The advancement of quantum computing threatens classical cryptographic systems, such as RSA and ECDSA, which can be broken by quantum algorithms like Shor's algorithm. This necessitates the development of post-quantum cryptographic systems resistant to quantum attacks. Lattice-based cryptography, particularly the Learning with Errors (LWE) and Learning with Rounding (LWR) problems, is a promising approach. This paper presents a threshold signature scheme based on the Kryzhovnik signature, an adaptation of the Crystals-Dilithium scheme for LWR. The scheme leverages the hardness of the Module Learning with Rounding (MLWR) and Module Short Integer Solution (MSIS) problems to ensure post-quantum security. It allows a group of N participants to collaboratively generate a signature, requiring at least t participants to create a valid signature, preventing forgery by individual participants. The scheme uses Shamir's Secret Sharing, ensuring the shared secret is never stored explicitly. Key advantages include efficiency, security, and threshold-based access control, making it suitable for IoT and other resource-constrained environments.
The advancement of quantum computing threatens classical cryptographic systems, such as RSA and ECDSA, which can be broken by quantum algorithms like Shor's algorithm. This necessitates the development of post-quantum cryptographic systems resistant to quantum attacks. Lattice-based cryptography, particularly the Learning with Errors (LWE) and Learning with Rounding (LWR) problems, is a promising approach. This paper presents a threshold signature scheme based on the Kryzhovnik signature, an adaptation of the Crystals-Dilithium scheme for LWR. The scheme leverages the hardness of the Module Learning with Rounding (MLWR) and Module Short Integer Solution (MSIS) problems to ensure post-quantum security. It allows a group of N participants to collaboratively generate a signature, requiring at least t participants to create a valid signature, preventing forgery by individual participants. The scheme uses Shamir's Secret Sharing, ensuring the shared secret is never stored explicitly. Key advantages include efficiency, security, and threshold-based access control, making it suitable for IoT and other resource-constrained environments.
A lightweight, robust, and efficient security mechanism is necessary to combat quantum-generation threats across multiple domains, including healthcare, transportation, and industrial automation, in the Internet of Things (IoT). Post-quantum cryptography has emerged in response to the increasing vulnerability of traditional cryptographic methods, such as RSA and ECC, to quantum attacks. Taking advantage of the hardness of Short Integer Solutions (SIS) and Learning with Errors (LWE), we propose a lattice-based signature scheme for IoT applications. A computationally efficient IoT device model that maintains authenticated, integrity, and anonymity is proposed. The scheme has the advantage of being faster and more efficient than existing key size schemes such as IBS, CLS, and FALCON, according to a detailed security assessment. The proposed scheme maintains practical deployment ability while reducing post-quantum security in IoT ecosystems.
With the rapid development of quantum computing technology, traditional collaborative signature schemes based on RSA and elliptic curve cryptography face significant security challenges. This paper proposes a lattice-based certificateless collaborative signature scheme (L-CCS) to address the security and efficiency requirements of multi-party collaboration in intelligent computing and network systems. By leveraging lattice problems such as the Small Integer Solution and Learning With Errors, our scheme ensures post-quantum security. The L-CCS eliminates the need for a trusted Key Generation Center and a dedicated aggregator, enhancing decentralization and system robustness. Our construction achieves existential unforgeability under adaptive chosen-message attacks in the random oracle model. Furthermore, we provide a practical implementation optimized for large-scale data sharing, demonstrating sublinear scalability in signature size and computation time.
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.
We propose a new lattice-based digital signature scheme MLWRSign by modifying Dilithium, which is one of the second-round candidates of NIST's call for post-quantum cryptographic standards. To the best of our knowledge, our scheme MLWRSign is the first signature scheme whose security is based on the (module) learning with rounding (LWR) problem. Due to the simplicity of the LWR, the secret key size is reduced by approximately 30% in our scheme compared to Dilithium, while achieving the same level of security. Moreover, we implemented MLWRSign and observed that the running time of our scheme is comparable to that of Dilithium.
This paper delves into lattice-based cryptography as a cornerstone of post-quantum cryptography (PQC), exploring its evolution, key principles, and applications. It examines how lattice-based schemes leverage the inherent hardness of problems such as the Shortest Vector Problem (SVP) and Learning With Errors (LWE) to provide quantum-resistant encryption, digital signatures, and homomorphic encryption. The paper also outlines the historical development of lattice-based cryptography, emphasizing its resilience to quantum attacks in contrast to traditional schemes like RSA and ECC, which are vulnerable to Shor's algorithm. Core concepts, including lattice trapdoors, parameter optimization, and real-world applications in blockchain, cryptocurrencies, and secure communication protocols, are explored in detail. Furthermore, the paper highlights ongoing standardization efforts led by NIST, ethical considerations, practical challenges, and future research directions aimed at improving efficiency, ensuring interoperability, and expanding lattice cryptography’s use in advanced security frameworks. Through comprehensive analysis, this research underscores the importance of lattice-based cryptography as a critical pillar for securing the digital ecosystem against the emerging threat of quantum computing.
The imminent threat posed by the development of cryptographically relevant quantum computers necessitates a paradigm shift in public-key cryptography. Traditional cryptosystems like RSA and Elliptic Curve Cryptography (ECC), which underpin global digital security, are vulnerable to quantum algorithms such as Shor's algorithm. This vulnerability mandates a proactive migration to post-quantum cryptography (PQC) to secure long-term sensitive data. Among the various candidates for post-quantum security, lattice-based cryptography has emerged as a particularly promising and robust solution. This paper explores the fundamental principles of lattice-based cryptography, detailing its security foundations rooted in the presumed hardness of lattice problems like the Short Integer Solution (SIS) and Learning With Errors (LWE) problems. We review the significant progress in the field, including its selection as a primary candidate in the NIST Post-Quantum Cryptography standardization process. We discuss its advantages in terms of provable security, versatility, and potential for efficient implementation across diverse platforms, from cloud infrastructure to the Internet of Things (IoT). We also address the practical implications and challenges of its deployment, asserting its indispensable role in fortifying public-key security against future quantum attacks, thereby establishing it as a post-quantum imperative.