We present 4 main outcomes of the project during the last reporting period.

First, 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(dlogC) for d-depth log-space uniform circuits (such as RAM programs). In addition Libra features a 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.

Then, we present a new succinct zero knowledge argument scheme for layered arithmetic circuits without trusted setup. The prover time is O (C+ n log n) and the proof size is O (D log C+ log2 n) for a D-depth circuit with n inputs and C gates. The verification time is also succinct, O (D log C+ log2 n), if the circuit is structured. Our scheme only uses lightweight cryptographic primitives such as collision-resistant hash functions and is plausibly post-quantum secure. We implement a zero knowledge argument system, Virgo, based on our new scheme and compare its performance to existing schemes. Experiments show that it only takes 53 seconds to generate a proof for a circuit computing a Merkle tree with 256 leaves, at least an order of magnitude faster than all other succinct zero knowledge argument schemes. The verification time is 50ms, and the proof size is 253KB, both competitive to existing systems. Underlying Virgo is a new transparent zero knowledge verifiable polynomial delegation scheme with logarithmic proof size and verification time. The scheme is in the interactive oracle proof model and may be of independent interest.

After Virgo, We introduce CHURP (CHUrn-Robust Proactive secret sharing). CHURP enables secure secret-sharing in dynamic settings, where the committee of nodes storing a secret changes over time. Designed for blockchains, CHURP has lower communication complexity than previous schemes: $O(n)$ on-chain and $O(n^2)$ off-chain in the optimistic case of no node failures. CHURP includes several technical innovations: An efficient new proactivization scheme of independent interest, a technique (using asymmetric bivariate polynomials) for efficiently changing secret-sharing thresholds, and a hedge against setup failures in an efficient polynomial commitment scheme. We also introduce a general new technique for inexpensive off-chain communication across the peer-to-peer networks of permissionless blockchains. We formally prove the security of CHURP, report on an implementation, and present performance measurements.

Finally we present PRIVGUARD, a new framework for automatic compliance checking of data privacy regulations in heterogeneous data processing infrastructures. Our key insight is to pair up a data subject’s data with a policy governing how the data is processed. Specified in our formal policy language: PRIVPOLICY, the policy is created and provided by the data subject alongside the data, and is associated with the data throughout the life-cycle of data processing (e.g., data transformation by data processing systems, data aggregation of multiple data subjects’ data). We introduce a solution for static enforcement of privacy policies based on the concept of residual policies, and present a novel algorithm based on abstract interpretation for deriving residual policies in PRIVPOLICY.

Last Modified: 09/14/2020
Modified by: Dawn Song