C. F. Gauss, “Theoria Residuorum Biquadraticorum,” 2nd Edition, Chelsea, New York, 1965, pp. 534-586. - References - Scientific Research Publishing

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C. F. Gauss, “Theoria Residuorum Biquadraticorum,” 2nd Edition, Chelsea, New York, 1965, pp. 534-586.

has been cited by the following article:

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.

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