Introduction to IBE with a focus on Weil pairing on supersingular elliptic curves

Venue: Department of Mathematics, via Sommarive, 14 - Povo (TN) - Sala Seminari "-1"
At: 4:30 pm

Speaker:

• Federico Mazzone (Percorso di Eccellenza Laurea Magistrale Matematica)

Abstract:
In this seminar we introduce the concept of identity-based encryption (IBE) and we highlight the differences with traditional public-key systems. In particular we define the concepts of Identity and Private Key Generator (PKG) and show some interesting properties. Moreover, we discuss the desirable security properties for a general IBE scheme and present the four algorithms that characterize it: Setup, Extract, Encrypt, Decrypt. The first two IBE schemes ever created will be introduced: the Cocks scheme and the Boneh-Franklin scheme. For the latter, we provide a detailed description of the basic algorithm (BasicIdent – IND-ID-CPA) and we show how to improve it through the Fujisaki-Okamoto transform (FullIdent – IND-ID-CCA). For both, we list the security properties, based respectively on the quadratic residuosity assumption and on the bilinear Diffie-Hellman assumption. Finally, we introduce supersingular elliptic curves and Weil pairing, in order to give a practical implementation of the Boneh-Franklin scheme; we conclude by giving a description of the Miller algorithm for the Weil pairing computation.

Contact person: Massimiliano Sala