In vector commitments, the complex process of generating and updating proofs, along with the large-sized proofs, seriously hinders the practicality of stateless cryptocurrencies. In this work, we present NTTproofs, containing two sub-schemes, a vector commitment (VC) and a mulit-vector commitment (MC). Both sub-schemes are maintainable and aggregatable, and they also enjoy fast openings (i.e., generating all the proofs) as well as efficient proof updates. MC in NTTproofs employs the Fast Number Theoretic Transform (NTT) and sharding technique to significantly improve the time of generating all proofs by up to$0.76 \times $and$0.32 \times $, respectively, over Balanceproofs, Matproofs. Moreover, our proposed MC in NTTproofs is efficiently maintainable and requires merely 15.78 milliseconds at$n_{1}=n_{2}=2^{12}$to update all proofs. Meanwhile, NTTproofs schemes exhibit superior aggregatability, taking 0.003 seconds in VC and 0.05 seconds in MC to aggregate 1024 proofs and reducing the size of an aggregated proof to a constant size of 96 Bytes. Finally, macrobenchmarks indicate that our proposed MC in NTTproofs outperforms the other schemes, but is slightly inferior to that of Balanceproofs.

Existing multitask outsourcing computations struggle to guarantee the fairness for participants and the correctness of the computation results. Some solutions use blockchain to address the fairness issue in outsourcing computations. However, blockchain suffers from poor data privacy due to its public and transparent nature, as well as the latency because of limited scalability. To effectively confront these problems, we propose the Libras: a fair, secure, verifiable and scalable outsourcing computation scheme based on blockchain. In Libras, tasks are divided into multiple sub-task blocks, coupled with a deposit mechanism that enforces fairness throughout the process. Libras integrates a commitment mechanism with on-chain and off-chain collaboration for security, where the computation results are securely stored off-chain while proofs of these results are immutably recorded on-chain. Moreover, it employs a Directed Acyclic Graph (DAG)-based ledger architecture to significantly expedite transaction confirmations and facilitate elastic scalability. Furthermore, we devise a batch verification algorithm to simultaneously verify the accuracy of all computation results. Theoretical analysis and experiments demonstrate that Libras is fair, secure, verifiable, and scalable. The comparison results indicate that the verification time is 1.2× that of FVP-EOC.