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Why cryptography is not based on NP-complete problems
Cryptography is not based on NP-complete problems - let me explain why. Hard problems in cryptography Cryptographic schemes are based on the computational difficulty of solving some ‘hard’ problem.
More concretely, cryptographic schemes rely on clients holding some kind of secret key, sampled at random, which instantiates the hard problem. There is a whole branch of computer science called complexity that analyzes the difficulty problems based on the asymptotic runtimes of the best-known algorithms to solve them. We don’t technically know whether these are NP-complete, but we are pretty confident that a random instance of any of them is ‘hard’ (i.e. would take >2128>2^{128}>2128 operations to solve) with overwhelming probability.
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