Cryptography
Abstract:
Cryptography is of course a vast subject. Cryptography is about communication in the presence of an adversary. The most ancient and basic problem of cryptography is secure communication over an insecure channel. The traditional solution to this problem is called private key encryption. The field of modern cryptography provides a theoretical foundation based on which we may understand what exactly these problems are, how to evaluate protocols that purport to solve them, and how to build protocols in whose security we can have confidence. We introduce the basic issues by discussing the problem of encryption.
Modern cryptography abandons the assumption that the Adversary has available infinite computing resources, and assumes instead that the adversary's computation is resource bounded in some reasonable way. In particular, in these notes we will assume that the adversary is a probabilistic algorithm who runs in polynomial time. Similarly, the encryption and decryption algorithms designed are probabilistic and run in polynomial time.
Accordingly, in modern cryptography, we speak of the infeasibility of breaking the encryption system and computing information about exchanged messages where as historically one spoke of the impossibility of breaking the encryption system and finding information about exchanged messages. We note that the encryption systems which we will describe and claim \secure" with respect to the new adversary are not secure" with respect to a computationally unbounded adversary in the way that the one-time pad system was secure against an unbounded adversary.
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