In recent years, there has been much focus on developing core cryptographic primitives based on lattice assumptions, driven by the NIST call for post-quantum key encapsulation and digital signature algorithms. However, more work must be conducted on efficient privacy-preserving protocols based on quantum-safe assumptions. Electronic voting is one such privacy-preserving protocol whose adoption is increasing across the democratic world. E-voting offers both a fast and convenient alternative to postal voting whilst further ensuring cryptographic privacy of votes and offering full verifiability of the process. Owing to the sensitivity of voting and its infrastructure challenges, it is crucial to ensure security against quantum computers is baked into e-voting solutions. We present an e-voting scheme from quantum-safe assumptions based on the hardness of the RLWE and NTRU lattice problems, providing concrete parameters and an efficient implementation. Our design achieves a factor 5.3 × reduction in ciphertext size, 2.5 × reduction in total communication cost, and 2 × reduction in total computation time compared to the state-of-the-art lattice-based voting scheme by Aranha et al. (ACM CCS 2023). We argue that the efficiency of this scheme makes it suitable for real-world elections. Our scheme makes use of non-ternary NTRU secrets to achieve optimal parameters. In order to compute the security of our design, we extend the ternary-NTRU work of Ducas and van Woerden (ASIACRYPT 2021) by determining the concrete fatigue point (for general secrets) of NTRU to be q = 0.0058 · σ 2 · d 2.484 (above which parameters become overstretched) for modulus q , ring dimension d , and secrets drawn from a Gaussian of parameter σ . We consider this relation to be of independent interest and demonstrate its significance by improving the efficiency of the (partially) blind signature scheme by del Pino and Katsumata (CRYPTO 2022).
In recent years, there has been much focus on developing core cryptographic primitives based on lattice assumptions, driven by the NIST call for post-quantum key encapsulation and digital signature algorithms. However, more work must be conducted on efficient privacy-preserving protocols based on quantum-safe assumptions. Electronic voting is one such privacy-preserving protocol whose adoption is increasing across the democratic world. E-voting offers both a fast and convenient alternative to postal voting whilst further ensuring cryptographic privacy of votes and offering full verifiability of the process. Owing to the sensitivity of voting and its infrastructure challenges, it is crucial to ensure security against quantum computers is baked into e-voting solutions. We present an e-voting scheme from quantum-safe assumptions based on the hardness of the RLWE and NTRU lattice problems, providing concrete parameters and an efficient implementation. Our design achieves a factor 5.3 × reduction in ciphertext size, 2.5 × reduction in total communication cost, and 2 × reduction in total computation time compared to the state-of-the-art lattice-based voting scheme by Aranha et al. (ACM CCS 2023). We argue that the efficiency of this scheme makes it suitable for real-world elections. Our scheme makes use of non-ternary NTRU secrets to achieve optimal parameters. In order to compute the security of our design, we extend the ternary-NTRU work of Ducas and van Woerden (ASIACRYPT 2021) by determining the concrete fatigue point (for general secrets) of NTRU to be q = 0.0058 · σ 2 · d 2.484 (above which parameters become overstretched) for modulus q , ring dimension d , and secrets drawn from a Gaussian of parameter σ . We consider this relation to be of independent interest and demonstrate its significance by improving the efficiency of the (partially) blind signature scheme by del Pino and Katsumata (CRYPTO 2022).
We propose a 2-round blind signature protocol based on the random oracle heuristic and the hardness of standard lattice problems (Ring/Module-SIS/LWE and NTRU) with a signature size of 20 KB. The protocol is round-optimal and has a transcript size that can be as small as 60 KB. This blind signature is around 4 times shorter than the most compact lattice-based scheme based on standard assumptions of del Pino and Katsumata (Crypto 2022) and around 2 times shorter than the scheme of Agrawal et al. (CCS 2022) based on their newly-proposed one-more-ISIS assumption. We also propose a "keyed-verification'' blind signature scheme in which the verifier and the signer need to share a secret key. This scheme has a smaller signature size of only 48 bytes, but further work is needed to explore the efficiency of its signature generation protocol.
The ultimate goal in modern secure e-voting is to enable everyone to verify whether the final election result correctly reflects the votes chosen by the (human) voters, without exposing how each individual voted. These fundamental security properties are called end-to-end verifiability and voter privacy. Unfortunately, it turns out to be very challenging to pursue these properties simultaneously, especially when the latter must be future-proofed against the rise of quantum computers. In this work, we show, for the first time, a practical approach to do this. We present Epoque, the first end-to-end verifiable, voter-private, post-quantum-secure homomorphic e-voting protocol. It achieves its properties through the combination of practical lattice-based cryptographic primitives only, in a novel way. We formally prove all our security claims under common trust and hardness assumptions. At the core of Epoque lies an efficient identity-based encryption (IBE) scheme with blazingly fast master-key decryption. It is the component that makes the efficient tallying of thousands or millions of ballots a practical possibility. In order to demonstrate its practicality, we fully implemented it and provide detailed benchmarks; we believe this latter contribution is of independent interest beyond the specific e-voting application.
