Abstract
Constrained verifiable random functions (VRFs) were first explicitly introduced by Fuchsbauer (SCN’14) as an extension of the standard concept of VRFs. In a standard VRF, there is a secret key sk that enables one to evaluate the function at any point of its domain, and enables generation of a proof that the function value is computed correctly. While, in a constrained VRF, it is allowed to derive constrained key \(sk_S\) for subset S (of the domain) from sk, which enables evaluation of function and generation of proofs only at points in S and nowhere else. In fact, there are many open questions in the study of VRFs, especially constructing them from a wide variety of cryptographic assumptions.
In this work, we show how to construct constrained VRFs with respect to a set system, which can be described by a polynomial-size circuit C, from one-way functions together with indistinguishability obfuscation (iO). Our construction may be interesting for at least two reasons:
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Given the results of Brakerski et al. (TCC09) and Fiore et al. (TCC12), in which they proved that VRFs cannot be constructed from one-way permutations and trapdoor permutations in a black-box manner, it is interesting to study their construction from other stronger cryptographic primitives. Our construction shows that one-way functions plus iO are sufficient.
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Compared to the multilinear-map-based construction of constrained VRFs (SCN’14), our iO-based one has its particular advantage:
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In current multilinear-based constrained VRFs, since the level of their group is \(n+d_{C}\) where n is the bit-length of input and \(d_{C}\) is the depth of circuit C, public key is dependent on the depth of circuit. However, our iO-based construction does not have this limitation since our public key is an obfuscated program which is independent on the circuit.
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Keywords
This research is supported by the Strategy Pilot Project of Chinese Academy of Sciences (Grant No. Y2W0012203).
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Liang, B., Li, H., Chang, J. (2015). Constrained Verifiable Random Functions from Indistinguishability Obfuscation. In: Au, MH., Miyaji, A. (eds) Provable Security. ProvSec 2015. Lecture Notes in Computer Science(), vol 9451. Springer, Cham. https://doi.org/10.1007/978-3-319-26059-4_3
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