Artículos

Searching Prime Numbers with Short Binary Signed Representation

Búsqueda de Números Primos con Representaciones Signadas Cortas

Jose de Jesús Angel Angel¹ and Guillermo Morales–Luna¹

¹ Computer Science Department CINVESTAV–IPN, Mexico: E–mails: 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 IKE–MODP 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 non–zero ±1–digits, 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 IKE–MODP 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 no–nulos ±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

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