Abstract Time-release cryptography is a flourishing research area with a long history and has been extensively studied. In this work, we enrich it by introducing a novel concept: a time-release zero-knowledge proof (TRZKP). A TRZKP is a non-interactive zero-knowledge proof that allows one to publish a proof for a given relation $$R_\mathcal {L}$$ R L , such that anyone can only finish the verification after time $$\textbf{T}$$ T by performing a sequential computation. This work formalizes the concept of TRZKP and presents light constructions for the time-release version of any NIZK obtained from a public-coin protocol via Fiat-Shamir transformation. TRZKPs can be applied to provide time-release authentication, for example, they can be employed to construct verifiable timed signatures (VTS), introduced by Thyagarajan et al. (CCS’20). Through both theoretical and practical analysis, our construction has advantages over existing VTS for Fiat-Shamir signatures. Specifically, when instantiated with Shnorr signature, our VTS signing time remains basically unchanged as the delay time grows, and is preferable for longer delay times; our VTS verification time is significantly small (on the level of milliseconds, while existing works on the level of seconds), and our VTS size is 67 times smaller than the state-of-the-art. It also has the time-verifiability property, which ensures the signature is recoverable after the specified time.

Abstract Recent years have seen the widespread adoption of zkSNARKs constructed over small fields, including but not limited to, the Goldilocks field, small Mersenne prime fields, and tower of binary fields. Their appeal stems primarily from their efficacy in proving computations with small bit widths, which facilitates efficient proving of general computations and offers significant advantages, notably yielding remarkably fast proving efficiency for tasks such as proof of knowledge of hash preimages. Nevertheless, employing these SNARKs to prove algebraic statements (e.g., RSA, ECDSA signature verification) presents efficiency challenges, particularly in critical applications like zk-bridges and zkVMs that require verifying standard cryptographic primitives. To address this problem, we first define a new circuit model: arithmetic circuits with additional exponentiation gates . These gates serve as fundamental building blocks for establishing more intricate algebraic relations. Then we present a Hash-committed Commit-and-Prove (HCP) framework to construct Non-interactive Zero-knowledge (NIZK) proofs for the satisfiability of these circuits. Specifically, when proving knowledge of group exponentiations in discrete logarithm hard groups and RSA groups, compared to verifying complex group exponentiations within SNARK circuits, our approach requires proving only more lightweight computations within the SNARK, such as zk-friendly hash functions (e.g., Poseidon hash function). The number of these lightweight computations depends solely on the security parameter. This differentiation leads to substantial speedups for the prover relative to direct SNARK methods, while maintaining competitive proof size and verification cost.

Abstract Data Availability Sampling (DAS) is a pivotal paradigm for addressing scalability challenges in blockchains. However, the predominant DAS schemes rely on KZG commitments, which necessitate a trusted setup. While the recently proposed FRIDA (Crypto’24) offers a transparent, FRI-based alternative, it suffers from large commitment sizes due to its restriction to the unique decoding radius. In this work, we generalize the protocol to the list decoding radius by leveraging the DEEP (Domain Extension for Eliminating Pretenders) technique. We provide a formal proof of the opening-consistency of the DEEP-FRI, established via the notion of mutual correlated agreement , instead of the weighted correlated agreement in the original DEEP-FRI protocol. In terms of efficiency, our scheme reduces the commitment size by a factor of $$1.2 \sim 1.8\times$$ 1.2 ∼ 1.8 × while preserving the computational efficiency of both the prover and the verifier.

Verifiable Computation over encrypted data (VCoed) has two popular paradigms: SNARK-FHE (applying SNARKs to prove FHE operations) and FHE-SNARK (homomorphically evaluating SNARK proofs). For the existing works, FHE-SNARK has a much better efficiency compared to SNARK-FHE.

Remote sensing observations of vegetation derived from satellite retrievals provide spatially comprehensive measurements that are well-suited for data assimilation in land surface modeling over large areas. However, the temporal intervals of such satellite-based observations are usually multi-daily or monthly, which may not be frequent enough to perform an effective data assimilation procedure. One way that can potentially improve the assimilation performance is to apply temporal interpolation to the satellite observations before merging them with the model estimates. This study assimilates satellite leaf area index (LAI) products in a land surface model with two methods: i) assimilation of satellite LAI products at their original temporal resolution, and ii) temporal interpolation of the satellite LAI to a finer resolution before assimilation. Results show that both LAI assimilation methods are effective to improve the model performance. In addition, the simulation assimilated with the temporally interpolated LAI observations performs better than the simulation assimilated with the original LAI observations in terms of the model estimated LAI and evapotranspiration estimates.