A general method for to decompose modular multiplicative inverse operators over Group of units

  • Luis A. Cortés Vega Antofagasta University.


In this article, the notion of modular multiplicative inverse operator (MMIO)

Biografía del autor/a

Luis A. Cortés Vega, Antofagasta University.
Department of Mathematics.


[1] H. M. AL-Matari, S. J. Aboud, N. F. Shilbayeh, Fast Fraction-Integer Method for Computing Multiplicative Inverse, J. of Computing, 1, pp. 131—135, (2009).

[2] O. Arazi, H. Qi, On calculiting multiplicative inverses modulo 2m, IEEE Trans. Comput 57, pp. 1435—1438, (2008).

[3] J—C. Bajard, L. Imbert, A full RNS implementation of RSA, IEEE Trans. Comput 53, pp. 769—774, (2004).

[4] J. W. Bos, Constant time modular inversion, J Cryptogr Eng 4, pp. 275—281, (2014).

[5] L. A. Cortés—Vega, A functional technique based on the Euclidean algorithm with applications to 2-D acoustic diffractal diffusers, J. Phys.: Conf. Ser 633, pp. 1—6, (2015).

[6] L. A. Cortés Vega, D. E. Rojas-Castro, Y.S. Santiago Ayala and S. C. RojasRomero, A technique based on the Euclidean algorithm and its applications to Cryptography and Nonlinear Diophantine
Equations, Proyecciones. J. Math., 26, pp. 309-333, (2007).

[7] T. J. Cox, P. D’Antonio, Acoustic Absorbers and Diffusers: Theory, Design and Application Spon Press, (2004).

[8] Y. Dai, A. B. Borisov, K. Boyer, C. K. Rhodes, Computation with inverse states in a Finite Field FPα : The muon neutrino mass, the Unified-Strong-Electroweak coupling constant, and the Higgs mass, Sandia National Laboratory, Report SAND2000-2043, pp. 1—11, (2000).

[9] Y. Dai, A.B. Borisov, K. Boyer, C.K. Rhodes, A p-Adic metric for particle mass scale organization with genetic divisors, Sandia National Laboratory, Report SAND2001-2903, pp. 1—12, (2001).

[10] C. Ding, D. Pey, A. Salomaa, Chinese remainder Theorem: Applications in Computing, Coding, Cryptography, Singapure; World Scientific, (1999).

[11] J-G. Dumas, On Newton-Rapshon iteration for multiplicative inverses modulo prime power, IEEE Trans. Comput 63, pp. 2106—2109, (2014).

[12] J. Eichenauer, J. Lehn, A. Topuzoglu, A Nonlinear congruential pseudorandom numer generator with power two modulus, Math of Compt 51, pp. 757—759, (1988).

[13] Y. Elrich, K. Chang, A. Gordon, R. Ronen, O. Navon, M. Rooks, G.J. Hanon, DNA Sudoku-harnessing high-throughput sequencing for multiplexed specimen analysis, Genome Res 19, pp. 1243—1253, (2009).

[14] M. A. Fiol, Finite Abelian groups and the Chinese remainder theorem, Discrete Math 67, pp. 101—105, (1987).

[15] L. Hars, Modular inverse algorithms without multiplications for cryptographic applications, J Embedded Systems 032192, pp. 1—13, (2006).

[16] M. Joye and P. Paillier, GCD-Free algorithms for computing modular inverses, C.D. Walter et. al. (Eds.):CHES 2003, LNCS 2779. Springer-Verlag Berlin Heidelberg, pp. 243-253, (2003).

[17] B. S. Jr. Kaliski, The montgomery inverse and its applications, IEEE Trans. Comput 44, pp. 1064—1065 (1995).

[18] D. E. Knuth, The art of computer programming, 2, Semi-Numerical Algorithms, 3rd Edition, Addison-Wesley, Reading, MA, (1997).

[19] W. H. Ko, Modular inverse and reciprocity formula, arXiv:1304.6778v1, pp. 1-7, (2013).

[20] R. Lórencz, New algorithm for classical modular inverse, in Kaliski, B.S., Jr., Ko ̧c, C.K., and Paar, C. (Eds.):CHES 2002, LNCS Springer-Verlag Berlin, pp. 57—70, (2003).

[21] D. R. Hankerson, A. J. Menezes, S. A. Vanstone, Guide to Elliptic curve cryptography, Springer, New York, N.Y, USA (2004).

[22] L. P. Montgomery, Modular multiplication without trial division, Math. Comp 44, pp. 519—52, (1985).

[23] T. Niven, S. H. Zuckerman, H. Montgomery, An introduction to the theory of numbers, 5nd ed. Jhon Wiley-Sons, Inc. (1991).

[24] S. Parthasarathy, An interesting property of multiplicative inverse in mod(M), Algologic Tech. Reports, pp. 1—3, (2012).

[25] E. Sava ̧s, C. K. Ko ̧c, The montgomery modular inverse revisited, IEEE Trans. Comput 49, pp. 763—766, (2000).

[26] E. Sava ̧s, M. Nasser, A. A-A Gutub, C. K. Ko ̧c, Efficient unified Montgomory inversion with multibit shifting, IEEE Proc. Comput. Digit. Tech 152, pp. 489—498, (2005).

[27] M. R. Schroeder, Number theory and in Science and comunication, 3rd ed. Springer, Berlin, (1997).

[28] R. J. Sullivan, Microwave Radar Imaging and Advanced Concepts, 2nd ed. Scitech Pub Inc., (2004).

[29] C. E. Towers, D. P. Towers, J. D. C. Jones, Time efficient Chinese remainder theorem algorithm for full-field fringe phase analysis in multiwavelenght interferometry, Optics Express 12, pp. 1136—1143, (2004).

[30] S. B. Verkhovsky, Enhanced Euclid algorithm for modular multiplicative inverse and its application in Cryptographic protocols, Int. J. Commun. Network and System Sc 3, pp. 901—906, (2010).

[31] S. Vollala, B.S. Degum, N. Ramasubramanian, Hardware desing for multiplicative modular inverse based on table look up technique, IEEE Computing and Network Commun (CoCoNet), pp. 520—523, (2015).

[32] Y. Wang, Residue to binary converters based on net Chinese remainder theorems, IEEE Trans Circuits Syst. 47, pp. 197—204, (2000).

[33] S. Wei, Computation of modular multiplicative inverse using residue signed-digit additions, IEEE Conf. Pub :2016 International SoC Design Conference (ISOCC), pp. 85—86, (2016).
Cómo citar
Cortés Vega, L. (2018). A general method for to decompose modular multiplicative inverse operators over Group of units. Proyecciones. Revista De Matemática, 37(2), 265-293. Recuperado a partir de http://www.revistaproyecciones.cl/article/view/2934