1. bookVolume 67 (2016): Issue 1 (January 2016)
Journal Details
License
Format
Journal
eISSN
1339-309X
First Published
07 Jun 2011
Publication timeframe
6 times per year
Languages
English
access type Open Access

Note on Modular Reduction in Extended Finite Fields and Polynomial Rings for Simple Hardware

Published Online: 17 Mar 2016
Page range: 56 - 60
Received: 08 Oct 2015
Journal Details
License
Format
Journal
eISSN
1339-309X
First Published
07 Jun 2011
Publication timeframe
6 times per year
Languages
English
Abstract

Modular reduction in extended finite fields and polynomial rings is presented, which once implemented works for any random reduction polynomial without changes of the hardware. It is possible to reduce polynomials of whatever degree. Based on the principal defined, two example RTL architectures are designed, and some useful features are noted furthermore. The first architecture is sequential and reduce whatever degree polynomials, taking 2 cycles per term. The second one is Parallel and designed for reduction of polynomials of 2(t −1) degree at most, taking 1 cycle for the whole reduction.

Keywords

[1] PATTERSON, N. J. : The Algebraic Decoding of Goppa Codes, IEEE Trans. on Information Theory 21 No. 2 (2012), 203–207.Search in Google Scholar

[2] FARKASOVA, K.—FARKAS, P.—RAKUS, M.—RUZICKY, E.—SILVA, A.—GAMEIRO, A. : Construction of Error Control Run Length Limited Codes Exploiting Some Parity Matrix Properties, Journal of Electrical Engineering 66 No. 3 (2015), 182–184.10.2478/jee-2015-0030Search in Google Scholar

[3] MALI, M.—NOVAK, F.—BIASIZZO, A. : Hardware Implementation of AES Algorithm, Journal of Electrical Engineering 56 No. 9-10 (2005,), 265–269.Search in Google Scholar

[4] RAKUS, M.—FARKAS, P. : Double Error Correcting Codes with Improved Code Rates, Journal of Electrical Engineering 55 No. 3-4 (2004,), 89–94.Search in Google Scholar

[5] EGOROV, S.—MARKARIAN, G. : Error Correction beyond the Conventional Error Bound for Reed-Solomon Codes, Journal of Electrical Engineering 54 No. 11-12 (2003), 305=-310.Search in Google Scholar

[6] RAKUS, M. : Comments on Weight Distribution of some Weighted Sum Codes for Erasure Correction, Journal of Electrical Engineering 53 No. 5-6 (2002), 138–142.Search in Google Scholar

[7] HEYSE, S.—GÜNEYSU, T. : Towards One Cycle per Bit Asymmetric Encryption: Code-Based Cryptography on Reconfigurable Hardware, CHES (2012), 340–355.10.1007/978-3-642-33027-8_20Search in Google Scholar

[8] SHOUFAN, A.—WINK, T.—MOLTER, H. G.—HUSS, S. A.—KOHNERT, E. : A Novel Cryptoprocessor Architecture for the McEliece Public-Key Cryptosystem, IEEE Trans. Computers 59 No. 11 (2010), 1533–1546.10.1109/TC.2010.115Search in Google Scholar

[9] BERNSTEIN, D. J.—LANGE, T.—PETERS, C. : Wild McEliece Incognito, 4th International Workshop, PQCrypto 2011, Proceedings, 2011, pp. 244–254.10.1007/978-3-642-25405-5_16Search in Google Scholar

[10] REPKA, M. : McEliece PKC Calculator, Journal of Electrical Engineering 65, No. 6 (2014), http://iris.elf.stuba.sk/JEEEC/data/pdf/6_114-03.pdf.10.2478/jee-2014-0056Search in Google Scholar

[11] REPKA, M.—CAYREL, P.-L. : Cryptography Based on Error Correcting Codes: A Survey, Multidisciplinary Perspectives in Cryptology and Information Security (Sattar B. Sadkhan Al Maliky, and Nidaa A. Abaas, ed.), IGI Global, 2014, pp. 133-156.10.4018/978-1-4666-5808-0.ch005Search in Google Scholar

[12] AN, H.-K. : Fast and Low cost GF(28) Multiplier Design based on Double Subfield Transformation, International Journal of Software Engineering and Its Applications 7 No. 4 (2013), 285–294.Search in Google Scholar

[13] CHUANPENG, CH.—ZHONGPING, Q. : Fast Algorithm and Hardware Architecture for Modular Inversion in GF(p), Intelligent Networks and Intelligent Systems, 2009. ICINIS ’09. Second International Conference on, 43-45, DOI: 10.1109/ICINIS.2009.20.10.1109/ICINIS.2009.20Search in Google Scholar

[14] MELIKOVIC, N. Z.—STANKOVIC, V.—MILIC, M. L. : Modular Design of Fast Leading Zeros Counting Circuit, Journal of Electrical Engineering 66 No. 6 (2015), 329–333.Search in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo