A REDUCED TABLEOF THE ZECHÂ´S LOGARITHM (JOURNAL OF ADVANCES IN MATHEMATICS, 2016)
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’âˆ’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.