Title :
Safe primes density and cryptographic applications
Author :
Díaz, R. Durán ; Vitini, F. Montoya ; Masqué, J. Muñoz
Author_Institution :
Inst. de Fisica Aplicada, CSIC, Madrid, Spain
Abstract :
Safe prime number deployment has proved to be a major concern when developing public key cryptographic applications. Most popular public key cryptosystems (PKC) are rooted in the grounds of a high-quality safe prime number generator being available. For instance, RSA-present almost anywhere a PKC is needed-is claimed to need the so-called “strong primes”, related to safe primes. Similarly, BBS (the Blum-Blum-Shub PKC) is founded on pseudo-random number generation by means of the so-called BBS generator, whose maximal length orbits are obtained precisely when 2-safe primes, verifying some other suitable conditions, are used to build up the congruence modulus. Interest in this type of number encourages research into its density and methods of computation. We present an estimate for the density of both 1-safe and 2-safe prime numbers
Keywords :
number theory; public key cryptography; random number generation; 1-safe prime numbers; 2-safe prime numbers; BBS generator; RSA; congruence modulus; pseudo-random number generation; public key cryptosystems; safe prime number density; Computer applications; Gaussian processes; Hidden Markov models; Orbits; Proposals; Public key cryptography; Upper bound;
Conference_Titel :
Security Technology, 1999. Proceedings. IEEE 33rd Annual 1999 International Carnahan Conference on
Conference_Location :
Madrid
Print_ISBN :
0-7803-5247-5
DOI :
10.1109/CCST.1999.797938
