Information Protection Based on Extraction of Square Roots of Gaussian Integers

References

[1] C. F. Gauss, “Disquisitiones Arithmeticae,” English Translation, Springer-Verlag, New York, 1985.

[2] A. N. El-Kassar, R. A. Haraty, Y. A. Awad and N. C. Debnath, “Modified RSA in the Domains of Gaussian Integers and Polynomials over Finite Fields,” Proceedings of the ISCA 18th International Conference on Computer Applications in Industry and Engineering, Honolulu, 9-11 November 2005, pp. 298-303.

[3] A. El-Kassar, M. Rizk, N. Mirza and Y. Awad, “ElGamal Public-Key Cryptosystem in the Domain of Gaussian Integers,” International Journal of Applied Mathematics, Vol. 7, No. 4, 2001, pp. 405-412.

[4] A. Karatsuba and Y. Ofman, “Multiplication of Many-Digital Numbers by Automatic Computers,” Doklady Akademii Nauk SSSR, Vol. 145, No. 2, 1962, pp. 293-294.

[5] B. Verkhovsky, “Enhanced Euclid Algorithm for Modular Multiplicative Inverse and Its Cryptographic Application,” International Journal of Communications, Network and System Sciences, Vol. 3, No. 12, 2010, pp. 901-906.
doi:10.4236/ijcns.2010.312123

[6] L. Euler, “Vollstandige Anleitung zur Algebra,” Reclam Publishing House, Leipzig, 1941, pp. 1-527.

[7] F. Lemmermeyer, “Reciprocity Laws: From Euler to Ei- senstein,” Springer-Verlag, New York, 2000.

[8] 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.

[9] H. Garner, “The Residue Number System,” IRE Transactions on Electronic Computers, Vol. EC-8, No. 2, 1959, pp. 140-147. doi:10.1109/TEC.1959.5219515

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

[11] B. Verkhovsky, “Cubic Root Extractors of Gaussian Integers and Their Application in Fast Encryption for Time-Constrained Secure Communication,” to appear in International Journal of Communications, Network and System Sciences, Vol. 4, No. 4, 2011.