Cryptology ePrint Archive: Report 2020/815

Cryptographic Divergences: New Techniques and New Applications

Marc Abboud and Thomas Prest

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 (Brandt and Damgċrd, CRYPTO 1992), and improve by an order of magnitude the efficiency of a prime number generator by Fouque and Tibouchi (ICALP 2014) and the washing machine technique by Ducas and Stehlé (EUROCRYPT 2016) for circuit-private FHE.

Category / Keywords: applications / Rényi divergence; RE-α divergence; prime number generators; circuit-private FHE

Original Publication (with major differences): SCN 2020

Date: received 1 Jul 2020

Contact author: marc abboud at ens fr, thomas prest@pqshield com

Available format(s): PDF | BibTeX Citation

Version: 20200706:133439 (All versions of this report)

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