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arXiv:2610.31814

SILMARILS-MV: Information-Theoretically Secure Multi-Verifier Signatures with Dealer-Free Key Issuance and Linear Aggregation for Permissioned Blockchains

Khadijeh Bagheri, Hassan Khodaiemehr, Chen Feng

cs.CRcs.DCcs.ITquant-phSubmitted Oct 22, 2026• Announced Oct 26, 2026
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Abstract

Permissioned blockchains authenticate transactions, votes and quorum certificates with computationally secure signatures, and post-quantum replacements inflate consensus traffic by orders of magnitude. Information-theoretic alternatives have required a trusted authority, quantum channels, per-signature interaction, or single-use keys with bounded transfer. We present SILMARILS-MV, a multi-verifier unconditionally secure signature in which a signature is the vector $α= A\,e(m)$ and each verifier holds a secret functional $c_i = Γ^T λ(x_i)$ derived from virtual anchors $Γ$ that nobody learns. Against unbounded adversaries corrupting up to $ω$ verifiers and any signers, and observing every decision, an honest verifier accepts a forged or invalid signature with probability at most $Q/q + 1/(q-1)$, a bound that is tight in its leading term. The scheme is strongly unforgeable, non-repudiable, transferable across unboundedly many hops, and linearly aggregatable. Keys are issued by the validators through perfectly secure MPC for $t < n/3$, without broadcast. To scale, we let the committee itself sign: in threshold notarization, finality certificates have constant size $32(ω+1)$ bytes and per-validator issuance cost no longer depends on $n$. Arbiter-verified keys give clients 32-byte signatures, robust redistribution supports membership changes and share refresh, and verifiers can be enrolled retroactively. A certificate verifies in 2.4 microseconds. In an analytic normal-case model at 1000 validators, threshold notarization needs 71 KiB of authentication traffic per validator per block, 22x less than ML-DSA-44 for admitted verifiers. In a Rust HotStuff prototype with 100 validators, SILMARILS-MV commits 2.8x more transactions per second than ML-DSA-44 with 67x less cryptographic CPU, and Monte-Carlo attacks match the bounds.

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24 pages, 8 figures

Related papers

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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 offers very compact keys and signatures for the blockchain settings we target, where standardized PQC schemes are already more than sufficient. Our goal is not to compare SILMARILS with PQC, but to highlight its suitability for lightweight TDV authentication. A fair comparison with other DV schemes is omitted due to space and the complexity of aligning models.

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The potential development of large-scale quantum computers has raised serious concerns about the security of classical cryptographic systems.In response, the field of post-quantum cryptography has emerged to design cryptographic schemes that remain secure even against quantum adversaries.Isogeny-based cryptography is the most recent addition to post-quantum cryptography and started garnering attention in the 2010s.Digital signature schemes are a fundamental part of public key cryptography, providing authenticity, integrity, and non-repudiation for digital messages.They are essential for secure communication, software updates, electronic transactions, and virtually all systems requiring trust and verification.Although the traditional digital signature scheme consists only of a single prover and verifier, numerous variants have been developed over the years to address specific needs, such as multi-signatures, ring signatures, group signatures, and proxy signatures.These variants extend the functionality of traditional signatures to support more complex security models in real-world applications, such as contact tracing.As isogeny-based cryptography is a relatively young research field, many commonly used cryptographic primitives, such as variants of signature schemes, have not yet been fully developed or widely implemented.This leaves room for exploration and optimization in designing secure and efficient isogeny-based alternatives, while taking advantage of its strength with its small keys and signature compared to other post-quantum based constructions such as lattice.Multi-signature schemes have been extensively studied for decades and form a well-established area of research in cryptography.These schemes enable a group of users to collaboratively generate a single, compact signature on a shared message, ensuring that all designated parties have approved the content.Their efficiency and security properties make them particularly valuable in applications such as blockchain transactions and distributed systems.Active security in multi-signature schemes requires the signature to be unforgeable even in the worst-case scenario, where malicious signers would collude to generate a multi-signature in a group with a single honest signer.Our first contribution is to propose an actively secure isogeny-based multi-signature scheme.Proxy signature schemes have been the subject of extensive research over the years, offering cryptographic solutions for secure delegation of signing authority.These schemes allows an original signer to designate a proxy signer to generate signatures on their behalf, within the limitations imposed by the original signer.Such mechanisms are particularly useful in settings like secure communications, delegated access control, and corporate approval systems where it is essential for operations to continue even in the absence of the designated signer.Proxy I would like to express my deepest gratitude to everyone who has supported me throughout my Ph.D. journey.First and foremost, I am deeply grateful to my supervisor, Professor Atsuko Miyaji, for giving me a chance to experience the field of research as an exchange student before accepting me once again as a Ph.D student.Her invaluable support and guidance throughout the course of those 3 years as a Ph.D student enabled me to make it this far.Additionally, I am deeply grateful to the NEC Corporation for its C&C Fellowship, as well as the Jisedai Program.Their generous support eased my financial burdens, allowing to focus completely on my research.I am also deeply grateful to the professors, staff, and colleagues at Miyaji Lab, who were always there whenever I needed it.I want to especially thank Hide Miyaji, for welcoming me with open arms as soon as I arrived for the first time in Japan and supporting me throughout my Ph.D journey.I am also profoundly grateful to Mohamed Bourefis, my French comrade, who shares a very similar

