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For cryptographic systems the method of confusion and diffusion is used as afundamental technique to achieve security. Confusion is reflected innonlinearity of certain Boolean functions describing the cryptographictransformation. In this paper, we present two balanced boolean functions whichhave low Walsh spectra and high nonlinearity. In the proof of the nonlinearity,a new method for evaluating some exponential sums over finite fields wasprovided.

Two Boolean functions with five-valued Walsh spectra and high nonlinearity