Aggregated signatures are a type of digital signatures that allow individual signatures obtained by different signers for different messages to be combined into a single signature that provides authenticity, integrity, and non-repudiation for all signed messages. In this case, the length of the resulting aggregated signature is much less than the sum of the lengths of the individual signatures. Sequential aggregated signatures are a subtype of aggregated signatures and allow individual signatures to be combined only during the signing procedure. Signatures of this type can be used in a variety of applications, including secure routing protocols, secure logging, sensor networks, public key infrastructure, blockchain. In this paper we present a new post-quantum aggregated signature scheme with lazy verification that eliminates the need for checking the current sequential aggregated signature during the signature process, which expands its possible application as compared to existing sequential post-quantum signature schemes. The proposed signature scheme is based on post-quantum HFEv- one-way trapdoor permutation, which is known to be resistant to quantum attacks; and Unified Framework of Gentry, O'Neill and Reyzin for obtaining lazy verification using an ideal cipher that can be implemented using the Feistel network and a block cipher. For the presented scheme we provide formal proofs of its security using Bellare-Rogaway game model: the security of the scheme was reduced to the security of a HFEv- one-way trapdoor permutation. We also present a set of parameters for the proposed scheme to meet 80 and 120-bit security levels.
Aggregated signatures are a type of digital signatures that allow individual signatures obtained by different signers for different messages to be combined into a single signature that provides authenticity, integrity, and non-repudiation for all signed messages. In this case, the length of the resulting aggregated signature is much less than the sum of the lengths of the individual signatures. Sequential aggregated signatures are a subtype of aggregated signatures and allow individual signatures to be combined only during the signing procedure. Signatures of this type can be used in a variety of applications, including secure routing protocols, secure logging, sensor networks, public key infrastructure, blockchain. In this paper we present a new post-quantum aggregated signature scheme with lazy verification that eliminates the need for checking the current sequential aggregated signature during the signature process, which expands its possible application as compared to existing sequential post-quantum signature schemes. The proposed signature scheme is based on post-quantum HFEv- one-way trapdoor permutation, which is known to be resistant to quantum attacks; and Unified Framework of Gentry, O'Neill and Reyzin for obtaining lazy verification using an ideal cipher that can be implemented using the Feistel network and a block cipher. For the presented scheme we provide formal proofs of its security using Bellare-Rogaway game model: the security of the scheme was reduced to the security of a HFEv- one-way trapdoor permutation. We also present a set of parameters for the proposed scheme to meet 80 and 120-bit security levels.
Distributed systems are widely used in modern environments such as cloud platforms, Internet of Things (IoT) networks, smart grids, and blockchain-based systems. These platforms often require digital signatures to maintain trust between devices or users. When many signatures are shared at once, the size of the communication grows, and processing takes more time. This becomes a problem in applications where quick message verification is important. Classical digital signature schemes, such as Rivest-Shamir-Adleman (RSA) and Elliptic Curve Digital Signature Algorithm (ECDSA), are not safe against quantum attacks. Post-quantum cryptography offers better protection, but it often increases communication size and computation cost. This paper introduces a quantum-resistant model that supports signature aggregation and constant-time verification. The method is based on lattice-based techniques, using structures similar to CRYSTALS-Dilithium. By combining several signatures into a single aggregated form, the model reduces the time needed for verification and the overall communication overhead. The design is suitable for real-time applications, offering strong accuracy and faster message handling. Simulation results show that the proposed method performs better than recent approaches in multiple areas. The model achieves a low authentication time, high verification accuracy, reduced message size, and improved throughput. These benefits help meet the needs of distributed systems where speed, accuracy, and security must work together. The architecture is designed to be flexible for use in real-world deployments. Future directions include support for multi-party signing, adaptive quantum-safe policies, and integration with quantum co-processors. This research supports the development of secure and efficient communication frameworks that remain effective even in the presence of future quantum threats.
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.
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(nlogq), compared to O(n2) size, where n 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.
With quantum computing now widely treated as a credible adversary to conventional public-key assumptions—most notably discrete logarithms and integer factorization—post-quantum cryptography has moved from a speculative research topic to an active engineering agenda. Within that broader landscape, lattice-based cryptography is routinely singled out as the leading candidate for next-generation digital signatures, largely because its security can be reduced to well-studied lattice problems believed resistant to quantum attacks. Aggregate signatures compress multiple individual signatures into a single compact object, translating into improved batch-verification throughput in settings such as blockchain and IoT. Against this backdrop, the present investigation offers a detailed analysis of lattice-based aggregate signature constructions. Core lattice notions are reviewed alongside security models, followed by an examination of two aggregation paradigms: unordered and ordered. Representative schemes are analyzed with respect to their construction logic and structural bottlenecks. A cross-scheme comparison is then used to motivate future research directions. By pulling together recent progress while isolating persistent obstacles, this investigation characterizes an ongoing shift from feasibility-oriented prototypes toward deployment-minded designs, offering a focused reference for standardization efforts targeting post-quantum-secure aggregate signatures.
