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By Atanasov D.V.

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If we can prove that an adversary who is able to break a cryptosystem is also able to solve the hard problem, then we can argue that it is very unlikely that such an adversary really exists and hence that the cryptosystem in question is likely to be secure. Michael O. 11) [11]. 2. The notion of (provable) security has fueled a lot of research since the late 1970s and early 1980s. In fact, there are many (public key) cryptosystems shown to be provably secure in exactly this sense. It is, however, important to note that a complexity-based proof is not absolute and that it is only relative to the (assumed) intractability of the underlying mathematical problem(s).

If, for example, we smash a bottle into pieces, it is generally infeasible (or at least prohibitively difficult) to put the pieces together and reconstruct the bottle. Similarly, if we drop a bottle from a bridge, it falls down. Cryptographic Systems 23 The reverse process does not frequently occur in the real world. Last but not least, life is one way, and it is (currently) not known how to travel back in time. In contrast to the real world, the idealized world of mathematics is less rich with one-way functions.

An answer to this question must specifiy, for example, the adversary’s computing power, available memory, available time, types of feasible attacks, and access to a priori or side information. For some of these parameters, it must be specified whether they are finite or not. Most importantly, it may be reasonable to assume that there are adversaries with infinite computing power at their disposal, meaning that they can perform infinitely many computations in a given amount of time. The alternative is to consider adversaries with finite computing power at their disposal.

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5th International Conference on Geometry and Applications by Atanasov D.V.

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