Large families of pseudorandom binary sequences and lattices are constructed by using the multiplicative inverse and estimates of exponential sums in a finite field. Pseudorandom measures of binary sequences and lattices are studied.
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In a series of papers many Boolean functions with good cryptographic properties were constructed using number-theoretic methods. We construct a large family of Boolean functions by using polynomials over finite fields, and study their cryptographic properties: maximum Fourier coefficient, nonlinearity, average sensitivity, sparsity, collision and avalanche effect.
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