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.
Highlights
The study of finite fields has made great progress in recent years because they are applied in areas as diverse as cryptography [1, 2, 3], coding theory [4, 5, 6], among other areas [7, 8]
Considering that multiplication of elements of a finite field is a polynomial multiplication it is convenient express the elements of the field as powers of a primitive element, so that the multiplication of them is reduced to the sum of their exponents
The results enabled us to detect regularities that allow us to build a reduced table ofZech'slogarithm, considering the p–cyclotomiccosetsmodulo pn − 1
Summary
The study of finite fields has made great progress in recent years because they are applied in areas as diverse as cryptography [1, 2, 3], coding theory [4, 5, 6], among other areas [7, 8]. Considering that multiplication of elements of a finite field is a polynomial multiplication it is convenient express the elements of the field as powers of a primitive element, so that the multiplication of them is reduced to the sum of their exponents.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
