Cryptographic Security of Individual Instances

CSI - PTDC/EIA-CCO/099951/2008

The foundation of modern cryptography is the notion of proof of security. There are two basic notions of security: information-theoretic security and computational security.

For symmetric cipher systems one can prove unconditional security against an opponent with unlimited computational power. The proof of perfect secrecy is based on the notion of entropy, introduced by Shannon, measuring the amount of information in situations where unlimited computational power is available.

However this measure does not provide a satisfactory framework to the analysis of public key cipher systems which are based on cryptographic assumptions, namely imposing limited computational power of an adversary. If we apply Shannon’s criterion of security to evaluate public key cryptography we conclude that there are different notions of information involved. The public key and the cipher text together contain all the Shannon information concerning the plaintext, but the information is computationally inaccessible.

So nowadays we face this intriguing and exciting question: "what is accessible information"? This is an important question in Theoretical Computer Science that may have a strong impact in the future of cryptography and this project propose to study it as its main line of research."