsqueda de Números Primos con Representaciones Signadas Cortas
Jose de Jesús Angel Angel1 and Guillermo MoralesLuna1
1 Computer Science Department CINVESTAVIPN, Mexico: Emails: jjangel@computacion.cs.cinvestav.mx ; gmorales@cs.cinvestav.mx
Article received on March 1, 2008
Accepted on June 14, 2008
Abstract
Modular arithmetic with prime moduli has been crucial in present day cryptography. The primes of Mersenne, Solinas, Crandall and the so called IKEMODP primes have been widely used in efficient implementations. In this paper we study the density of primes with binary signed representation involving a small number of nonzero ±1digits, and its repercussion in the generation of those primes.
Keywords: Pairing cryptography, prime numbers, signed representation.
Resumen
La aritmetica de residuos con números primos es crucial en la criptografía actual. Los números primos de Mersenne, Solinas, Crandall y los llamados IKEMODP han sido extensamente utilizados en diversas implementaciones. Estudiamos aquí la densidad de los primos con representaciones signadas que involucran sólo un número pequeño de dígitos nonulos ±1, así como su impacto en la generacion de tales primos.
Palabras Claves: Criptografía de emparejamientos, números primos, representaciones signadas.
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References
1. Chung, J. and A. Hasan (2003, April). More generalized mersenne number. Technical Report CORR200317, Dept. of Computer Science, University of Waterloo. [ Links ]
2. Crandall, R. E. (1994). Method and apparatus for public key exchange in a cryptographic system. Technical Report [ Links ]5463690, U.S. Patents.
3. (FIPS), F. I. P. S. (2000). Digital signature standard. Technical Report 1862, National Institute of Standards and Technology (NIST). [ Links ]
4. Knuth, D. E. (1997, November). Art of Computer Programming, Volume 2: Seminumerical Algorithms (3rd Edition). AddisonWesley Professional. [ Links ]
5. Solinas, J. (1999). Generalized Mersenne numbers. Technical Report CORR 199939, University of Waterloo. [ Links ]
6. Wagstaff, S. S. (2000). Prime numbers with a fixed number of one bits and zero bits in their binary representation. Experimental Mathematics 10(2), 267273. [ Links ]
7. Yie, I., S. Lim, S. Kim, and D. Kim (2003). Prime numbers of diffiehellman groups for ikemodp. In T. Johansson and S. Maitra (Eds.), INDOCRYPT, Volume 2904 of Lecture Notes in Computer Science, pp. 228234. Springer. [ Links ]