Cryptographic Applications of Analytic Number Theory

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This book explores advanced techniques that establish rigorous lower bounds on the complexity of number-theoretic and cryptographic problems, focusing on pseudorandom properties of cryptographic primitives. It employs methods involving character sums and polynomial equations over finite fields, alongside sieve methods and lattice reduction algorithms. While the results are unconditionally proven and independent of conjectures, they are weaker than commonly accepted truths. The text also presents open problems and research proposals, emphasizing the significance of lower bounds in various mathematical functions and their implications for discrete logarithms.