The Analysis and Investigation of Multiplicative Inverse Searching Methods in the Ring of Integers Modulo M
Автор: Zhengbing Hu, I. A. Dychka, Onai Mykola, Bartkoviak Andrii
Журнал: International Journal of Intelligent Systems and Applications(IJISA) @ijisa
Статья в выпуске: 11 vol.8, 2016 года.
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In this article an investigation into search operations for the multiplicative inverse in the ring of integers modulo m for Error Control Coding tasks and for data security is shown. The classification of the searching operation of the multiplicative inverse in the ring of integers modulo m is provided. The best values of parameters for Joye-Paillier method and Lehmer algorithm were also found. The improved Bradley modification for the extended Euclidean algorithm is also offered, which gives the operating speed improvement for 10-15%. The integrated experimental research of basic classes of searching methods for multiplicative inverse in the ring of integers modulo m is conducted for the first time and the analytical formulas for these calculations of random access memory necessary space when operated at k-ary RS-algorithms and their modifications are shown.
Integers modulo m, Error control coding, Data security, Euclidean algorithm
Короткий адрес: https://sciup.org/15010871
IDR: 15010871
Список литературы The Analysis and Investigation of Multiplicative Inverse Searching Methods in the Ring of Integers Modulo M
- Darrel Hankerson Guide to EllipticCurve Cryptography / Hankerson Darrel, Menezes Alfred, Vanstone Scott // Springer-Verlag New York, USA. — 2004. — 311 p.
- Richard Crandall Prime Numbers A Computational Perspective / Crandall Richard, Pomerance Carl// Springer-Verlag New York, USA. — 2005. — 597 p.
- Guerric Meurice de Dormale, Philippe Bulens, Jean-Jacques Quisquater Efficient Modular Division Implementation ECC over GF(p) Affine Coordinates Application / Meurice de Dormale Guerric, Bulens Philippe, Quisquater Jean-Jacques // The 14th International Conference on Field Programmable Logic and Applications, FPL 2004, Volume 3203 of Lecture Notes in Computer Science. — 2004. — Pp. 231-240.
- Donald E. Knuth Art of Computer Programming, Volume 2: Seminumerical Algorithms / Knuth Donald // 3rd Edition by Addison-Wesley Professional, Canada. — 1997. — 784 p.
- Richard E. Blahut Theory and Practice of Error Control Codes / Blahut Richard E. // Addison-Wesley. — 1983. — 500 p.
- Henri Cohen A Course in Computational Algebraic Number Theory / Cohen Henri // Springer Science & Business Media. — 1993. — 534 p.
- S. Parthasarathy Multiplicative inverse in mod(m) / Parthasarathy S. // Algologic Technical Report #1/2012. — 2012. — P. 1-3.
- Robert Lorencz New Algorithm for Classical Modular Inverse/ Lorencz Robert // Cryptographic Hardware and Embedded Systems. International Workshop. — 2002. — P. 57-70.
- WolframMathWorld: http://mathworld.wolfram.com/CarmichaelFunction.html
- W. Fischer Note on fast computation of secret RSA exponents / Fischer W., Seifert J.-P. // Information Security and Privacy (ACISP 2002), vol. 2384 of Lecture Notes in Computer Science, Springer-Verlag. — 2002. — Pp. 136–143.
- Marc Joye GCD-Free Algorithms for Computing Modular Inverses / Joye Marc, Paillier Pascal // CHES 2003: Cologne, Germany. — 2003. — Pp. 243-253.
- Jonathan Sorenson Two fast GCD algorithms / Sorenson Jonathan // Journal of Algorithms 16 (1). — 1994. — Pp. 110-144.
- A.W. Bojanczyk A systolic algorithm for extended GCD / BojanczykA.W., BrentR.P. // Comput. Math. Applic. Vol. 14, No. 4. — 1987. — Pp. 233-238.
