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zkSecurity offers a hands-on tutorial on π«π©π¬π«π¦, helping readers understand its complex building blocks, including selector polynomials, wiring permutations, quotient tests, random challenges, and KZG commitments through step-by-step examples.
This article delves into Circle FFT in Circle STARKs, explaining its principles and steps by comparing it with Cooley-Tukey FFT, and discusses the dimension gap in the polynomial space of Circle FFT and its impact.
Threshold Encrypted Mempools (Threshold encrypted mempools) can effectively protect the privacy of blockchain transactions before they are confirmed on-chain, serving as a promising method to counter Miner Extracted Value (MEV) attacks in decentralized blockchains.
Recent research has proposed two critical properties required for encryption schemes to achieve scalability in large-scale decentralized blockchains like Ethereum: (1) Silent Setup [Garg-Kolonelos-Policharla-Wang, CRYPTO'24], which requires threshold encryption schemes to have no interaction during the initialization phase and rely solely on the existence of a public key infrastructure; and (2) Batched Decryption [Choudhuri-Garg-Piet-Policharla, USENIX'24], which requires the ability to decrypt an entire block containing encrypted transactions with communication overhead that is independent of (or only linearly dependent on) the block size, without leaking the privacy of unconfirmed transactions.
Although existing constructions achieve one of these properties, a truly decentralized and scalable encrypted mempool must satisfy both properties simultaneously. In this paper, we propose the first "silent setup batched threshold encryption scheme" constructed using pairings. We provide a formal definition for this primitive and present a security proof in the Generic Group Model. Additionally, we introduce several optimizations and implement the proposed scheme, evaluating its performance. Experimental results demonstrate that the scheme is practically feasible and efficient for deployment in blockchain systems.