Electronic voting (e-voting) has emerged as a transformative technology in the modern digital era. Many countries across the world are using e-voting systems in different types of elections, from political to non-political. One of the primary goals of e-voting is ensuring both verifiability and privacy simultaneously, which we refer to as security. Verifiability is a security feature that guarantees voters can confirm their vote is reflected in the final election result, while privacy guarantees that no one is able to link a vote to the voter who cast it. Verifiability needs to hold only for the duration of the election, whereas privacy needs to extend beyond the election period, even decades after the election. This property, known as everlasting privacy in the literature, ensures that even computationally unbounded adversaries cannot compromise voter privacy, securing elections against future advances in computing, including quantum computing. Researchers have proposed a wide variety of protocols to achieve this ambitious goal in secure e-voting, however, these protocols differ significantly, making the analysis and state-of-the-art complicated. In this thesis, we first address this fragmentation by systematically analyzing all existing e-voting protocols designed to ensure everlasting privacy. We map out the relationships and dependencies among these protocols, evaluate their security and efficiency under realistic assumptions, and identify unresolved challenges in the field. Our work provides a foundational reference for researchers aiming to design secure e-voting systems with everlasting privacy, paving the way for privacypreserving elections in the post-quantum era. Building on these insights, we propose a novel e-voting system that integrates the best practices from prior research while addressing their limitations. Leveraging the Hyperion scheme as a foundation, we develop an enhanced protocol that not only guarantees everlasting privacy but also introduces everlasting receipt-freeness and coercion mitigation. Unlike existing systems like Selene and Hyperion, which rely on computational assumptions for privacy, our protocol offers privacy even against adversaries with unlimited computational power. In secure electronic voting systems with everlasting privacy, the focus is on futureproofing privacy, while sometimes election verifiability relies on the computational soundness of zero-knowledge proofs (ZKP), which are vulnerable to quantum adversaries. Therefore, a key technical challenge is designing e-voting systems with efficient post-quantum cryptographic primitives to secure both privacy and verifiability against quantum attacks. In this thesis, we advance the state of post-quantum ZKPs by focusing on the ZKPs proposed by Jain et al., which are based on the conservative Learning Parity with Noise (LPN) assumption. We optimize the efficiency of these ZKPs, achieve formal security verification using EasyCrypt, and uncover flaws in existing implementations, demonstrating their vulnerability to malicious provers. Additionally, we construct the first code-based ZKP of shuffle, enabling a verifiable and privacy-preserving e-voting protocol with mixing-based tallying. Our e-voting system ensures both verifiability and vote privacy through the computational difficulty of decoding random linear codes, marking it as the first verifiable code-based e-voting system.
Electronic voting solutions are built on complex cryptographic tools to guarantee security and fairness. Currently, those tools are based on hardness assumptions of discrete logarithm, factorization and other classical problems. While they are hard to break in classical computers, there are efficient quantum algorithms to solve using quantum computers of the near future. Thus, there is a need to develop voting protocols that are resistant to quantum attacks. Verifiable shuffling based voting systems are a popular use-case of mix-networks first proposed by Chaum four decades ago [Cha81] as a general tool for building anonymous communication systems. A decade later the quantum threat was known and since then only a few studies searched for post-quantum secure mix-nets. Recently, Costa, Martinez and Morillo introduced new arguments of shuffle for RLWE ciphertexts and how to prove the correctness of the shuffling without leaking sensitive info [CMM17]. In this thesis, we provide exact, shorter proof of Costa et al.’s lattice-based shuffling arguments. As a result, we obtain a practical non-interactive zero-knowledge proof having a runtime of 1 second per voter.
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 imminent threat of quantum computing poses a significant challenge to the security of current public-key cryptographic systems, most notably RSA. These classical algorithms rely on mathematical problems, such as integer factorization and discrete logarithms, which are efficiently solvable by Shor's algorithm on a sufficiently powerful quantum computer. This paper explores ideal lattices as a robust post-quantum foundation for asymmetric cryptography, offering a compelling alternative to traditional schemes. We delve into the mathematical underpinnings of ideal lattices, including the Ring Learning With Errors (RLWE) and Shortest Vector Problem (SVP), which are conjectured to be hard even for quantum computers. The advantages of ideal lattice-based cryptography, such as its quantum resistance, efficiency, and versatility in constructing various cryptographic primitives, are thoroughly discussed. We examine prominent examples like NTRU and CRYSTALS-Kyber, highlighting their design principles and performance characteristics. Furthermore, the paper addresses the ongoing standardization efforts by NIST and the practical considerations for migrating to lattice-based schemes. The objective is to present a comprehensive analysis demonstrating why ideal lattices are a leading candidate for securing digital communications in the quantum era, providing a secure and efficient pathway beyond the limitations of RSA.