Multilinear and Aggregate Pseudorandom Functions: New Constructions and Improved Security
نویسندگان
چکیده
Since its introduction, pseudorandom functions (PRFs) have become one of the main building blocks of cryptographic protocols. In this work, we revisit two recent extensions of standard PRFs, namely multilinear and aggregate PRFs, and provide several new results for these primitives. In the case of aggregate PRFs, one of our main results is a proof of security for the Naor-Reingold PRF with respect to read-once boolean aggregate queries under the standard Decision Diffie-Hellman problem, which was an open problem. In the case of multilinear PRFs, one of our main contributions is the construction of new multilinear PRFs achieving indistinguishability from random symmetric and skew-symmetric multilinear functions, which was also left as an open problem. In order to achieve these results, our main technical tool is a simple and natural generalization of the recent linear independent polynomial framework for PRFs proposed by Abdalla, Benhamouda, and Passelègue in Crypto 2015, that can handle larger classes of PRF constructions. In addition to simplifying and unifying proofs for multilinear and aggregate PRFs, our new framework also yields new constructions which are secure under weaker assumptions, such as the decisional k-linear assumption.
منابع مشابه
Multilinear Pseudorandom Functions
We define the new notion of a multilinear pseudorandom function (PRF), and give a construction with a proof of security assuming the hardness of the decisional Diffie-Hellman problem. A direct application of our construction yields (non-multilinear) PRFs with aggregate security from the same assumption, resolving an open question in [CGV15]. Additionally, multilinear PRFs give a new way of view...
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عنوان ژورنال:
- IACR Cryptology ePrint Archive
دوره 2015 شماره
صفحات -
تاریخ انتشار 2015