International Association for Cryptologic Research

International Association
for Cryptologic Research


Dawn Song

Affiliation: UC Berkeley


Libra: Succinct Zero-Knowledge Proofs with Optimal Prover Computation 📺
We present Libra, the first zero-knowledge proof system that has both optimal prover time and succinct proof size/verification time. In particular, if C is the size of the circuit being proved (i) the prover time is O(C) irrespective of the circuit type; (ii) the proof size and verification time are both $$O(d\log C)$$ for d-depth log-space uniform circuits (such as RAM programs). In addition Libra features an one-time trusted setup that depends only on the size of the input to the circuit and not on the circuit logic. Underlying Libra is a new linear-time algorithm for the prover of the interactive proof protocol by Goldwasser, Kalai and Rothblum (also known as GKR protocol), as well as an efficient approach to turn the GKR protocol to zero-knowledge using small masking polynomials. Not only does Libra have excellent asymptotics, but it is also efficient in practice. For example, our implementation shows that it takes 200 s to generate a proof for constructing a SHA2-based Merkle tree root on 256 leaves, outperforming all existing zero-knowledge proof systems. Proof size and verification time of Libra are also competitive.
Private and Continual Release of Statistics
We ask the question – how can websites and data aggregators continually release updated statistics, and meanwhile preserve each individual user’s privacy? Suppose we are given a stream of 0’s and 1’s. We propose a differentially private continual counter that outputs at every time step the approximate number of 1’s seen thus far. Our counter construction has error that is only poly-log in the number of time steps. We can extend the basic counter construction to allow websites to continually give top-k and hot items suggestions while preserving users’ privacy.
Provable Data Possession at Untrusted Stores
We introduce a model for {\em provable data possession} ($\pdp$) that allows a client that has stored data at an untrusted server to verify that the server possesses the original data without retrieving it. The model generates probabilistic proofs of possession by sampling random sets of blocks from the server, which drastically reduces I/O costs. The client maintains a constant amount of metadata to verify the proof. The challenge/response protocol transmits a small, constant amount of data, which minimizes network communication. Thus, the $\pdp$ model for remote data checking supports large data sets in widely-distributed storage systems. Previous work offers guarantees weaker than data possession, or requires prohibitive overhead at the server. We present two provably-secure $\pdp$ schemes that are more efficient than previous solutions, even when compared with schemes that achieve weaker guarantees. In particular, the overhead at the server is low (or even constant), as opposed to linear in the size of the data. Experiments using our implementation verify the practicality of $\pdp$ and reveal that the performance of $\pdp$ is bounded by disk I/O and not by cryptographic computation.
Quasi-Efficient Revocation of Group Signatures
A group signature scheme allows any group member to sign on behalf of the group in an anonymous and unlinkable fashion. In the event of a dispute, a designated trusted entity can reveal the identity of the signer. Group signatures are claimed to have many useful applications such as voting and electronic cash. A number of group signature schemes have been proposed to-date. However, in order for the whole group signature concept to become practical and credible, the problem of secure and efficient group member revocation must be addressed. In this paper, we construct a new revocation method for group signatures based on the signature scheme by Ateniese et al. at Crypto 2000. This new method represents an advance in the state-of-the-art since the only revocation schemes proposed thus far are either: 1) based on implicit revocation and the use of fixed time periods, or 2) require the signature size to be linear in the number of revoked members. Our method, in contrast, does not rely on time periods, offers constant-length signatures and constant work for the signer.