Number Theoretic Methods in Cryptography

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Focusing on advanced number theory and cryptography, this book presents innovative techniques that establish rigorous lower bounds on the complexity of various mathematical problems. It explores character sums and polynomial equation solutions over finite fields and residue rings, offering significant findings on -polynomials, algebraic functions, and Boolean functions. The text delves into the implications of these results for computing the discrete logarithm, particularly emphasizing the role of quadratic residues and providing insights into the complexity of Boolean circuits. Open problems and research proposals are also included.