期刊
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
卷 10, 期 3, 页码 531-554出版社
SPRINGER
DOI: 10.1007/s12095-017-0236-7
关键词
Finite fields; Permutation polynomials; Trinomials
资金
- National Basic Research Program of China [2013CB338002]
- Nature Science Foundation of China (NSFC) [61272484, 11531002, 61572026]
- Program for New Century Excellent Talents in University (NCET)
- Basic Research Fund of National University of Defense Technology [CJ 13-02-01]
- Open Foundation of State Key Laboratory of Cryptology
Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. Particularly, permutation polynomials with few terms are more popular for their simple algebraic form and additional extraordinary properties. Very recently, G. Kyureghyan and M.E. Zieve (2016) studied permutation polynomials over F-qn of the form x + gamma Tr-qn/q (x(k)), where q is odd, and nine classes of permutation polynomials were constructed. In this paper, we present fifteen new classes of permutation polynomials of the form cx + Tr-ql/q (x(a)) over finite fields with even characteristic, which explain most of the examples with q = 2(k) , k > 1, kl < 14 and c epsilon F-ql(*) Furthermore, we also construct four classes of permutation trinomials.
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