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

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References

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

[2]
M. Kirsch, “Tutorial on Gaussian Arithmetic Based on Complex Modulus,” 2008.
http://wlym.com/~animations/ceres/index.html

[3]
B. Verkhovsky, “Information Protection Based on Extraction of Square Roots of Gaussian Integers,” International Journal of Communications, Network and System Sciences, Vol. 4, No. 3, 2011, pp. 133-138.
doi:10.4236/ijcns.2011.43016

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B. Verkhovsky and A. Koval, “Cryptosystem Based on Extraction of Square Roots of Complex Integers,” In: S. Latifi, Ed., Proceedings of 5th International Conference on Information Technology: New Generations, Las Vegas, 7-9 April 2008, pp. 1190-1191.

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R. Crandall and C. Pomerance, “Prime Numbers: A computational Perspective,” Springer, New York, 2001.

[7]
R. Schoof, “Elliptic Curves over Finite Fields and the Computation of Square Roots Mod p,” Mathematics of Computation, Vol. 44, No. 170, 1985, pp. 483-494.

[8]
R. V. Churchill, J. W. Brown and R. F. Verhey, “Complex Variables and Applications,” 3rd Edition, McGraw Hill, New York, 1976.

[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

[10]
M. Rabin, “Digitized Signatures and Public-Key Functions as Intractable as Factorization,” MIT/LCS Technical Report, TR-212, 1979.