A New Characterization of Semi-bent and Bent Functions on Finite Fields*

@article{Khoo2006ANC,
  title={A New Characterization of Semi-bent and Bent Functions on Finite Fields*},
  author={Khoongming Khoo and Guang Gong and Douglas R. Stinson},
  journal={Des. Codes Cryptography},
  year={2006},
  volume={38},
  pages={279-295}
}
We present a new characterization of semi-bent and bent quadratic functions on finite fields. First, we determine when a GF (2)-linear combination of Gold functions Tr(x i+1) is semi-bent over GF (2), n odd, by a polynomial GCD computation. By analyzing this GCD condition, we provide simpler characterizations of semi-bent functions. For example, we deduce that all linear combinations of Gold functions give rise to semi-bent functions over GF (2) when p belongs to a certain class of primes… CONTINUE READING

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