Lecture
This lecture discusses the concept of efficient set accumulators and their application in verifiable computation. The instructor begins by explaining the importance of set accumulators, particularly focusing on Merkle trees and RSA accumulators. The lecture details how these structures allow for membership proofs and efficient state updates. The instructor introduces the concept of Vesolevsky proofs, which facilitate proving exponentiation in a computationally efficient manner. The discussion then shifts to the implementation of batched operations, highlighting the advantages of using RSA accumulators for multiple insertions and removals. The lecture emphasizes the significance of minimizing constraints in verifiable computation to enhance proof generation and verification speed. The instructor presents a novel sequential state update mechanism called multiswap, which optimizes the process of state updates in payment systems and random access memory applications. The lecture concludes with a comparison of the computational costs associated with traditional methods and the proposed multiswap approach, demonstrating its efficiency for moderate to large batch sizes.