A REDUCED TABLEOF THE ZECH´S LOGARITHM

O C Justiz, E M Capó, P F Arrozarena, G S Gómez
2016 JOURNAL OF ADVANCES IN MATHEMATICS  
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 𝑮𝑭(𝒑𝒏) in p-cyclotomic cosets modulo (𝒑𝒏−𝟏). This reduces, in a significant way, the quantity of information to store and it facilitates its use in several
more » ... 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.
doi:10.24297/jam.v12i7.5483 fatcat:u5utnxc6ebg6pmcklzclrf3btu