期刊
INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE
卷 31, 期 3, 页码 411-419出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0129054120500161
关键词
Almost perfect nonlinear function; generalized almost perfect nonlinear function; exceptional exponent; algebraic degree; finite field
Generalized almost perfect nonlinear (GAPN) functions were defined to satisfy some generalizations of basic properties of almost perfect nonlinear (APN) functions for even characteristic. In particular, on finite fields of even characteristic, GAPN functions coincide with APN functions. in this paper, we study monomial GAPN functions for odd characteristic. We give monomial GAPN functions whose algebraic degree are maximum or minimum on a finite field of odd characteristic. Moreover, we define a generalization of exceptional APN functions and give typical examples.
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