Affiliation:
1. Faculty of Engineering, Nippon Bunri University, Oita, Japan
Abstract
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.
Publisher
World Scientific Pub Co Pte Lt
Subject
Computer Science (miscellaneous)
Reference18 articles.
1. A few more functions that are not APN infinitely often
2. On Almost Perfect Nonlinear Permutations
3. Perfect nonlinear functions and cryptography
4. Subfield value sets of polynomials over finite fields
5. J. F. Dillon, Geometry, Codes and Difference Sets: Exceptional Connections, Ohio State University Mathematical Research Institute Publications, eds. K. Arasu and Á. Seress (Walter de Gruyter, Berlin, New York, 2002), pp. 73–85.
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献