INFORMATION THEORY AND THE ZETA FUNCTION

It has been said that if the Riemann hypothesis were solved, all the keys to cryptography and cybersecurity could be broken; no one has specified how that could lead to faster factorization methods, but at least it reminds us of the close relationship between a hitherto intractable problem, cryptography and information theory.

Such speculations are only based on the fact that the Riemann zeta function establishes a connection between prime numbers and the zeros of an infinitely differentiable function that provides the most powerful method for exploring this field, prime numbers being the basis of classical cryptography. But we have already seen that the zeta is way more than this.

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