Ring Signatures: Stronger Definitions, and Constructions without Random Oracles
Ring signatures, first introduced by Rivest, Shamir, and Tauman, enable a user to sign a message so that a ring of possible signers (of which the user is a member) is identified, without revealing exactly which member of that ring actually generated the signature. In contrast to group signatures, ring signatures are completely ``ad-hoc'' and do not require any central authority or coordination among the various users (indeed, users do not even need to be aware of each other); furthermore, ring signature schemes grant users fine-grained control over the level of anonymity associated with any particular signature. This paper has two main areas of focus. First, we examine previous definitions of security for ring signature schemes and suggest that most of these prior definitions are too weak, in the sense that they do not take into account certain realistic attacks. We propose new definitions of anonymity and unforgeability which address these threats, and give separation results proving that our new notions are strictly stronger than previous ones. Second, we show the first constructions of ring signature schemes in the standard model. One scheme is based on generic assumptions and satisfies our strongest definitions of security. Two additional schemes are more efficient, but achieve weaker security guarantees and more limited functionality.
Reducing Complexity Assumptions for Statistically-Hiding Commitment
Determining the minimal assumptions needed to construct various cryptographic building blocks has been a focal point of research in theoretical cryptography. For most --- but not all! --- cryptographic primitives, complexity assumptions both necessary and sufficient for their existence are known. Here, we revisit the following, decade-old question: what are the minimal assumptions needed to construct a statistically-hiding bit commitment scheme? Previously, it was known how to construct such schemes based on any one-way permutation. In this work, we show that regular one-way functions suffice. We show two constructions of statistically-hiding commitment schemes from regular one-way functions. Our first construction is more direct, and serves as a ``stepping-stone'' for our second construction which has improved round complexity. Of independent interest, as part of our work we show a compiler transforming any commitment scheme which is statistically-hiding against an honest-but-curious receiver to one which is statistically-hiding against a malicious receiver. This demonstrates the equivalence of these two formulations of the problem. Our results also improve the complexity assumptions needed for statistical zero-knowledge arguments.