Electronic voting (e-voting) systems have gained prominence as secure, efficient, and scalable alternatives to traditional paper-based voting. However, the advent of quantum computing poses a serious threat to classical cryptographic techniques like Rivest–Shamir–Adleman and elliptic curve cryptography, which are commonly used in securing e-voting platforms. This creates an urgent need for post-quantum cryptographic solutions that can preserve the core security properties of confidentiality, integrity, verifiability, and unforgeability under quantum attacks. This chapter addresses these challenges by introducing post-quantum lattice-based signcryption scheme for electronic voting (PQLS-EVote), a novel signcryption scheme based on lattice-based cryptography. The scheme leverages the hardness of the learning with errors (LWE) and short integer solution (SIS) problems to achieve post-quantum security. A major novelty of PQLS-EVote lies in its use of rejection sampling to optimize ring signature generation, minimizing computational overhead. Additionally, a ( https://www.w3.org/1998/Math/MathML" display="inline"> t , n ) threshold mechanism is incorporated to ensure decentralized trust and fault tolerance. Security is formally analyzed in the random oracle model. Performance evaluation and comparison with existing schemes confirm that PQLS-EVote achieves strong security guarantees, improved efficiency, and scalability, making it a promising candidate for secure quantum-resistant e-voting systems.
Electronic voting (e-voting) systems have gained prominence as secure, efficient, and scalable alternatives to traditional paper-based voting. However, the advent of quantum computing poses a serious threat to classical cryptographic techniques like Rivest–Shamir–Adleman and elliptic curve cryptography, which are commonly used in securing e-voting platforms. This creates an urgent need for post-quantum cryptographic solutions that can preserve the core security properties of confidentiality, integrity, verifiability, and unforgeability under quantum attacks. This chapter addresses these challenges by introducing post-quantum lattice-based signcryption scheme for electronic voting (PQLS-EVote), a novel signcryption scheme based on lattice-based cryptography. The scheme leverages the hardness of the learning with errors (LWE) and short integer solution (SIS) problems to achieve post-quantum security. A major novelty of PQLS-EVote lies in its use of rejection sampling to optimize ring signature generation, minimizing computational overhead. Additionally, a ( https://www.w3.org/1998/Math/MathML" display="inline"> t , n ) threshold mechanism is incorporated to ensure decentralized trust and fault tolerance. Security is formally analyzed in the random oracle model. Performance evaluation and comparison with existing schemes confirm that PQLS-EVote achieves strong security guarantees, improved efficiency, and scalability, making it a promising candidate for secure quantum-resistant e-voting systems.
The advent of quantum computing poses a significant threat to the cryptographic foundations of current electronic voting (e-voting) systems, which commonly rely on algorithms such as Rivest-Shamir-Adleman (RSA) and Elliptic Curve Cryptography (ECC). These algorithms are believed to be vulnerable to attacks imposed by quantum computers, jeopardizing core e-voting properties, including ballot secrecy, integrity, and auditability. To address these challenges, this work presents a quantum-resistant electronic-voting (e-voting) system, named post-quantum e-voting system (PQEVS) built entirely upon cryptographic primitives standardized by the National Institute of Standards and Technology (NIST) for post-quantum security. The proposed PQEVS utilizes Dilithium for secure voter authentication, Brakerski/Fan-Vercauteren (BFV)-based Fully Homomorphic Encryption (FHE) for privacy-preserving vote tallying, and Picnic-based Zero-Knowledge Proofs (ZKPs) to ensure vote validity without compromising voter anonymity. Designed for modularity and scalability, our PQEVS delivers enhanced security while achieving significant performance gains, reducing vote processing latency by 85% and supporting throughputs of up to 36,000 votes per second. These results highlight the practicality and robustness of post-quantum cryptography in securing large-scale electoral processes, setting a new benchmark for verifiable and future-proof e-voting systems.