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•Mar 11, 2026•0 citations
Permissioned blockchains authenticate transactions, votes and quorum certificates with computationally secure signatures, and post-quantum replacements inflate consensus traffic by orders of magnitude. Information-theoretic alternatives have required a trusted authority, quantum channels, per-signature interaction, or single-use keys with bounded transfer. We present SILMARILS-MV, a multi-verifier unconditionally secure signature in which a signature is the vector α=A e(m)α= A\,e(m)α=Ae(m) and each verifier holds a secret functional ci=ΓTλ(xi)c_i = Γ^T λ(x_i)ci​=ΓTλ(xi​) derived from virtual anchors ΓΓΓ that nobody learns. Against unbounded adversaries corrupting up to ωωω verifiers and any signers, and observing every decision, an honest verifier accepts a forged or invalid signature with probability at most Q/q+1/(q−1)Q/q + 1/(q-1)Q/q+1/(q−1), a bound that is tight in its leading term. The scheme is strongly unforgeable, non-repudiable, transferable across unboundedly many hops, and linearly aggregatable. Keys are issued by the validators through perfectly secure MPC for t<n/3t < n/3t<n/3, without broadcast. To scale, we let the committee itself sign: in threshold notarization, finality certificates have constant size 32(ω+1)32(ω+1)32(ω+1) bytes and per-validator issuance cost no longer depends on nnn. Arbiter-verified keys give clients 32-byte signatures, robust redistribution supports membership changes and share refresh, and verifiers can be enrolled retroactively. A certificate verifies in 2.4 microseconds. In an analytic normal-case model at 1000 validators, threshold notarization needs 71 KiB of authentication traffic per validator per block, 22x less than ML-DSA-44 for admitted verifiers. In a Rust HotStuff prototype with 100 validators, SILMARILS-MV commits 2.8x more transactions per second than ML-DSA-44 with 67x less cryptographic CPU, and Monte-Carlo attacks match the bounds.
SILMARILS is built from a minimal algebraic core over Fp\mathbb{F}_pFp​ using true randomness and perfect 222-out-of-222 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 rrr enabling public verification, yet even with rrr, 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 EUF-CMA¬DV\mathsf{EUF\text{-}CMA}^{\neg\mathsf{DV}}EUF-CMA¬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/p1/p1/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 offers very compact keys and signatures for the blockchain settings we target, where standardized PQC schemes are already more than sufficient. Our goal is not to compare SILMARILS with PQC, but to highlight its suitability for lightweight TDV authentication. A fair comparison with other DV schemes is omitted due to space and the complexity of aligning models.
Cross-organizational authentication often requires credentials from several authorities. We construct a lattice-based protocol with independently issued capabilities bound to a periodic pseudonym authenticated by a trusted user registry and aggregated locally into one proof. Setup requires no system-wide lattice master trapdoor or cross-authority joint lattice secret. Repartitioning a fixed witness among authorities preserves the aggregate relation and proof dimensions. We prove fixed-witness selective unforgeability of the ideal protocol under honest issuance, authentication-signature security, normal-form module learning with errors (Module-LWE), and homogeneous module short-integer solution (Module-SIS). The proof uses classical random oracles, a programmable extendable-output function (XOF), an integer norm certificate, and a reference sampler with quantified error. A C++17 research prototype was evaluated in 23 configurations. Its 78,522-byte token becomes smaller than the per-attribute Module-Lattice-Based Digital Signature Algorithm (ML-DSA)-44 reference at 33 attributes and is 49.51% smaller at 64 attributes. With 64 attributes and 64 authorities, online signing and prepared verification took 56.038 and 8.729 ms, respectively. Complete local cold signing took 370.050 ms, and public matrices for 64 capabilities occupied 29.75 mebibytes (MiB). Aggregation reduces repeated token communication for larger witnesses, at the cost of preparation, public-state storage, and higher measured computation than the ML-DSA references.
