Open AccessA REDUCED TABLEOF THE ZECH´S LOGARITHM
Author(s) -
O C Justiz,
E M CapÃ,
P F Arrozarena,
G S GÃmez
Publication year - 2016
Publication title -
journal of advances in mathematics
Language(s) - English
Resource type - Journals
ISSN - 2347-1921
DOI - 10.24297/jam.v12i7.5483
Subject(s) - mathematics , modulo , finite field , coset , logarithm , discrete logarithm , cryptography , partition (number theory) , field (mathematics) , element (criminal law) , discrete mathematics , algebra over a field , arithmetic , pure mathematics , public key cryptography , algorithm , combinatorics , encryption , computer science , mathematical analysis , political science , law , operating system
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.