A novel post-quantum threshold oblivious signature scheme is presented. Oblivious signatures enable a requester to obtain a signature on a single selected message from a set of candidates without revealing the selection to the signer. Unlike blind signatures, the signer may be aware of the candidate set. To mitigate single-point failures the scheme employs Shamir’s secret sharing to distribute signing authority among multiple participants. To address quantum threats, it leverages isogeny-based cryptography founded on the Group Action Inverse Problem for post-quantum resilience. The construction adapts an existing isogeny-based oblivious signature by introducing a trusted dealer. The signing protocol is multi-party; verification confirms signature validity on the selected message without revealing secret information. Security reduces to the hardness of Group Action Inverse Problem and the security of the secret-sharing scheme in the semi-honest model, covering corrupted dealers, users, and coalitions of fewer than the threshold number of signers. The threshold design eliminates dependence on a single signer, preventing unauthorized signatures after key compromise. Theoretical contributions advance threshold cryptography with post-quantum primitives; practical applications include anonymous voting, secure transactions, and privacy-preserving distributed systems. Future directions include malicious adversary models and integrations with other post-quantum primitives.
A novel post-quantum threshold oblivious signature scheme is presented. Oblivious signatures enable a requester to obtain a signature on a single selected message from a set of candidates without revealing the selection to the signer. Unlike blind signatures, the signer may be aware of the candidate set. To mitigate single-point failures the scheme employs Shamir’s secret sharing to distribute signing authority among multiple participants. To address quantum threats, it leverages isogeny-based cryptography founded on the Group Action Inverse Problem for post-quantum resilience. The construction adapts an existing isogeny-based oblivious signature by introducing a trusted dealer. The signing protocol is multi-party; verification confirms signature validity on the selected message without revealing secret information. Security reduces to the hardness of Group Action Inverse Problem and the security of the secret-sharing scheme in the semi-honest model, covering corrupted dealers, users, and coalitions of fewer than the threshold number of signers. The threshold design eliminates dependence on a single signer, preventing unauthorized signatures after key compromise. Theoretical contributions advance threshold cryptography with post-quantum primitives; practical applications include anonymous voting, secure transactions, and privacy-preserving distributed systems. Future directions include malicious adversary models and integrations with other post-quantum primitives.
Blind signatures are a central tool for privacy-preserving protocols. They allow users to obtain signatures from a signer without the signer seeing the signed message. For instance, it enables electronic cash: signatures correspond to coins which can be issued by the bank in a privacy-preserving manner via blind signing. To mitigate the risk of key compromise, threshold blind signatures allow the distribution of the signing key amongst N parties. While recent works have focused on improving the security of this primitive in the classical setting, no construction is known to date in the post-quantum setting. We present the first construction of a threshold blind signature secure in the post-quantum setting, based on lattices. We prove its security under an interactive variant of the SIS assumption introduced in [Agrawal et al., CCS’22]. Our construction has a reasonable overhead of a factor of roughly 1.4 X to 2.5 X in signature size over comparable non-threshold blind signatures over lattices under heuristic but natural assumptions.
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
Modern distributed computing systems and applications with strict privacy requirements demand robust data confidentiality. A primary challenge involves enabling parties to exchange data or perform joint computations. These interactions must avoid revealing private information about the data. Protocols with the obliviousness property, known as oblivious protocols, address this issue. They ensure that no party learns more than necessary. This survey analyzes the security and performance of post-quantum oblivious protocols, with a focus on oblivious transfer and oblivious pseudorandom functions. The evaluation assesses resilience against malicious adversaries in the Universal Composability framework. Efficiency is quantified through communication and computational overhead. It identifies optimal scenarios for these protocols. This paper also surveys related primitives, such as oblivious signatures and data structures, along with their applications. Key findings highlight the inherent trade-offs between computational cost and communication complexity in post-quantum oblivious constructions. Open challenges and future research directions are outlined. Emphasis is placed on quantum-resistant designs and formal security proofs in stronger adversarial models.
Threshold signature schemes distribute the signing process among T parties out of N. They enable a variety of applications and their research is also motivated by a recent NIST call. However, applications are dominated by pre-quantum signatures, which are more efficient but not secure in the post-quantum setting. This paper investigates existing post-quantum signatures, based on a variety of paradigms: lattice problems, one-way (hash) functions, cryptographic group actions, isogenies and multivariate systems. We propose a classification (divided by paradigm) of existing tools that are used to build T-out-of-N schemes from digital signatures. We also include general approaches based on FHE, MPC or ZKP.
The advent of quantum computing poses a significant threat to the security of current cryptographic systems, including those underpinning secure multi-party computation (MPC). While considerable research has focused on developing post-quantum cryptographic (PQC) primitives, their integration into MPC protocols often inherits the computational security assumptions characteristic of classical cryptography. This paper explores the information-theoretic foundations for designing and analyzing post-quantum secure MPC protocols, aiming to achieve security guarantees that are independent of computational hardness assumptions and resilient against adversaries with unbounded computational power, including quantum adversaries. We delve into how information-theoretic primitives, such as secret sharing and oblivious transfer, can be adapted or combined with post-quantum techniques to construct MPC protocols with enhanced security. The work reviews existing paradigms, identifies challenges in achieving robust post-quantum information-theoretic security, and proposes conceptual frameworks for constructing such protocols. We examine the trade-offs between information-theoretic security, efficiency, and the practical implementation of post-quantum MPC, offering a theoretical perspective on how to achieve strong, long-term security in a quantum era. Our findings suggest that a hybrid approach, leveraging the strengths of both information theory and carefully selected post-quantum primitives, is crucial for building resilient MPC solutions.
Threshold signature schemes enable distribution of the signature issuing capability to multiple users, to mitigate the threat of signing key compromise. Though a classic primitive, these signatures have witnessed a surge of interest in recent times due to relevance to modern applications like blockchains and cryptocurrencies. In this work, we study round-optimal threshold signatures in the post-quantum regime and improve the only known lattice-based construction by Boneh et al. [CRYPTO'18] as follows: - Efficiency. We reduce the amount of noise flooding used in the construction from 2^Ω(λ) down to √Q, where Q is the bound on the number of generated signatures and λ is the security parameter. By using lattice hardness assumptions over polynomial rings, this allows to decrease the signature bit-lengths from Õ(λ³) to Õ(λ), bringing them significantly closer to practice. Our improvement relies on a careful analysis using Rényi divergence rather than statistical distance in the security proof. - Instantiation. The construction of Boneh et al. requires a standard signature scheme to be evaluated homomorphically. To instantiate this, we provide a homomorphism-friendly variant of Lyubashevsky’s signature [EUROCRYPT '12] which achieves low circuit depth by being "rejection-free" and uses an optimal, moderate noise flooding of √Q, matching the above. - Towards Adaptive Security. The construction of Boneh et al. satisfies only selective security, where all the corrupted parties must be announced before any signing query is made. We improve this in two ways: in the Random Oracle Model, we obtain partial adaptivity where signing queries can be made before the corrupted parties are announced but the set of corrupted parties must be announced all at once. In the standard model, we obtain full adaptivity, where parties can be corrupted at any time but this construction is in a weaker pre-processing model where signers must be provided correlated randomness of length proportional to the number of signatures, in an offline preprocessing phase.