Ahmet Ramazan Ağırtaş, Arda Buğra Özer, Zülfükar SAYGI, Oğuz Yayla
Unbiased and unpredictable randomness is a cornerstone of Web3 security, underpinning everything from consensus protocols to DeFi logic. Although Distributed Verifiable Random Functions (DVRFs) eliminate central points of failure, current designs often have to compromise performance. Most existing protocols are hindered by one of three limitations: proofs that scale linearly with the number of participants, high computational cost of bilinear pairings, or latency introduced by mandatory interactive steps during generation. In this work, we present Icy-DVRF, a protocol that improves DVRFwCP by employing a preprocessing scheme similar to FROST to reduce the number of interaction rounds among participants and lowering the additional communication cost from <inline-formula> <tex-math notation="LaTeX">$O(n^{2} t)$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$O(t)$ </tex-math></inline-formula> while maintaining constant-size proofs. The downside of our construction is that, relative to DDH-DVRF and GLOW-DVRF, this approach incurs an additional off-chain communication round due to the threshold structure of our non-interactive zero-knowledge proof. This architecture ensures that verification costs remain low, regardless of the set of participants. While theoretical estimates suggest verification costs of approximately one quarter of those of standard designs, our empirical benchmarks on the Sepolia testnet, utilizing the EIP-2537: Precompile for BLS12-381 curve operations, confirm that Icy-DVRF requires only 88,803 gas for full execution. This represents a significant 43.02% reduction in total gas consumption compared to existing pairing-based constructions, saving 67,035 gas per on-chain verification. Off-chain, eliminating DVRFwCP’s Augmented Secure-DKG round yields a per-node speedup ranging from a factor of 1.46 at <inline-formula> <tex-math notation="LaTeX">$(n,t)=(5,3)$ </tex-math></inline-formula> to a factor of 4.43 at <inline-formula> <tex-math notation="LaTeX">$(n,t)=(50,34)$ </tex-math></inline-formula>.
Open access
Generative Adversarial Networks and Image Synthesis
The number theoretic transform (NTT) provides a practical and efficient technique to perform multiplication of very large degree polynomials typically found in fully homomorphic encryption (FHE), lattice-based cryptography, and non-interactive succinct zero-knowledge proof systems such as zk-SNARK. In this paper, we focus on this aspect and present two robust algorithms for efficient NTT using readily available GPU cards as hardware accelerators. These algorithms are based on the radix-2 Cooley-Tukey (CT) and 4-Step techniques, which are rooted in classical FFT research. To this end, our algorithms leverage novel strategy to optimize memory access patterns adaptive to input size, which often is very large. Our approach: i) reduces and optimizes the number of accesses required for global memory for thread synchronization on the GPU device, and ii) systematically improves and enhances the use of spatial locality. We achieve this effect by carefully controlling parameters such as the number of kernels, thread block size and shape, and thread layout, which directly impact overall NTT performance. The proposed optimizations enable our NTT implementation to handle very large polynomial sizes up to 228, which are usually a limiting factor in existing approaches, and achieve remarkable performance. To the best of our knowledge, our proposed technique is unique and provides a recipe for selecting suitable configurable parameter combinations to achieve top performance for a given polynomial degree. Furthermore, we perform thorough experiments and empirically assess the performance of our proposed algorithms on three mainstream commercial GPU cards by NVIDIA. Finally, we demonstrate that our algorithms compare favorably and outperform an existing commercial-grade open-source implementation in this arena.
The communities of blockchains and distributed ledgers have been stirred up by the introduction of zero-knowledge proofs (ZKPs). Originally designed to solve privacy issues, ZKPs have now evolved into an effective remedy for scalability concerns and are applied in Zcash (internet money like Bitcoin). To enable ZKPs, Rank-1 Constraint Systems (R1CS) offer a verifier for bi-linear equations. To accurately and efficiently represent R1CS, several language tools like Circom, Noir, and Snarky have been proposed to automate the compilation of advanced programs into R1CS. However, due to the flexible nature of R1CS representation, there can be significant differences in the compiled R1CS forms generated from circuit language programs with the same underlying semantics. To address this issue, this paper uses a data-flow-based R1CS paradigm algorithm, which produces a standardized format for different R1CS instances with identical semantics. By using the normalized R1CS format circuits, the complexity of circuits' verification can be reduced. In addition, this paper presents an R1CS normalization algorithm benchmark, and our experimental evaluation demonstrates the effectiveness and correctness of our methods.