Random beacons play a crucial role in blockchains. Most random beacons in a blockchain are performed in a distributed approach to secure the generation of random numbers. However, blockchain nodes are in an open environment and are vulnerable to adversary reboot attacks. After such an attack, the number of members involved in a random number generation decreases. The random numbers generated by the system become insecure. To solve this problem while guaranteeing fast recovery of capabilities, we designed a threshold signature scheme based on share recovery. A bivariate polynomial was generated among the participants in the distributed key generation phase. While preserving the threshold signature key share, it can also help participants who lost their shares to recover. The same threshold setting for signing and recovery guarantees the security of the system. The results of our scheme show that we take an acceptable time overhead in distributed key generation and simultaneously enrich the share recovery functionality for the threshold signature-based random number generation scheme.

With the increasing demand for privacy protection in the blockchain, the universal zero-knowledge proof protocol has been developed and widely used. Because hash function is an important cryptographic primitive in a blockchain, the zero-knowledge proof of hash preimage has a wide range of application scenarios. However, it is hard to implement it due to the transformation of efficiency and execution complexity. Currently, there are only zero-knowledge proof circuits of some widely used hash functions that have been implemented, such as SHA256. SM3 is a Chinese hash function standard published by the Chinese Commercial Cryptography Administration Office for the use of electronic authentication service systems, and hence might be used in several cryptographic applications in China. As the national cryptographic hash function standard, the zero-knowledge proof circuit of SM3 (Chinese Commercial Cryptography) has not been implemented. Therefore, this paper analyzed the SM3 algorithm process, designed a new layered circuit structure, and implemented the SM3 hash preimage zero-knowledge proof circuit with a circuit size reduced by half compared to the automatic generator. Moreover, we proposed several extended practical protocols based on the SM3 zero-knowledge proof circuit, which is widely used in blockchain.

Random beacons are of paramount importance in distributed systems (e.g., blockchain, electronic voting, governance). The sheer scale of nodes inherent in distributed environments necessitates minimizing communication overhead per node while ensuring protocol availability, particularly under adversarial conditions. Existing solutions have managed to reduce the optimistic overhead to a minimum of O(n²), where n represents the node count of the system. In this paper, we step further by proposing and implementing RandFlash, a leaderless random beacon protocol that achieves an optimistic communication complexity of O(n log n). Evaluation results demonstrate that RandFlash outperforms existing constructions, RandPiper (CCS’21) and OptRand (NDSS’23), in terms of the number of random beacons generated within largescale networks comprising 64 nodes or more (e.g., in sizes of 80 and 128). Furthermore, RandFlash exhibits resilience, capable of withstanding up to one-third of the nodes acting maliciously, all without the need for strongly trusted setups (i.e., embedding a secret trapdoor by trusted third parties). We also provide formal security proofs validating all properties upheld by this lineage.