Verifiable Random Functions: Relations to IdentityBased Key Encapsulation and New Constructions
 Michel Abdalla,
 Dario Catalano,
 Dario Fiore
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In this paper we show a relation between the notions of verifiable random functions (VRFs) and identitybased key encapsulation mechanisms (IBKEMs). In particular, we propose a class of IBKEMs that we call VRFsuitable, and we propose a direct construction of VRFs from VRFsuitable IBKEMs. Informally, an IBKEM is VRFsuitable if it provides what we call unique decapsulation (i.e., given a ciphertext C produced with respect to an identity ID, all the secret keys corresponding to identity ID′, decapsulate to the same value, even if ID≠ID′), and it satisfies an additional property that we call pseudorandom decapsulation. In a nutshell, pseudorandom decapsulation means that if one decapsulates a ciphertext C, produced with respect to an identity ID, using the decryption key corresponding to any other identity ID′, the resulting value looks random to a polynomially bounded observer. Our construction is of interest both from a theoretical and a practical perspective. Indeed, apart from establishing a connection between two seemingly unrelated primitives, our methodology is direct in the sense that, in contrast to most previous constructions, it avoids the inefficient Goldreich–Levin hardcore bit transformation. As an additional contribution, we propose a new VRFsuitable IBKEM based on the decisional ℓweak Bilinear Diffie–Hellman Inversion assumption. Interestingly, when applying our transformation to this scheme, we obtain a new VRF construction that is secure under the same assumption, and it efficiently supports a large input space.
 Title
 Verifiable Random Functions: Relations to IdentityBased Key Encapsulation and New Constructions
 Journal

Journal of Cryptology
Volume 27, Issue 3 , pp 544593
 Cover Date
 201407
 DOI
 10.1007/s001450139153x
 Print ISSN
 09332790
 Online ISSN
 14321378
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Verifiable random functions
 Identitybased encryption
 Pseudorandomness
 Industry Sectors
 Authors

 Michel Abdalla ^{(1)}
 Dario Catalano ^{(2)}
 Dario Fiore ^{(3)}
 Author Affiliations

 1. Département d’Informatique, Ecole Normale Supérieure, Paris, France
 2. Dipartimento di Matematica e Informatica, Università di Catania, Catania, Italy
 3. Max Planck Institute for Software Systems (MPISWS), Saarbrücken, Germany