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- W4320154833 abstract "At CRYPTO 1994, Cramer, Damgård and Schoenmakers proposed a general method to construct proofs of knowledge (PoKs), especially for k-out-of-n partial knowledge, of which relations can be expressed in disjunctive normal form (DNF). Since then, proofs of k-out-of-n partial knowledge have attracted much attention and some efficient constructions have been proposed. However, many practical scenarios require efficient PoK protocols for partial knowledge in other forms. In this paper, we mainly focus on PoK protocols for k-conjunctive normal form (k-CNF) relations, which have n statements and can be expressed as follows: (i) k statements constitute a clause via “OR” operations, and (ii) the relation consists of multiple clauses via “AND” operations. We propose an alternative Sigma protocol (called DAG- $${Sigma }$$ protocol) for k-CNF relations (in the discrete logarithm setting), by converting these relations to directed acyclic graphs (DAGs). Our DAG- $${Sigma }$$ protocol achieves less communication cost and smaller computational overhead compared with Cramer et al.’s general method." @default.
- W4320154833 created "2023-02-13" @default.
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- W4320154833 date "2022-01-01" @default.
- W4320154833 modified "2023-10-16" @default.
- W4320154833 title "DAG-$$Sigma $$: A DAG-Based Sigma Protocol for Relations in CNF" @default.
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- W4320154833 doi "https://doi.org/10.1007/978-3-031-22966-4_12" @default.
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