TITLE:
Protection of Sensitive Messages Based on Quadratic Roots of Gaussians: Groups with Complex Modulus
AUTHORS:
Boris S. Verkhovsky
KEYWORDS:
Complex Modulus; Computational Efficiency; Cryptographic Algorithm; Digital Isotopes; Multiplicative Control Parameter; Octadic Roots, Quartic Roots, Rabin Algorithm, Reduction of Complexity, Resolventa, Secure Communication, Square Roots
JOURNAL NAME:
International Journal of Communications, Network and System Sciences,
Vol.4 No.5,
May
12,
2011
ABSTRACT: This paper considers three algorithms for the extraction of square roots of complex integers {called Gaussians} using arithmetic based on complex modulus p + iq. These algorithms are almost twice as fast as the analogous algorithms extracting square roots of either real or complex integers in arithmetic based on modulus p, where is a real prime. A cryptographic system based on these algorithms is provided in this paper. A procedure reducing the computational complexity is described as well. Main results are explained in several numeric illustrations.