@article {10.3844/jcssp.2009.614.618,
article_type = {journal},
title = {Accelerated Search for Gaussian Generator Based on Triple Prime Integers},
author = {Verkhovsky, Boris S. and Sadik, Md Shiblee},
volume = {5},
number = {9},
year = {2009},
month = {Sep},
pages = {614-618},
doi = {10.3844/jcssp.2009.614.618},
url = {https://thescipub.com/abstract/jcssp.2009.614.618},
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.},
journal = {Journal of Computer Science},
publisher = {Science Publications}
}