RSA-like cryptosystems with conics
- Day - Time: 07 November 2018, h.11:30
- Place: Area della Ricerca CNR di Pisa - Room: C-29
- Nadir Murru (Dipartimento di Matematica "Giuseppe Peano”, Università di Torino)
The RSA scheme is one of the most widespread public-key cryptographic systems.
However, besides one-to-one communication scenario, there also exist cryptographic scenarios, such as broadcast applications, where RSA leaks some vulnerabilities. RSA-like schemes have been proposed in order to avoid some of these attacks. Some of these schemes turn to have also a faster decryption procedure. They are based on isomorphism between two groups, one of which is the set of points over a curve, usually a cubic or a conic.
In this talk, we present an improvement of such schemes based on a special class of conics derived from the Pell equation. We provide a new RSA-like scheme based on isomorphism over a conic, with the fastest isomorphism with respect to the ones known. Furthermore, the scheme exploits the Rédei rational functions, which allow to have the fastest decryption procedure. We provide security proofs and efficiency comparisons.