Browse Theses

Cryptography is about constructing protocols that remain secure in the presence of adversaries. Secure cryptographic protocols base their existence on mathematical tools, called cryptographic primitives. The advance of this research field makes the attacks available to adversaries more and more challenging for the protocol designer, who therefore needs to amplify the security of such cryptographic primitives.

This dissertation is about the amplification of the security properties of cryptographic primitives. We consider three basic primitives, such as one-way functions, commitment schemes, and public-key encryption, and exhibit, for each of them, new techniques for the amplification of their security properties. The main result concerns a very basic and long standing open problem in cryptography: we present a technique transforming “weak one-way functions” (i.e., functions that can be efficiently inverted for a large amount of the inputs) to “strong one-way functions” (i.e., functions that can be inverted for a negligible amount of the input). Our technique applies to a large class of functions, thus generalizing what was known in the literature. Our second main result is about the construction of a non-interactive commitment scheme satisfying an additional security property, called “non-malleability”. Our third main result is about the construction of a public-key encryption scheme which is “timed-release”; such scheme satisfies an additional security property, namely not even the receiver is able to decrypt before some “release-time”.

In all three cases our results are obtained by using original techniques and represent strict improvements over the previous results in the literature.