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Protection of Sensitive Messages Based on Quadratic Roots of Gaussians: Groups with Complex Modulus
Computer Science Department, New Jersey Institute of Technology, University Heights, Newark, USA
- 1 Computer Science Department, New Jersey Institute of Technology, University Heights, Newark, USA
International Journal of Communications, Network and System Sciences·Volume 04 (2011)·Pages 287–296·Published 12 May 2011·DOI10.4236/ijcns.2011.45033
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Abstract
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.
KeywordsComplex ModulusComputational EfficiencyCryptographic AlgorithmDigital IsotopesMultiplicative Control ParameterOctadic RootsQuartic RootsRabin AlgorithmReduction of ComplexityResolventaSecure CommunicationSquare Roots
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