Due to the scalability of the stateless and compact JSON Web Tokens (JWT), they are increasingly used in securing modern applications to support single-sign-on context and establish trust in microservices or connected-devices architectures. However, currently JWT relies on traditional encryption algorithms that are based on integer factorization or discrete logarithm problems; this exposes JWT signatures to vulnerability when quantum computers become available. Recently, NIST has announced new standards which are quantum safe. In this paper, we investigate the usage of two quantum-resistant algorithms, which are NIST candidates of round 2 standardization process in 2019, to create and verify JWT signatures. Namely, we consider lattice-based schemes (DILITHIUM and qTESLA) and compare their performance against RSA for digital signature for different security levels defined by NIST. The results show that lattice-based digital signature schemes have better performance than RSA in terms of request per seconds and average response time. DILITHIUM has demonstrated the best performance while also having smaller performance loss when scaling the security level.
Due to the scalability of the stateless and compact JSON Web Tokens (JWT), they are increasingly used in securing modern applications to support single-sign-on context and establish trust in microservices or connected-devices architectures. However, currently JWT relies on traditional encryption algorithms that are based on integer factorization or discrete logarithm problems; this exposes JWT signatures to vulnerability when quantum computers become available. Recently, NIST has announced new standards which are quantum safe. In this paper, we investigate the usage of two quantum-resistant algorithms, which are NIST candidates of round 2 standardization process in 2019, to create and verify JWT signatures. Namely, we consider lattice-based schemes (DILITHIUM and qTESLA) and compare their performance against RSA for digital signature for different security levels defined by NIST. The results show that lattice-based digital signature schemes have better performance than RSA in terms of request per seconds and average response time. DILITHIUM has demonstrated the best performance while also having smaller performance loss when scaling the security level.
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.
Alongside the growth of technology is the increasing demand for security of data and communication channels. As attacking power grows, devices become smaller and data expands, the security needs to be stronger yet less resource-consuming than ever before. Public key cryptography (PKC) is used in the majority of today's communications systems. The security of public-key cryptographic schemes, such as RSA and elliptic curve cryptography (ECC), is based on underlying mathematical problems such as factoring large integers or solving the discrete log problem. However, the discovery of Shor's Algorithm in 1994 insinuates that these schemes will be insecure when a full-scale quantum computer is developed, as these problems will be solvable in polynomial time. Therefore attention has moved towards post-quantum, or quantum-safe, cryptography (QSC). In 2016, the National Institute of Standards and Technology (NIST) announced the beginning of their efforts to migrate to QSC, a standardisation process which has involved the cryptographic community worldwide. There are five main types of QSC being considered for standardisation; lattice-based, code-based, multivariate-based, hash-based and isogeny-based. Lattice-based cryptography (LBC) offers a promising alternative to today's classical approaches. Hard problems based on lattices are believed to be unsolvable, even by a quantum-computer, in a feasible amount of time. In 1995, Ajtai showed that the average case complexity of these problems is at least as hard as solving the problems in the worst case. Furthermore, lattice-based schemes are the only remaining contender in the NIST process to provide the important primitives of encryption, key encapsulation and digital signature schemes (DSSs). A well-recognised open problem surrounding quantum-safe cryptography is its increase in bandwidth and computational complexity in comparison to existing cryptography. However, in comparison to other quantum-safe schemes, LBC has been shown to be relatively efficient. In this thesis, novel software designs of lattice-based schemes are presented and shown to be competitive with existing PKC. Additionally, physical attacks are considered and countermeasures are incorporated into the designs. DSSs are required for authentication, integrity and non-repudiation of data. This thesis provides an evaluation of three leading signature schemes, BLISS-B, Dilithium and \textsc{Falcon}, which vary in terms of their key features, such as the sampling processes used, and the structure of the lattices. Physical attacks on the three schemes are considered and the effect on performance of appropriate attack countermeasures is evaluated. A novel fault attack on the NIST candidate \textsc{Falcon} is also proposed. A further advantage of LBC is the ability to support cryptographic primitives with extended capabilities to facilitate certificate management and compute on encrypted data. The complexity of today's technology advances mean applications require more sophisticated primitives, which contrastingly are required to run on even smaller platforms. This thesis presents novel quantum-safe advanced cryptographic schemes, specifically lattice-based identity-based encryption (IBE) and hierarchical identity-based encryption (HIBE). IBE removes the need for certificate management, as a user's public key depends on their public identity. IBE is currently used in vital applications such as emergency services communication and so the development of a high-performance quantum-safe alternative is imperative. This thesis also introduces the first scalable HIBE scheme based on lattices. The first HIBE scheme based on structured lattices, Latte, was proposed by the National Centre for Cyber Security (NCSC) in 2017. However, the public key and ciphertext sizes increased with each delegation and hence it was not feasible to scale the algorithm. Skinny Latte, proposed in this thesis, remedies this issue by fixing the dimension of the lattice, thereby making public key and ciphertext sizes constant. This research also shows that it is practical for real-world deployment. Overall, this thesis demonstrates that lattice-based cryptography is practical for real-world applications. It considers both theoretical and physical attacks, and presents novel designs of advanced quantum-safe cryptographic primitives, which have only yet been realised by lattices.
