Accelerated search for Gaussian generator based on triple prime integers

Document Type

Article

Publication Date

9-22-2009

Abstract

Problem statement: Modern cryptographic algorithms are based on complexity of two problems: Integer factorization of real integers and a Discrete Logarithm Problem (DLP). Approach: The latter problem is even more complicated in the domain of complex integers, where Public Key Cryptosystems (PKC) had an advantage over analogous encryption-decryption protocols in arithmetic of real integers modulo p: The former PKC have quadratic cycles of order O (p2) while the latter PKC had linear cycles of order O(p). Results: An accelerated non-deterministic search algorithm for a primitive root (generator) in a domain of complex integers modulo triple prime p was provided in this study. It showed the properties of triple primes, the frequencies of their occurrence on a specified interval and analyzed the efficiency of the proposed algorithm. Conclusion: Numerous computer experiments and their analysis indicated that three trials were sufficient on average to find a Gaussian generator. © 2009 Science Publications.

Identifier

70349188462 (Scopus)

Publication Title

Journal of Computer Science

External Full Text Location

https://doi.org/10.3844/jcssp.2009.614.618

ISSN

15493636

First Page

614

Last Page

618

Issue

9

Volume

5

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