Abstract
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.
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