[Resource Topic] 2023/364: Zero-Knowledge Arguments for Subverted RSA Groups

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Zero-Knowledge Arguments for Subverted RSA Groups

Authors: Dimitris Kolonelos, Mary Maller, Mikhail Volkhov


This work investigates zero-knowledge protocols in subverted RSA groups where the prover can choose the modulus and where the verifier does not know the group order. We introduce a novel technique for extracting the witness from a general homomorphism over a group of unknown order that does not require parallel repetitions. We present a NIZK range proof for general homomorphisms such as Paillier encryptions in the designated verifier model that works under a subverted setup. The key ingredient of our proof is a constant sized NIZK proof of knowledge for a plaintext. Security is proven in the ROM assuming an IND-CPA additively homomorphic encryption scheme. The verifier’s public key is reusable, can be maliciously generated and is linear in the number of proofs to be verified.

ePrint: https://eprint.iacr.org/2023/364

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