Finite field elements of high order on a base of modified Gao approach.
Słowa kluczowe:
Finite field, multiplicative order, lower boundAbstrakt
Elements of high multiplicative order in finite fields are of great interest in several applications (cryptography, error correcting codes) that use finite fields. Obviously, the best possible are primitive elements, but there is no any algorithm to find them. Therefore, they consider a less ambitious question: to find an element with provable high order
Bibliografia
A. Conflitti, On elements of high order in finite fields, In Cryptography and computational number theory, Singapore (1999), volume 20 of Progr. Comput. Sci. Appl. Logic, Birkhauser, Basel (2001), 11–14.
R. Dunets, B. Popovych and R. Popovych, On construction of high order elements in arbitrary finite fields, JP J. Algebra Number Theory Appl. 42 (2019), no. 1, 71–76.
S. Gao, Elements of provable high orders in finite fields, Proc. Amer. Math. Soc. 127 (1999), no. 6, 1615–1623.
G. L. Mullen and D. Panario, Handbook of Finite Fields, CRC Press, Boca Raton, 2013.
R. Popovych, On elements of high order in general finite fields, Algebra Discr. Math. 18 (2014), no. 2, 295–300.
M. Young, On the multiplicative independence of rational iterates, preprint (2018), available at https://arxiv.org/abs/1708.00944.
