Better Security for Functional Encryption for Inner Product Evaluations

Michel Abdalla (1, 2, 3, 4) , Florian Bourse (1, 2, 3, 4) , Angelo de Caro (1, 2, 3, 4) , David Pointcheval (1, 2, 3, 4)

1 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
2 ENS-PSL - École normale supérieure - Paris
3 PSL - Université Paris sciences et lettres
4 LIENS - Laboratoire d'informatique de l'école normale supérieure

Functional encryption is a new public key paradigm that solves, in a non-interactive way, most of the security challenges raised by cloud computing. A recent paper by Abdalla, Bourse, De Caro, and Pointcheval shows a functional encryption scheme for evaluations of inner products whose security can be proven under simple assumptions. Inner product evaluation is a simple, but quite powerful functionality, that suffices for many concrete applications. We analyze the different security notions for functional encryption for inner product evaluation and propose a new generic construction that achieves security against adaptive adversaries. We show 3 instantiations based on the ElGamal encryption (plain DDH assumption), Paillier/BCP encryption (DCR assumption), and Regev encryption (LWE assumption). All of them have different advantages and drawbacks, but with acceptable trade-offs, and rely on standard assumptions.

Mots clés: public-key cryptography; Functional Encryption; Adaptive Security; Inner-Product; Generic Constructions

Domaines: Cryptographie et sécurité [cs.CR]

Michel Abdalla, Florian Bourse, Angelo de Caro, David Pointcheval. Better Security for Functional Encryption for Inner Product Evaluations. [Technical Report] Cryptology ePrint Archive: Report 2016/011, IACR. 2016. ⟨hal-01380726⟩