Randomness generation for advanced cryptography – RAGE

The rise of the Internet over the last decades has significantly impacted our privacy, with the multiplication of online services that store private information. This trend has even accentuated with the era of Big Data, as personal data have become valuable. Traditional encryption does not really help solving this privacy issue due to its all-or-nothing nature:either a user can decrypt and learn everything, either it cannot and cannot use the data, preventing the applications for which we share data in the first place. Fortunately, recent advances in cryptography made possible encryption with fine-grained decryption policy, but these powerful primitives are still not practical. This project aims to study a basic tool in cryptography, termed pseudorandom functions, that allows to extract an large amount of randomness from a small secret key. This notion can play a central role to improve the security, the efficiency, as well as the functionality of advanced protocols.
The principal coordinator of this project recently proposed new and simple constructions of pseudorandom function that could serve as a building block for these advanced applications. These constructions rely on a novel approach and their security remains to be assessed. The goal of this project is to analyse in more depth these constructions in order to assess their security or to propose new constructions if attacks were to be found. In addition, this project also aims at developing applications based on these new constructions, and notably applications to computation over encrypted data. Finally, this project will also study a more advanced form of pesudorandom functions, termed constrained pseudorandom functions. This notion recently emerged in cryptography and has been at the origin of numerous advances in the recent years.