A REDUCED TABLEOF THE ZECH´S LOGARITHM
DOI:
https://doi.org/10.24297/jam.v12i7.5483Keywords:
Finite field, Zech's logarithm, cyclotomiccoset.Abstract
In this work we will solve the problem of expression of the sum of two given elements of a finite field, as power of the primitive element of the field. We obtain a reduced table of the Zech's logarithm from our proposal that relate the Zech'slogarithm with the partition of the exponents of the powers of elements over finite field ð‘®ð‘(ð’‘ð’) in p-cyclotomic cosets modulo (ð’‘ð’−ðŸ). This reduces, in a significant way, the quantity of information to store and it facilitates its use in several cryptographic algorithms, specifically in asimetric cryptography. It is illustrated the computationof the Zech'slogarithm of any element thatdoesn't appear in the obtained reduced table.Downloads
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2. Johansson T.2014.Low weight polynomials in crypto.
3. Kiihn G. J. and W. Penzhorn T. 1994. Using Zech's Logarithm to Find Low-Weight Parity Checks for Linear Recurring Sequences. Communications and cryptography.
4. Elsenhans A.-S., KohnertA. and Wassermann A. 2010. Construction of Codes for Network Coding. In Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems – MTNS 2010.
5. LiJ. 2004. Combinatorially Designed LDPC Codes Using Zech Logarithms and Congruential Sequences.Coding, Cryptographyand Combinatorics.
6. Huber K.1990. Some Comments on Zech’s Logarithms. IEEE Transactions on Information Theory.
7. Meyer-Baese U. 2004. Digital Signal Processing with Field Programmable Gate Arrays. SecondEdition.
8. MullenG. L.and Panario D.2013. Handbook of Finite Fields, CRC Pres.Taylor& Francis Group.
9. Golomb S. W. 1981. Shift Register Sequences, Aegean Park Press. Laguna Hills, CA, USA.
10. Rani M. J. 2013 Cyclic Codes of length N over GF(q)q- ciclotomiccosets modulo N and application of Burnside´s lemma. InternationalJournal of Scientific and Research Publications.
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Published
2016-07-18
How to Cite
Justiz, O. C., Capó, E. M., Arrozarena, P. F., & Gómez, G. S. (2016). A REDUCED TABLEOF THE ZECH´S LOGARITHM. JOURNAL OF ADVANCES IN MATHEMATICS, 12(7), 6422–6428. https://doi.org/10.24297/jam.v12i7.5483
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