Random numbers play a crucial role in decen-tralized applications (dApps) like decentralized finance (DeFi) and non-fungible tokens (NFTs). However, their generation faces challenges due to blolckchain's deterministic and decentralized nature, risking smart contract security and ecosystem stability. Prior solutions, including Oracles, employing commit-execute schemes, suffer from higher transaction fees, extended processing times, and increased on-chain storage, compromising efficiency. This paper proposes a novel random number provider (RNP) protocol for smart contracts, eliminating dependencies on traditional commit-execute approaches. Furthermore, we systematically identify potential random number-related attacks on smart contracts, particularly Post-reveal Undo Attacks (PUAs), where attackers may reverse contract operations when randomness is unfavorable, and discuss the security requirements. Our protocol addresses these attacks by (1) incorporating distributed random beacons (D RBs) with consensus processes, bridging the semantic gap between DRB and consensus, and (2) thoroughly analyzing and classifying four types of PUA and offering robust mitigations, alongside presenting a security proof. Our experiments show the protocol significantly enhances response times and security for random number queries in smart contracts, slashing request fees by at least 89 % and reducing on-chain data by 76.4% versus current methods. This work advances the integration of DRB protocols and consensus mechanisms, securing and optimizing random number applications in dApps, thus fostering the creation of more dependable, robust systems.

We present an efficient zero-knowledge argument of knowledge system customized for the Paillier cryptosystem. Our system enjoys sublinear proof size, low verification cost, and acceptable proof generation effort, while also supporting batch proof generation/verification. Existing works specialized for Paillier cryptosystem feature linear proof size and verification time. Using existing sublinear argument systems for generic statements (e.g., zk-SNARK) results in unaffordable proof generation cost since it involves translating the relations to be proven into an inhibitive large Boolean or arithmetic circuit over a prime order field. Our system does not suffer from these limitations.The core of our argument systems is a constraint system defined over the ring of residue classes modulo a composite number, together with novel techniques tailored for arguing binary values in this setting. We then adapt the approach from Bootle et al. (EUROCRYPT 2016) to compile the constraint system into a sublinear argument system. Our constraint system is generic and can be used to express typical relations in Paillier cryptosystems including range proof, correctness proof, relationships between bits of plaintext, relationships of plaintexts among multiple ciphertexts, and more. Our argument supports batch proof generation and verification, with the amortized cost outperforming state-of-the-art protocol specialized for Paillier when the number of Paillier ciphertext is in the order of hundreds.We report an end-to-end prototype and conduct comprehensive experiments across multiple scenarios. Scenario 1 is Paillier with packing. When we pack 25.6K bits into 400 ciphertexts, a proof that all these ciphertexts are correctly computed is 17 times smaller and is 3 times faster to verify compared with the naive implementation: using 25.6K OR-proofs without packing. Furthermore, we can prove additional statements almost for free, e.g., one can prove that the sum of a subset of the witness bits is less than a threshold t. Another scenario is range proof. To prove that each plaintext in 200 Paillier ciphertexts is of size 256 bits, our proof size is 10 times smaller than the state-of-the-art. Our analysis suggests that our system is asymptotically more efficient than existing protocols, and is highly suitable for scenarios involving a large number (more than 100) of Paillier ciphertexts, which is often the case for data analytics applications.