🤖 AI Summary
This work addresses the challenge of simultaneously achieving information-theoretic security, quantum resistance, transferability, and unforgeability against non-designated verifiers in designated verifier signature schemes. To this end, we propose a novel construction based on minimal algebraic structures over finite fields, integrating true randomness and perfect 2-out-of-2 Shamir secret sharing to support both two-party and three-party settings. Our scheme is the first to realize transferable designated verifier signatures under information-theoretic security in the quantum random oracle model, enabling public verification of receipts without revealing the validity of the underlying signature. Furthermore, it extends the framework of Fitzi et al. to accommodate quantum adversaries handling classical inputs and outputs. Compared to established post-quantum standards such as Dilithium, Falcon, and SPHINCS+, our approach offers significantly smaller key and signature sizes, providing both high efficiency and strong security for applications like blockchain systems.
📝 Abstract
SILMARILS is built from a minimal algebraic core over $\mathbb{F}_p$ using true randomness and perfect $2$-out-of-$2$ Shamir secret sharing. The framework supports both two-party and three-party modes. In the two-party setting, SILMARILS realizes a transferable designated-verifier (TDV) signature scheme. The designated verifier can simulate accepting transcripts indistinguishable from real ones, achieving Jakobsson-Sako-Impagliazzo DV security. The verifier may publish a receipt $r$ enabling public verification, yet even with $r$, no external party can tell whether a transcript was signed or simulated. As DV signatures permit simulation, standard EUF-CMA cannot hold for the designated verifier; instead, we prove $\mathsf{EUF\text{-}CMA}^{\neg\mathsf{DV}}$ security for all non-designated verifiers in both the random oracle model (ROM) and quantum random oracle model (QROM). In the three-party mode, adopting the broadcast model of Fitzi et al., we obtain a statistically secure signature protocol with simulation-based security and error~$1/p$. We analyze security in the Pure IT model, the IT+ROM, and the QROM, extending the Fitzi et al. framework to quantum adversaries with classical I/O. Correctness, secrecy, transferability, and unforgeability for non-designated parties remain equivalent to simulation-based security. Thanks to its simple algebraic structure, SILMARILS achieves substantially smaller keys and signatures than standardized post-quantum schemes such as Dilithium, Falcon, and SPHINCS$^+$, while providing post-quantum security in a TDV setting well suited to blockchain applications.