Paper 2023/1076

Non-Interactive Threshold BBS+ From Pseudorandom Correlations

Abstract

The BBS+ signature scheme is one of the most prominent solutions for realizing anonymous credentials. Its prominence is due to properties like selective disclosure and efficient protocols for creating and showing possession of credentials. Traditionally, a single credential issuer produces BBS+ signatures, which poses significant risks due to a single point of failure. In this work, we address this threat via a novel $t$-out-of-$n$ threshold BBS+ protocol. Our protocol supports an arbitrary security threshold $t \leq n$ and works in the so-called preprocessing setting. In this setting, we achieve non-interactive signing in the online phase and sublinear communication complexity in the number of signatures in the offline phase, which, as we show in this work, are important features from a practical point of view. As it stands today, none of the widely studied signature schemes, such as threshold ECDSA and threshold Schnorr, achieve both properties simultaneously. To this end, we design specifically tailored presignatures that can be directly computed from pseudorandom correlations and allow servers to create signature shares without additional cross-server communication. Both our offline and online protocols are actively secure in the Universal Composability model. Finally, we evaluate the concrete efficiency of our protocol, including an implementation of the online phase and the expansion algorithm of the pseudorandom correlation generator (PCG) used during the offline phase. The online protocol without network latency takes less than $15 ms$ for $t \leq 30$ and credentials sizes up to $10$. Further, our results indicate that the influence of $t$ on the online signing is insignificant, $< 6 \%$ for $t \leq 30$, and the overhead of the thresholdization occurs almost exclusively in the offline phase. Our implementation of the PCG expansion is the first considering correlations between more than $3$ parties and shows that even for a committee size of $10$ servers, each server can expand a correlation of up to $2^{16}$ presignatures in about $600$ ms per presignature.