# Continuous improvement of script-driven verifiable random functions for reducing computing power in blockchain consensus protocols

## Abstract

In order to solve the problem of low efficiency and high energy consumption of the Proof-of-Work (PoW) consensus protocol in blockchain within a peer-to-peer network, some new protocols based on Verifiable Random Function (VRF) have emerged recently. However, these VRF-based consensus protocols do not actually give a concrete and efficient VRF construction. In view of this, we present three simple and practical VRF constructions from the RSA hardness assumption, the Decisional Diffie-Hellman (DDH) assumption and the Leftover Hash Lemma (LHL) respectively, the output size of which is continuously reduced for the design of efficient consensus protocol in blockchain. We also give a complete security analysis of our VRF constructions. Furthermore, we show a specific application of our VRF constructions in the famous Algorand consensus protocol. We illustrate a general approach to integrate our VRF constructions with block structure in blockchain. Comparing with PoW-based mining, we demonstrate the detailed process of VRF-based consensus protocol. Meanwhile, three new opcodes are designed for the scripting system in blockchain to develop a script pair, scriptProof and scriptHash, which provides secure and efficient block verification. Finally, we evaluate the performance of our VRF constructions in terms of storage and computational overheads, and the experimental evaluation results show our VRF constructions can significantly reduce the computing power of consensus protocol in blockchain.

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## Notes

1. 1.

Randomness: We say that F(skx) and $$\{0,1\}^{out(\kappa )}$$ are statistically indistinguishable if there exists a negligible statistical difference $$\mu$$ such that

\begin{aligned} \begin{array}{l} \frac{1}{2}\sum \nolimits _{\alpha }\left| \Pr [F(sk,x)=\alpha ] -\Pr [\{0,1\}^{out(\kappa )}=\alpha ] \right| \le \mu (\kappa ). \end{array} \end{aligned}
2. 2.

For example, Shanks algorithm, one of the famous sieve methods, can realize the computational complexity of $$\mathcal {O}(\sqrt{N})$$ to find out r and $$r'$$.

3. 3.

one exahash is one quintillion hashes, i.e., 1 EH = $$10^{18}$$ hashes.

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## Acknowledgements

This work was supported by the National Key Technologies R&D Programs of China (2018YFB1402702) and the National Natural Science Foundation of China (61972032).

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Correspondence to Yan Zhu.

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Guo, G., Zhu, Y., Chen, E. et al. Continuous improvement of script-driven verifiable random functions for reducing computing power in blockchain consensus protocols. Peer-to-Peer Netw. Appl. (2021). https://doi.org/10.1007/s12083-021-01243-x