The Study For Computational Security

The Original Text

In Chapter 2 we introduced the notion of perfect secrecy. While perfect secrecy is a worthwhile goal, it is also unnecessarily strong. Perfect secrecy requires that absolutely no information about an encrypted message is leaked, even to an eavesdropper with unlimited computational power. For all practical purposes, however, an encryption scheme would still be considered secure if it leaked information with some tiny probability to eavesdroppers with bounded computational power. For example, a scheme that leaks information with probability at most $2^{-60}$ to eavesdroppers investing up to 200 years of computational effort on the fastest available supercomputer (or cluster of computers) would be more than adequate for real-world applications. Computational security definitions take into account computational limits on an attacker, and allow for a small probability that security is violated, in contrast to notions (such as perfect secrecy) that are information-theoretic in nature. Computational security is now the de facto way in which security is defined for almost all cryptographic applications.

Q&A format

Q: What is “perfect secrecy”?
A: Perfect secrecy is the requirement that no information about an encrypted message can be leaked to anyone, even to someone with unlimited computational power who might be eavesdropping.

Q: Why is perfect secrecy too strong of a requirement for practical purposes?
A: Perfect secrecy is too strong of a requirement for practical purposes because it requires that absolutely no information about an encrypted message is leaked, even to an eavesdropper with unlimited computational power. This level of security is not necessary for most real-world applications.

Q: What is computational security?
A: Computational security is a type of security definition that takes into account computational limits on an attacker and allows for a small probability that security is violated. This is in contrast to notions (such as perfect secrecy) that are information-theoretic in nature.

Q: What is an example of an encryption scheme that would be considered secure in the real world?
A: An encryption scheme that leaks information with probability at most 2−60 to eavesdroppers investing up to 200 years of computational effort on the fastest available supercomputer (or cluster of computers) would be more than adequate for real-world applications.

Q: What is the de facto way in which security is defined for almost all cryptographic applications?
A: Computational security has become the de facto way in which security is defined for almost all cryptographic applications.