Implementation Study of Cost-Effective Verification for Pietrzak's Verifiable Delay Function in Ethereum Smart Contracts
CoRR(2024)
摘要
Verifiable Delay Function (VDF) is a cryptographic concept that ensures a
minimum delay before output through sequential processing, which is resistant
to parallel computing. Among the two well-known VDF protocols, Wesolowski and
Pietrzak VDF, we focus on the Pietrzak VDF due to its computational efficiency
and suitability for blockchain environments. Pietrzak's approach uses a
recursive proof verification with the halving protocol, offering a practical
alternative despite the longer proof length than Wesolowski's approach. Given
the scarcity of research on practical VDF verification implementation,
especially within smart contracts, this paper aims to implement cost-effective
verification for the Pietrzak VDF in an Ethereum-based environment without
compromising the VDF verification's integrity and reliability. Firstly, we
propose generalized proof generation and verification algorithms for potential
efficiency improvement. Secondly, we categorize and measure the gas cost of
each part in a transaction for VDF verification. Thirdly, based on the
analysis, we theoretically predict the optimized proof construction. Finally,
we demonstrate the theoretical prediction matches the implementation results.
Furthermore, our research shows that the proof length of the Pietrzak VDF is
generated under 8 KB with the security level of 2048 bits, much smaller than
the previous expectation. This implies that the Pietrzak VDF can be practically
used for cryptographic applications on blockchains.
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