Another Proof of Kasami's Theorem |
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| Authors: | Hans Dobbertin |
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| Institution: | (1) German Information Security Agency, P. O. Box 20 03 63, D-53133 Bonn, Germany |
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| Abstract: | We give a short direct proof for a famous theorem published by Kasami in 1971. In terms of Walsh analysis it states that for d = 22k
- 2k + 1 the Walsh spectrum of the Boolean function Tr(x
d
) on GF(2
n
) consists precisely of the three values 0, ±2(n+s)/2 if s = gcd(k, n) = gcd(2k, n). |
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| Keywords: | power functions Walsh transform nonlinearity m sequences cross correlation Kasami's Theorem |
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