CS Colloquium: Jiaheng Zhang
UPDATE: This event has been postponed until further notice.
Speaker: Jiaheng Zhang (UC Berkeley)
Host: Yufei Ding
Title: Polynomial Commitment with a One-to-Many Prover and Applications
Verifiable Secret Sharing (VSS) is a foundational cryptographic primitive that serves as an essential building block in multi-party computation and decentralized blockchain applications. One of the most practical ways to construct VSS is through a polynomial commitment, where the dealer commits to a random polynomial whose 0-th coefficient encodes the secret to be shared, and proves the evaluation of the committed polynomial at a different point to each of N verifiers, i.e., the polynomial commitment is used in a “one-to-many” fashion. The recent work of Tomescu et al. (IEEE S&P 2020) was the first to consider polynomial commitment with “one-to-many prover batching”, such that the prover can prove evaluations at N different points at the cost of O(1) proofs. However, their scheme is not optimal and requires a trusted setup. In this paper, we asymptotically improve polynomial commitment with one-to-many prover batching. We propose two novel schemes. First, we propose a scheme with optimal asymptotics in all dimensions in the trusted setup setting. Second, we are the first to consider one-to-many prover batching for transparent polynomial commitments, and we propose a transparent scheme whose performance approximately matches the best-known scheme in the trusted setup setting. We implement our schemes and evaluate their performance. Our scheme in the trusted setup setting improves the proof size by 20× and the verifier time by 7.8× for 2 21 parties, with a small overhead on the prover time. Our transparent polynomial commitment removes the trusted setup and further improves the prover time by 2.3×.
Jiaheng is a fourth-year Ph.D. student in Computer Science at UC Berkeley, where he is advised by Prof. Dawn Song. He also works closely with Prof. Yupeng Zhang. And he is a member of RISE Lab, Initiative for Cryptocurrencies & Contracts Lab (IC3) and Berkeley AI Research (BAIR). His research interests lie in computer security and cryptography, especially zero-knowledge proofs and their applications on blockchains and machine learning models. Prior to coming to Berkeley, he received his Bachelor's degree in ACM Honors Class of Shanghai Jiao Tong University, where he worked under the supervision of Prof. Xiaotie Deng. During his undergraduate, he was also a research intern at Cornell, advised by Prof. Elaine Shi. He received the Facebook Fellowship in Security and Privacy in 2021.