Cryptographic Divergences: New Techniques and New Applications.

In the recent years, some security proofs in cryptography have known significant improvements by replacing the statistical distance with alternative divergences. We continue this line of research, both at a theoretical and practical level. On the theory side, we propose a new cryptographic divergence with quirky properties. On the practical side, we propose new applications of alternative divergences: circuit-private FHE and prime number generators. More precisely, we provide the first formal security proof of the prime number generator PRIMEINC [8], and improve by an order of magnitude the efficiency of a prime number generator by Fouque and Tibouchi [16, 17] and the washing machine technique by Ducas and Stehle [15] for circuit-private FHE.