Digital signatures are indispensable for security on the Internet, because they guarantee authenticity, integrity, and non-repudiation, of namely e-mails, software updates, and in the Transport Layer Security (TLS) protocol which is used for secure data transfer, for example. Most signature schemes that are currently in use such as the RSA signature scheme, are considered secure as long as the integer factorization problem or the discrete logarithm (DL) problem are computationally hard. At present, no algorithms have yet been found to solve these problems on conventional computers in polynomial time. However, in 1997, Shor published a polynomial-time algorithm that uses quantum computation to solve the integer factorization and the DL problem. In particular, this means that RSA signatures are considered broken as soon as large-scale quantum computers exist. Due to significant advances in the area of quantum computing, it is reasonable to assume that within 20 years, quantum computers that are able to break the RSA scheme, could exist. In order to maintain authenticity, integrity, and non-repudiation of data, cryptographic schemes that cannot be broken by quantum attacks are required. In addition, these so-called post-quantum secure schemes should be sufficiently efficient to be suitable for all established applications. Furthermore, solutions enabling a timely and secure transition from classical to post-quantum schemes are needed. This thesis contributes to the above-mentioned transition. In this thesis, we present the two lattice-based digital signature schemes TESLA and qTESLA, whereby lattice-based cryptography is one of five approaches to construct post-quantum secure schemes. Furthermore, we prove that our signature schemes are secure as long as the so-called Learning With Errors (LWE) problem is computationally hard to solve. It is presumed that even quantum computers cannot solve the LWE problem in polynomial time. The security of our schemes is proven using security reductions. Since our reductions are tight and explicit, efficient instantiations are possible that provably guarantee a selected security level, as long as the corresponding LWE instance provides a certain hardness level. Since both our reductions (as proven in the quantum random oracle model) and instantiations, take into account quantum attackers, TESLA and qTESLA are considered post-quantum secure. Concurrently, the run-times for generating and verifying signatures of qTESLA are similar (or faster) than those of the RSA scheme. However, key and signature sizes of RSA are smaller than those of qTESLA. In order to protect both the theoretical signature schemes and their implementations against attacks, we analyze possible vulnerabilities against implementation attacks. In particular, cache-side-channel attacks resulting from observing the cache behavior and fault attacks, which recover secret information by actively disrupting the execution of an algorithm are focused. We present effective countermeasures for each implementation attack we found. Our analyses and countermeasures also influence the design and implementation of qTESLA. Although our schemes are considered (post-quantum) secure according to state-of-the-art LWE attacks, cryptanalysis of lattice-based schemes is still a relatively new field of research in comparison to RSA schemes. Hence, there is a lack of confidence in the concrete instantiations and their promised security levels. However, due to developments within the field of quantum computers, a transition to post-quantum secure solutions seems to be more urgently required than ever. To solve this dilemma, we present an approach to combine two schemes, e.g., qTESLA and the RSA signature scheme, so that the combination is secure as long as one of the two combined schemes is secure. We present several of such combiners to construct hybrid signature schemes and hybrid key encapsulation mechanisms to ensure both authenticity and confidentiality in our Public-Key Infrastructure (PKI). Lastly, we also demonstrate how to apply the resulting hybrid schemes in standards such as X.509 or TLS. To summarize, this work presents post-quantum secure candidates which can, using our hybrid schemes, add post-quantum security to the current classical security in our PKI.
In the forward secure sequential aggregate (FssAgg) signature scheme, the signer combines signatures generated in different intervals under different secret keys incrementally and sequentially in a layered “onion-like” fashion with the first signature innermost in the aggregate. In contrast with general (not forward-secure) aggregate signature schemes which aggregate signatures from multiple signers, a FssAgg signature scheme aggregates signatures of a single signer not the signatures of different signers, so the verifier uses a single public key to verify the entire aggregate. With the advantages of forward secure signature and the aggregate signature at the same time, the FssAgg signature scheme has been widely applied in logging systems and blockchain since it was proposed in 2007. Although there have been several FssAgg signature schemes, all of them are based on the classic number theory problem, which are no longer secure in the quantum era. So looking for the quantum-immune FssAgg signature is much urgent. Based on the small integer solution over lattice, a FssAgg signature in the standard model is proposed. In order to improve the efficiency, this paper uses the fixed-dimensional lattice basis delegation technique to update the keys, and the forward security is achieved. This paper uses the message addition technique and the pre-image sampling technique to embed the message and the small integer solution into the signature process, and the existentially unforgeability of the scheme is also guranteed in the standard model.