Statically Aggregate Verifiable Random Functions and Application to E-Lottery
Journal article, 2020

Cohen, Goldwasser, and Vaikuntanathan (TCC'15) introduced the concept of aggregate pseudo-random functions (PRFs), which allow efficiently computing the aggregate of PRF values over exponential-sized sets. In this paper, we explore the aggregation augmentation on verifiable random function (VRFs), introduced by Micali, Rabin and Vadhan (FOCS'99), as well as its application to e-lottery schemes. We introduce the notion of static aggregate verifiable random functions (Agg-VRFs), which perform aggregation for VRFs in a static setting. Our contributions can be summarized as follows: (1) we define static aggregate VRFs, which allow the efficient aggregation of VRF values and the corresponding proofs over super-polynomially large sets; (2) we present a static Agg-VRF construction over bit-fixing sets with respect to product aggregation based on the q-decisional Diffie-Hellman exponent assumption; (3) we test the performance of our static Agg-VRFs instantiation in comparison to a standard (non-aggregate) VRF in terms of costing time for the aggregation and verification processes, which shows that Agg-VRFs lower considerably the timing of verification of big sets; and (4) by employing Agg-VRFs, we propose an improved e-lottery scheme based on the framework of Chow et al.'s VRF-based e-lottery proposal (ICCSA'05). We evaluate the performance of Chow et al.'s e-lottery scheme and our improved scheme, and the latter shows a significant improvement in the efficiency of generating the winning number and the player verification.

verifiable random functions

pseudorandom functions

aggregate verifiable random functions

aggregate pseudorandom functions


Bei Liang

Chalmers, Computer Science and Engineering (Chalmers), Networks and Systems (Chalmers)

Gustavo Souza Banegas

Chalmers, Computer Science and Engineering (Chalmers), Networks and Systems (Chalmers)

Aikaterini Mitrokotsa

Chalmers, Computer Science and Engineering (Chalmers), Networks and Systems (Chalmers)


2410-387X (eISSN)

Vol. 4 4 37

PRECIS: Privacy and security in wearable computing devices

Swedish Research Council (VR) (2014-4845), 2015-01-01 -- 2018-12-31.

CryptoQuaC: Cryptography meets Verifiable Quantum Computation

GENIE, Chalmers Gender Initiative for Excellence, 2020-01-01 -- .

The Chalmers University Foundation, 2020-01-01 -- .

Subject Categories

Computer Engineering

Probability Theory and Statistics

Computer Science



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