Accelerated Search for Gaussian Generator Based on Triple Prime Integers | Science Publications

Journal of Computer Science

Boris S. Verkhovsky¹  Md S. Sadik¹ 

关键词: Communication network security;    crypto-immunity;    primitive root;    public-key cryptography;   

DOI  :  10.3844/jcssp.2009.614.618

学科分类：计算机科学（综合）

来源: Science Publications

【 摘 要 】

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.

【 授权许可】

Unknown