The landscape of modern cryptography, traditionally anchored in the computational hardness of number-theoretic problems such as integer factorization and the discrete logarithm problem, faces an existential threat from the advent of quantum computing. Shor's algorithm, discovered in 1994, demonstrates the theoretical capability of a sufficiently powerful quantum computer to efficiently solve these problems, rendering widely used cryptographic schemes like RSA and Elliptic Curve Cryptography (ECC) insecure. This imminent threat necessitates a paradigm shift towards post-quantum cryptography (PQC), which aims to develop cryptographic algorithms resistant to both classical and quantum attacks. Among the various candidates for PQC, lattice-based cryptography has emerged as a particularly promising area. This paper provides a comprehensive overview of the transition from classical number theory-based cryptography to lattice-based schemes. We explore the fundamental mathematical principles underlying lattices, introduce key lattice problems such as the Shortest Vector Problem (SVP), Closest Vector Problem (CVP), Small Integer Solution (SIS), and Learning With Errors (LWE), and discuss their application in constructing quantum-resistant cryptographic primitives. Furthermore, we analyze the security, efficiency, and practical considerations of prominent lattice-based cryptosystems, highlighting their role in the ongoing NIST post-quantum cryptography standardization process. The paper concludes by discussing the challenges and future directions in the deployment and research of lattice-based cryptographic solutions.
The advent of quantum computing poses a significant threat to the security of current asymmetric cryptographic systems, which underpin much of modern digital communication and security. These systems, predominantly RSA and Elliptic Curve Cryptography (ECC), rely on the computational hardness of mathematical problems such as integer factorization and the discrete logarithm problem. Shor's algorithm, a quantum algorithm, demonstrates the ability to efficiently solve these problems, rendering classical public-key cryptography vulnerable to attacks by sufficiently powerful quantum computers. This paper argues for and thoroughly examines the strategic imperative of transitioning from these classical cryptographic foundations to a new paradigm based on lattices, which are believed to be resistant to quantum attacks. We delve into the fundamental mathematical problems underlying lattice-based cryptography, such as the Shortest Vector Problem (SVP) and the Learning With Errors (LWE) problem, whose worst-case hardness is leveraged to achieve cryptographic security. A comprehensive literature review is provided, tracing the evolution of quantum threats and the emergence of lattice-based schemes. The methodology details the construction principles of prominent lattice-based cryptosystems. Results demonstrate their theoretical security against quantum adversaries and highlight their practical attributes, including compact key sizes and competitive performance. The discussion section contextualizes lattice-based cryptography within the broader landscape of post-quantum candidates, examining their strengths, weaknesses, and the ongoing standardization efforts by organizations like NIST. We conclude that lattice-based cryptography offers a robust and promising foundation for building resilient asymmetric cryptographic systems in the post-quantum era, ensuring the long-term security of digital information through a necessary re-architecture of cryptographic primitives.
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.
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.
The advent of large-scale quantum computers poses an existential threat to the security of current public-key cryptosystems, such as RSA and Elliptic Curve Cryptography (ECC), which rely on the computational intractability of integer factorization and discrete logarithms. This paper explores lattice-based cryptography as a promising candidate for post-quantum security. We delve into the mathematical foundations of lattices, specifically focusing on hard problems like the Shortest Vector Problem (SVP), Closest Vector Problem (CVP), Small Integer Solution (SIS), and Learning With Errors (LWE) problems, which are believed to remain intractable even for quantum computers. We provide a comprehensive review of prominent lattice-based constructions, including NTRU, Kyber, and Dilithium, highlighting their security proofs, efficiency considerations, and suitability for various cryptographic primitives such as public-key encryption, key-exchange mechanisms, and digital signatures. Furthermore, we discuss the challenges and opportunities associated with their deployment, including parameter selection, resistance to side-channel attacks, and integration into existing cryptographic infrastructures. By examining the theoretical underpinnings and practical implications, this work aims to solidify understanding of lattice-based methods as a robust and essential component of the cryptographic landscape in the quantum era, moving beyond the traditional RSA frontier.