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.
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.
Public key cryptography plays a pivotal role in maintaining digital security and privacy, with its foundations built on the hardness of certain mathematical problems. However, the emergence of quantum computing threatens the security of current cryptographic systems, making the adoption of post-quantum cryptography (PQC) an urgent necessity. Digital signature schemes are essential components in secure communications, providing authentication, non-repudiation, and data integrity. This paper examines the state of post-quantum digital signature schemes across various cryptographic approaches, including lattice-based, code-based, multivariate polynomial-based, hash-based, symmetric-key-based, and isogeny-based systems, alongside advancements in Multi-Party Computation in the Head (MPC-in-the-head) schemes. The paper then explores application-specific signatures such as blind, undeniable, threshold, chameleon, aggregate, and ring signatures, explaining their main use cases and the existing post-quantum cryptographic classifications that support these constructions individually. Software implementations of selected prominent PQC digital signature schemes were carried out, and their performance was systematically analysed using metrics such as bandwidth consumption, latency, and computational efficiency. These results provide key observations regarding the suitability of different schemes for both resource-constrained and high-performance environments. Subsequently, a detailed literature review of implementations on embedded and hardware platforms is presented, focusing on ARM-based devices and FPGA accelerators to evaluate deployment feasibility beyond general-purpose processors. Based on the software and implementation-level findings, a comparative analysis across software, embedded, and hardware platforms is conducted to highlight architectural influences on performance, scalability, and practicality. Furthermore the cryptanalytic attacks on post-quantum digital signature schemes across various PQC classifications are examined in this paper, taking into account both classical and quantum adversarial models. To evaluate realistic security constraints, implementation-oriented vulnerabilities such as side-channel and fault-based attacks are also examined. In addition, the applicability of post-quantum digital signature schemes within TLS, IoT, and related practical deployment scenarios is analysed. The study also discusses possible directions for further investigation, focusing on the requirement for effective and expandable PQC systems that can satisfy changing cybersecurity requirements. In order to protect sensitive data in the digital era, this study emphasizes the need for implementing quantum-secure systems by fusing theoretical understandings with real-world applications.
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.
Abstract Lattice-based digital signature has become one of the widely recognized post-quantum algorithms because of its simple algebraic operation, rich mathematical foundation and worst-case security, and also an important tool for constructing cryptography. This survey explores lattice-based digital signatures, a promising post-quantum resistant alternative to traditional schemes relying on factoring or discrete logarithm problems, which face increasing risks from quantum computing. The study covers conventional paradigms like Hash-and-Sign and Fiat-Shamir, as well as specialized applications including group, ring, blind, and proxy signatures. It analyzes the versatility and security strengths of lattice-based schemes, providing practical insights. Each chapter summarizes advancements in schemes, identifying emerging trends. We also pinpoint future directions to deploy lattice-based digital signatures including quantum cryptography.
Quantum computing represents one of the most disruptive technological advancements of the 21st century, with profound implications for modern cryptographic systems. Traditional digital signature algorithms—such as RSA, DSA, and Elliptic Curve Cryptography (ECC)—derive their security from mathematical problems like integer factorization and discrete logarithms, which are computationally infeasible for classical computers. However, the advent of quantum algorithms, particularly Shor’s and Grover’s algorithms, poses a direct threat to these cryptographic assumptions by drastically reducing the time required to solve such problems. This development renders existing Digital Signature infrastructures potentially obsolete once large-scale quantum computers become operational. To counter this threat, researchers have proposed a range of post-quantum cryptographic (PQC) algorithms, including lattice-based, hash-based, and multivariate polynomial-based signature schemes, which are designed to resist quantum attacks. This paper critically examines the extent of quantum vulnerability in current Digital Signature systems and evaluates the comparative performance, efficiency, and security trade-offs of post-quantum alternatives. The study aims to provide a structured understanding of the ongoing transition toward quantum-resistant digital authentication and to propose a roadmap for secure implementation in future cryptographic environments.
The emergence of quantum computers, coupled with relentless advancements in technology, calls for the immediate transition from classical to modern cryptography for efficient data transfer across optic fibers. This paper assesses different proposed post-quantum signature schemes pertaining to their plausibility of being useful against quantum computers’ capabilities. The ability of quantum computers to solve mathematical equations at speeds significantly faster than those of classical computers is remarkable. Existing cryptographic frameworks that depend on discrete logarithms and integer factorization are seriously threatened by this exceptional efficiency. In order to protect sensitive data in a post-quantum world, it may be necessary to reevaluate existing encryption techniques as the introduction of quantum computing has the potential to seriously compromise the security of many popular cryptographic systems. Hence, during the post-quantum epoch, the implementation of cryptographic measures to safeguard the confidentiality, integrity, and authenticity of all data amid the challenges instigated by quantum computers is an undertaking that must be addressed tactically and strategically. This document endeavors to depict the state-of-the-art methodologies in post-quantum cryptography outlining lattice, hash, code, and multivariate polynomial lattice-based schemes. By discussing their advantages, disadvantages, and implementation hurdles, this work seeks to educate academics and industry experts about the steps that must be taken to safeguard digital communications in the age of quantum technology.
The transition to post-quantum cryptography has been an enormous challenge and effort for cryptographers over the last decade, with impressive results such as the future NIST standards. However, the latter has so far only considered central cryptographic mechanisms (signatures or KEM) and not more advanced ones, e.g., targeting privacy-preserving applications. Of particular interest is the family of solutions called blind signatures, group signatures and anonymous credentials, for which standards already exist, and which are deployed in billions of devices. Such a family does not have, at this stage, an efficient post-quantum counterpart although very recent works improved this state of affairs by offering two different alternatives: either one gets a system with rather large elements but a security proved under standard assumptions or one gets a more efficient system at the cost of ad-hoc interactive assumptions or weaker security models. Moreover, all these works have only considered size complexity without implementing the quite complex building blocks their systems are composed of. In other words, the practicality of such systems is still very hard to assess, which is a problem if one envisions a post-quantum transition for the corresponding systems/standards.