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Protection of Sensitive Messages Based on Quadratic Roots of Gaussians: Groups with Complex Modulus

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DOI: 10.4236/ijcns.2011.45033    3,360 Downloads   6,468 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

B. Verkhovsky, "Protection of Sensitive Messages Based on Quadratic Roots of Gaussians: Groups with Complex Modulus," International Journal of Communications, Network and System Sciences, Vol. 4 No. 5, 2011, pp. 287-296. doi: 10.4236/ijcns.2011.45033.

References

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[9] B. Verkhovsky, “Cubic Root Extractors of Gaussian Integers and Their Application in Fast Encryption for Time-Constrained Secure Communication,” International Journal of Communications, Network and System Sciences, Vol. 4, No. 4, 2011, pp. 197-204. doi:10.4236/ijcns.2011.44024
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