%0 Journal Article
%T Protection of Sensitive Messages Based on Quadratic Roots of Gaussians: Groups with Complex Modulus
%A Boris S. Verkhovsky
%J Int'l J. of Communications, Network and System Sciences
%P 287-296
%@ 1913-3723
%D 2011
%I Scientific Research Publishing
%R 10.4236/ijcns.2011.45033
%X This paper considers three algorithms for the extraction of square roots of complex integers {called Gaussians} using arithmetic based on complex modulus <i>p</i> + <i>iq</i>. 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 <i>p</i>, 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.
%K Complex Modulus
%K Computational Efficiency
%K Cryptographic Algorithm
%K Digital Isotopes
%K Multiplicative Control Parameter
%K Octadic Roots
%K Quartic Roots
%K Rabin Algorithm
%K Reduction of Complexity
%K Resolventa
%K Secure Communication
%K Square Roots
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=4839