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Signatures of Knowledge for Boolean Circuits under Standard Assumptions (Full version)

Abstract : This paper constructs unbounded simulation sound proofs for boolean circuit satisfiability under standard assumptions with proof size O(n + d) bilinear group elements, where d is the depth and n is the input size of the circuit. Our technical contribution is to add unbounded simulation soundness to a recent NIZK of González and Ràfols (ASIACRYPT'19) with very small overhead. We give two different constructions: the first one is more efficient but not tight, and the second one is tight. Our new scheme can be used to construct Signatures of Knowledge based on standard assumptions that also can be composed universally with other cryptographic protocols/primitives. As an independent contribution we also detail a simple formula to encode Boolean circuits as Quadratic Arithmetic Programs.
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https://hal.inria.fr/hal-03118271
Contributor : Alonso González <>
Submitted on : Friday, January 22, 2021 - 10:32:09 AM
Last modification on : Saturday, January 23, 2021 - 3:27:15 AM

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Karim Baghery, Alonso González, Zaira Pindado, Carla Ràfols. Signatures of Knowledge for Boolean Circuits under Standard Assumptions (Full version). AFRICACRYPT 2020 - 12th International Conference on Cryptology in Africa, Jul 2020, Cairo / Virtual, Egypt. ⟨10.1007/978-3-030-51938-4_2⟩. ⟨hal-03118271⟩

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