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Almost perfect nonlinear power functions on GF(2n): the Welch case

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1 Author(s)
H. Dobbertin ; Inf. Security Agency, Bonn, Germany

We summarize the state of the classification of almost perfect nonlinear (APN) power functions xd on GF(2n) and contribute two new cases. To prove these cases we derive new permutation polynomials. The first case supports a well-known conjecture of Welch stating that for odd n=2m+1, the power function x2m+3 is even maximally nonlinear or, in other terms, that the crosscorrelation function between a binary maximum-length linear shift register sequence of degree n and a decimation of that sequence by 2m+3 takes on precisely the three values -1, -1±2m+1

Published in:

IEEE Transactions on Information Theory  (Volume:45 ,  Issue: 4 )