An ID-based DNF signature scheme is an ID-based signature scheme with an access structure which is expressed as a disjunctive normal form (DNF) with literals of signer identities. ID-based DNF signature schemes are useful to achieve not only signer-privacy but also a multi-user access control. In this paper, we formally define a notion of a (non-interactive) ID-based DNF signature and propose the first $non-interactive$ ID-based DNF signature schemes that are secure under the computational Diffie-Hellman and subgroup decision assumptions. Our first scheme uses random oracles, and our second one is designed without random oracles. To construct the second one, we use a novel technique that converts a non-interactive witness indistinguishable proof system of encryption of one bit into a corresponding proof system of encryption of a bit-string. This technique may be of independent interest. The second scheme straightforwardly yields the first ID-based ring signature that achieves anonymity against full key exposure without random oracles. We finally present two extensions of the proposed ID-based DNF signature schemes to support multiple KGCs and different messages.
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