Digital signatures are fundamental cryptographic primitives that ensure the authenticity and integrity of digital communication. However, in scenarios involving sensitive interactions -- such as e-voting or e-cash -- there is a growing need for more controlled signing mechanisms. Strong-Designated Verifier Signature (SDVS) offers such control by allowing the signer to specify and restrict the verifier of a signature. The existing state-of-the-art SDVS are mostly based on number-theoretic hardness assumptions. Thus, they are not secure against quantum attacks. Moreover, Post-Quantum Cryptography (PQC)-based SDVS are inefficient and have large key and signature sizes. In this work, we address these challenges and propose an efficient post-quantum SDVS (namely, LaSDVS) based on ideal lattices under the hardness assumptions of the Ring-SIS and Ring-LWE problems. LaSDVS achieves advanced security properties including strong unforgeability under chosen-message attacks, non-transferability, non-delegatability, and signer anonymity. By employing the algebraic structure of rings and the gadget trapdoor mechanism of Micciancio et al., we design LaSDVS to minimize computational overhead and significantly reduce key and signature sizes. Notably, our scheme achieves a compact signature size of O(nlog⁡q)\mathcal{O}(n\log q)O(nlogq), compared to O(n2)\mathcal{O}(n^2)O(n2) size, where nnn is the security parameter, in the existing state-of-the-art PQC designs. To the best of our knowledge, LaSDVS offers the \textit{smallest private key and signature size} among the existing PQC-based SDVS schemes.
The potential development of large-scale quantum computers has raised serious concerns about the security of classical cryptographic systems.In response, the field of post-quantum cryptography has emerged to design cryptographic schemes that remain secure even against quantum adversaries.Isogeny-based cryptography is the most recent addition to post-quantum cryptography and started garnering attention in the 2010s.Digital signature schemes are a fundamental part of public key cryptography, providing authenticity, integrity, and non-repudiation for digital messages.They are essential for secure communication, software updates, electronic transactions, and virtually all systems requiring trust and verification.Although the traditional digital signature scheme consists only of a single prover and verifier, numerous variants have been developed over the years to address specific needs, such as multi-signatures, ring signatures, group signatures, and proxy signatures.These variants extend the functionality of traditional signatures to support more complex security models in real-world applications, such as contact tracing.As isogeny-based cryptography is a relatively young research field, many commonly used cryptographic primitives, such as variants of signature schemes, have not yet been fully developed or widely implemented.This leaves room for exploration and optimization in designing secure and efficient isogeny-based alternatives, while taking advantage of its strength with its small keys and signature compared to other post-quantum based constructions such as lattice.Multi-signature schemes have been extensively studied for decades and form a well-established area of research in cryptography.These schemes enable a group of users to collaboratively generate a single, compact signature on a shared message, ensuring that all designated parties have approved the content.Their efficiency and security properties make them particularly valuable in applications such as blockchain transactions and distributed systems.Active security in multi-signature schemes requires the signature to be unforgeable even in the worst-case scenario, where malicious signers would collude to generate a multi-signature in a group with a single honest signer.Our first contribution is to propose an actively secure isogeny-based multi-signature scheme.Proxy signature schemes have been the subject of extensive research over the years, offering cryptographic solutions for secure delegation of signing authority.These schemes allows an original signer to designate a proxy signer to generate signatures on their behalf, within the limitations imposed by the original signer.Such mechanisms are particularly useful in settings like secure communications, delegated access control, and corporate approval systems where it is essential for operations to continue even in the absence of the designated signer.Proxy I would like to express my deepest gratitude to everyone who has supported me throughout my Ph.D. journey.First and foremost, I am deeply grateful to my supervisor, Professor Atsuko Miyaji, for giving me a chance to experience the field of research as an exchange student before accepting me once again as a Ph.D student.Her invaluable support and guidance throughout the course of those 3 years as a Ph.D student enabled me to make it this far.Additionally, I am deeply grateful to the NEC Corporation for its C&C Fellowship, as well as the Jisedai Program.Their generous support eased my financial burdens, allowing to focus completely on my research.I am also deeply grateful to the professors, staff, and colleagues at Miyaji Lab, who were always there whenever I needed it.I want to especially thank Hide Miyaji, for welcoming me with open arms as soon as I arrived for the first time in Japan and supporting me throughout my Ph.D journey.I am also profoundly grateful to Mohamed Bourefis, my French comrade, who shares a very similar
