![]() ![]() ![]() However, if one considers a more restricted model of computation, which captures reasonable restrictions on the power of an algorithm, then very strong lower bounds can be proved. Unfortunately, for this general model of computation, no proofs of useful lower bounds on the complexity of a computational problem are known. In modern cryptography, and more generally in theoretical computer science, the complexity of a problem is defined via the number of steps it takes for the best program on a universal Turing machine to solve the problem. As cryptography is a mathematical science, one needs a (mathematical) definition of computation and of the complexity of computation. This means that one wants to prove that the computational problem of breaking the scheme is infeasible, i.e., its solution requires an amount of computation beyond the reach of current and even foreseeable future technology. ![]() This chapter explores a topic in the intersection of two fields to which Alan Turing has made fundamental contributions: the theory of computing and cryptography.Ī main goal in cryptography is to prove the security of cryptographic schemes. ![]()
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