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5

In practice, in order to pick a uniformly random $x\in \mathbb{Z}^*_q$, we reduce that task to the problem of picking uniformly random and independent bits. On a modern computer system, there will be some operating system service supplying such bits, e.g. /dev/urandom on many Unix derivatives (we'll get back to the problem of how such bits have been obtained ...


-1

Nearly reversible computation will eventually replace conventional computation since reversible computation will be more energy efficient than conventional computation. Furthermore, symmetric encryption and decryption are very well suited for reversible computing, so we should expect for symmetric encryption and decryption to eventually be computed on ...


-3

Can you categorically prove that AES isn't broken today, or won't be in October 2021? See NOBUS. The one time pad with key size = message size. Facilitated via quantum key distribution. That's one of the the main areas of cryptographic research today in budgetary terms.


3

This is already answered here for 1 iteration, and here for many iterations, but since the latter answer presents an heuristic argument I'll leave here Lemma 4 of Functional Graphs and Their Applications in Generic Attacks on Iterated Hash Constructions which gives a good approximation based on Theorem 2 of Random Mapping Statistics, and (3.10) of On the ...


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