The emergence of cryptographically relevant quantum computers (CRQCs) would compromise today’s dominant public-key primitives (RSA, DiffieHellman, ECDSA), threatening long-lived confidentiality, authentication, and integrity guarantees across AI pipelines and blockchain networks. This manuscript proposes a unified, quantum-resilient architecture that blends NISTstandardized post-quantum cryptography (PQC)—MLKEM for key establishment and ML-DSA or SLH-DSA for digital signatures—with defense-in-depth controls for AI model protection, data privacy, and blockchain protocol evolution. We first motivate the need for migration by outlining quantum attacks (Shor for factoring and discrete logarithms; Grover for quadratic search speedups) and summarize PQC standardization milestones and transition guidance. We then review the literature on lattice-based and hash-based cryptography, homomorphic encryption for privacy-preserving AI, and secure aggregation/differential privacy as complementary privacy technologies. Building on this foundation, we present a methodology for designing and evaluating quantum-resistant AI and blockchain systems, including key-lifecycle hardening, protocol-level hybrids, and crypto-agility. A simulated deployment (1,000 clients; 16 validator nodes; TLS 1.3 with ML-KEM and hybrid handshakes; blockchain transactions signed with ML-DSA and SLH-DSA) measures handshake and signing overheads, throughput, and model-training privacy-utility trade-offs. Results indicate that: (i) PQC-only handshakes add modest latency yet remain acceptable for online APIs; (ii) hybrid ECDHE+ML-KEM offers near-term defense against “store-now-decrypt-later,” with predictable cost; (iii) ML-DSA is practical for blockchain validation at common block sizes, while SLH-DSA suits firmware/codesigning and archival integrity; and (iv) combining PQC with secure aggregation and differentially private training preserves model utility with bounded overhead.
Abstract The rapid advancement of quantum computing poses escalating threats to the cryptographic foundations of blockchain consensus mechanisms deployed in consumer applications. This paper proposes QS-BFT (Quantum-Secured Byzantine Fault Tolerance), a novel quantum-resistant blockchain consensus framework designed to protect consumer-oriented blockchain systems against adversaries operating under an information-theoretically unbounded threat model—that is, adversaries with unlimited classical and quantum computational resources against whom only information-theoretic security (ITS) provides meaningful protection. This is a strictly stronger threat model than the computational security (CS) model assumed by standard post-quantum cryptographic schemes such as lattice-based signatures. QS-BFT integrates Quantum Key Distribution (QKD) networks to address the fundamental vulnerabilities of classical public-key digital signature schemes. By combining QKD with a multilinear hash function family, the framework introduces the MH-USS (Multilinear Hash Unconditionally Secure Signature) scheme, whose signatures are provably unforgeable, non-repudiable, and transferable under ITS, while remaining compatible with deployment on existing consumer devices. To overcome the throughput limitations of classical Byzantine Fault Tolerance approaches such as PBFT, QS-BFT introduces a dual-mode consensus strategy comprising fast mode and standard mode, and permits nodes to vote on empty blocks, thereby eliminating the need for computationally expensive view-change processes. Formal proofs establish the safety and liveness of the protocol under the ITS threat model. Performance evaluations on a local testbed demonstrate that QS-BFT achieves substantially higher throughput and lower latency than PBFT across all tested network configurations. This work advances quantum-resistant blockchain technology by achieving a principled balance between unconditional cryptographic security and practical consensus efficiency.