Cryptographic algorithms such as RSA, ECDSA, and HMAC-SHA256 underpin modern secure communication, relying on the difficulty of solving complex mathematical problems in polynomial time. However, with quantum computers, Shor’s and Grover’s algorithms may break RSA and ECDSA in polynomial time. Even without quantum computers, adversaries can adopt a “harvest now, decrypt later” approach, prompting research on the standardization of quantum-safe, or post-quantum, cryptography (PQC). This paper proposes a CRYSTALS-Dilithium-driven framework for securing API endpoints. The proposed framework secures APIs using Dilithium-signed JWTs with nonces for authorization claims and request payloads, utilizing Dilithium FIPS-204 “ML-DSA-44,” “ML-DSA-65,” and “ML-DSA-87” from the Open Quantum Safe project. Analysis shows that only legitimate parties can issue and verify tokens; JWTs and keys resist quantum and classical attacks, replay attacks, and offer non-repudiation, data integrity, and authenticity. The protocol was compared with classical algorithms for key generation, signing, decoding, and storage overhead. Benchmarking results indicate that MLDSA-44 (NIST strength category 2) offers the ideal balance between performance, reliability, and quantum readiness. Tamarin-Prover, with its ability to model the unique mathematical structures, larger key sizes, and specific failure modes inherent to PQC algorithms, was used for formal analysis. The proposed framework provides an approach to securing JWTs and APIs with PQC Dilithium, backed by formal guarantees.
The advent of large-scale quantum computers poses a profound and imminent threat to the foundational public-key cryptographic systems that secure modern digital communication, including RSA and Elliptic Curve Cryptography (ECC). These widely deployed algorithms rely on the computational intractability of factoring large integers and solving discrete logarithm problems, which are known to be efficiently solvable by Shor's algorithm on a sufficiently powerful quantum computer. This paper explores the transition to a post-quantum cryptographic (PQC) era, with a particular focus on lattice-based cryptography as a leading candidate for quantum-resistant solutions. We provide a comprehensive overview of the quantum threat, delve into the mathematical underpinnings of lattice problems, and examine prominent lattice-based schemes such as Kyber, Dilithium, and NTRU. Through a detailed literature review, theoretical analysis, and comparison with other PQC families, we highlight the security properties, efficiency considerations, and implementation challenges of lattice-based cryptography. The paper discusses the ongoing standardization efforts, particularly by the US National Institute of Standards and Technology (NIST), and evaluates the suitability of lattice-based schemes for securing critical infrastructure in the face of quantum adversaries. We conclude by emphasizing the urgency of cryptographic migration and the pivotal role lattice-based solutions are poised to play in safeguarding digital security in the post-RSA era.
The advent of quantum computing poses a significant existential threat to current public-key cryptographic standards, particularly RSA and Elliptic Curve Cryptography (ECC), which underpin global digital security. Shor's algorithm, if implemented on a sufficiently powerful quantum computer, can efficiently break these foundational schemes, rendering vast amounts of encrypted data vulnerable. This paper investigates lattice-based cryptography as a robust and promising candidate for post-quantum security. We provide a comprehensive analysis of its theoretical underpinnings, focusing on hard problems like the Shortest Vector Problem (SVP) and Learning With Errors (LWE), which are believed to be intractable even for quantum adversaries. Through a detailed literature review and methodological exposition, we examine the construction principles of prominent lattice-based Key Encapsulation Mechanisms (KEMs) and digital signature schemes, such as Kyber and Dilithium, highlighting their inherent security properties and performance characteristics. Our results demonstrate that lattice-based schemes offer competitive efficiency, compact key sizes, and strong security guarantees against both classical and quantum attacks, positioning them as essential building blocks for the post-RSA cryptographic landscape. The discussion elaborates on the practical implications, standardization efforts by NIST, and the challenges associated with the transition to quantum-resilient cryptographic infrastructure. We conclude that lattice-based cryptography is a cornerstone of quantum resilience, critical for securing future digital communications and data integrity.
The advent of large-scale quantum computers poses a profound and imminent threat to the security foundations of modern cryptography. Widely deployed public-key cryptosystems, such as RSA and Elliptic Curve Cryptography (ECC), rely on problems like integer factorization and discrete logarithms, which Shor's algorithm can efficiently solve. This necessitates a proactive transition to post-quantum cryptography (PQC). Among leading candidates, lattice-based cryptography stands out due to its robust security guarantees, based on hard problems lacking known efficient quantum solutions, and structural properties facilitating efficient implementation. This paper explores the fundamental principles of lattice-based cryptography, detailing underlying mathematical hard problems such as the Shortest Vector Problem (SVP) and Learning With Errors (LWE). We review the evolution of lattice-based schemes, from early constructions to contemporary candidates like Kyber and Dilithium, emphasizing their suitability for Key Encapsulation Mechanisms (KEMs) and Digital Signature Schemes (DSS). Furthermore, we analyze their performance characteristics, security assumptions, and resilience against classical and quantum attacks, providing a critical comparison with other PQC families. This comprehensive overview, structured through a systematic critical analysis framework, highlights the ascendancy of lattice-based cryptography as a cornerstone for future quantum-resistant security infrastructure, offering theoretical underpinnings, practical implications, and actionable future research directions for a post-quantum world.