J4 ›› 2011, Vol. 46 ›› Issue (3): 26-30.

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A construction of perfect nonlinear functions

GUO Fei-wang, ZHANG Xi-yong, HAN Wen-bao   

  1. Institute of Information Engineering, Information Engineering University, Zhengzhou 450002, Henan, China
  • Received:2010-09-18 Published:2011-04-21


 Perfect nonlinear functions are widely used in cryptography and algebra combinatorics. By using two known perfect nonlinear functions, a quadratic perfect nonlinear function over finite fields of odd characteristic was constructed based on determining the root of a linearized function.This quadratic function was proved to be inequivalent to x2, and then an example was used to analyzed its inequivalence to xps+1.

Key words: perfect nonlinear function; almost perfect nonlinear function; CCZ-equivalence;EA-equivalence; linearized permutation

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