Equivocal Blind Signatures and Adaptive UC-Security

We study the design of practical blind signatures in the universal composability (UC) setting against adaptive adversaries. We introduce a new property for blind signature schemes that is fundamental for managing adaptive adversaries: an equivocal blind signature is a blind signature protocol where a simulator can construct the internal state of the client so that it matches a simulated transcript even after a signature was released. We present a general construction methodology for building practical adaptively secure blind signatures: the starting point is a 2-move “lite blind signature”, a lightweight 2-party signature protocol that we formalize and implement both generically as well as number theoretically: formalizing a primitive as “lite” means that the adversary is required to show all private tapes of adversarially controlled parties; this enables us to conveniently separate zero-knowledge (ZK) related security requirements from the remaining security properties in the primitive’s design methodology. We then focus on the exact ZK requirements for building blind signatures. To this effect, we formalize two special ZK ideal functionalities, single-verifier-ZK (SVZK) and single-prover-ZK (SPZK) and we investigate the requirements for realizing them in a commit-and-prove fashion as building blocks for adaptively secure UC blind signatures. SVZK can be realized without relying on a multi-session UC commitment; as a result, we realize SVZK in a very efficient manner using number theoretic mixed commitments while employing a constant size common reference string and without the need to satisfy non-malleability. Regarding SPZK we find the rather surprising result that realizing it only for static adversaries is sufficient to obtain adaptive security for UC blind signatures. This important observation simplifies blind signature design substantially as one can realize SPZK very efficiently in a commit-and-prove fashion using merely an extractable commitment. We instantiate all the building blocks of our design methodology efficiently thus presenting the first practical UC blind signature that is secure against adaptive adversaries in the common reference string model. In particular, we present (1) a lite equivocal blind signature protocol that is based on elliptic curves and the 2SDH assumption of Okamoto, (2) efficient implementations of SPZK, SVZK for the required relations. Our construction also takes advantage of a round optimization method we discuss and it results in a protocol that has an overall communication overhead of as little as 3Kbytes, employing six communication moves and a constant length common reference string. We also present alternative implementations for our equivocal lite blind signature thus demonstrating the generality of our approach. Finally we count the exact cost of realizing blind signatures with our protocol design by presenting the distance between the FBSIG-hybrid world and the FCRS-hybrid world as a function of environment parameters. The distance calculation is facilitated by a basic lemma we prove about structuring UC proofs that may be of independent interest. ∗Unpublished manuscript. †University of Connecticut, Computer Science and Engineering, Storrs, CT, USA, {aggelos,hszhou}@cse.uconn.edu.