In the realm of algorithmic economics, voting systems are evaluated and compared by examining the properties or axioms they satisfy. While this pursuit has yielded valuable insights, it has also led to seminal impossibility results such as Arrow's and Gibbard-Satterthwaite's Impossibility Theorems, which pose challenges in designing ideal voting systems. Enter the domain of quantum computing: recent advancements have introduced the concept of quantum voting systems, which have many potential applications including in security and blockchain. Building on recent works that bypass Arrow's Impossibility Theorem using quantum voting systems, our research extends Quantum Condorcet Voting (QCV) to counter the Gibbard-Satterthwaite Impossibility Theorem in a quantum setting. To show this, we introduce a quantum-specific notion of truthfulness, extend ideas like incentive compatibility and the purpose of onto to the quantum domain, and introduce new tools to map social welfare functions to social choice functions in this domain.
In the realm of algorithmic economics, voting systems are evaluated and compared by examining the properties or axioms they satisfy. While this pursuit has yielded valuable insights, it has also led to seminal impossibility results such as Arrow's and Gibbard-Satterthwaite's Impossibility Theorems, which pose challenges in designing ideal voting systems. Enter the domain of quantum computing: recent advancements have introduced the concept of quantum voting systems, which have many potential applications including in security and blockchain. Building on recent works that bypass Arrow's Impossibility Theorem using quantum voting systems, our research extends Quantum Condorcet Voting (QCV) to counter the Gibbard-Satterthwaite Impossibility Theorem in a quantum setting. To show this, we introduce a quantum-specific notion of truthfulness, extend ideas like incentive compatibility and the purpose of onto to the quantum domain, and introduce new tools to map social welfare functions to social choice functions in this domain.
The election, a cornerstone of democracy, is one of the best-recognizable symbols of democratic governance. Voters' confidence in elections is essential, and these days, we can watch practically in live broadcast what consequences distrust in the fairness of elections may have. From the times of the celebrated Gibbard-Satterthwaite theorem, it is well-known in the social-choice community that most voting systems are vulnerable to the efforts of various players to influence elections. Luckily for us, computing such influence to affect election outcomes is a hard problem from the computational complexity perspective. This intractability is regarded as a ``complexity shield'' that secures voting rules against this malicious behavior. In this work, we consider quantum computers to be a new threat to the complexity shield described above, as they break out of standard computing paradigms and unlock additional computational resources. To this end, we provide an overview of possible attacks on election, discuss the abilities of quantum computing, and chart possible directions for future research in this area.
Recent advances at Google, IBM, as well as a number of research groups indicate that quantum computers will soon be reality. Motivated by the ever more realistic threat quantum computers pose to existing classical cryptographic protocols, researchers have developed several schemes to resist "quantum attacks". In particular, for electronic voting, several e-voting schemes relying on properties of quantum mechanics have been proposed. However, each of these proposals comes with a different and often not well-articulated corruption model, has different objectives, and is accompanied by security claims which are never formalized and are at best justified only against specific attacks. In this paper, we systematize and evaluate the security of suggested e-voting protocols based on quantum technology. We examine the claims of these works concerning privacy, correctness and verifiability, and if they are correctly attributed to the proposed protocols. In all non-trivial cases, we identified specific quantum attacks that violate these properties. We argue that the cause of these failures lies in the absence of formal security models and in a more general lack of reference to the existing cryptographic literature.
Recent advances indicate that quantum computers will soon be reality. Motivated by this ever more realistic threat for existing classical cryptographic protocols, researchers have developed several schemes to resist “quantum attacks.” In particular, for electronic voting (e-voting), several schemes relying on properties of quantum mechanics have been proposed. However, each of these proposals comes with a different and often not well-articulated corruption model, has different objectives, and is accompanied by security claims that are never formalized and are at best justified only against specific attacks. To address this, we propose the first formal security definitions for quantum e-voting protocols. With these at hand, we systematize and evaluate the security of previously proposed quantum e-voting protocols; we examine the claims of these works concerning privacy, correctness, and verifiability, and if they are correctly attributed to the proposed protocols. In all non-trivial cases, we identify specific quantum attacks that violate these properties. We argue that the cause of these failures lies in the absence of formal security models and references to the existing cryptographic literature.
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.
Quantum voting, inspired by quantum game theory, provides a framework in which the quantum majority rule (QMR) constitution of Bao and Yunger Halpern [Phys. Rev. A 95, 062306 (2017)] violates the quantum analogue of Arrow's impossibility theorem. We evaluate this QMR constitution analytically on classical profile data and implement its final measurement stage as a quantum circuit, running on both noiseless simulators and noisy IBM quantum hardware to map how realistic noise deforms the resulting societal ranking distribution. Moderate-high single-qubit noise does not change the qualitative behavior of QMR, whereas strong noise shifts the distribution toward other dominant winners than the classical one. We quantify this behavior using winner-agreement rates, Condorcet-winner flip rates, and Jensen-Shannon divergence between societal ranking distributions. In a second, exploratory component, we demonstrate an explicitly entanglement-based variant of the QMR constitution that serves as a testbed for multi-voter quantum correlations under noise, which we refer to as the QMR2-inspired variant. There, GHZ-type and separable superpositions over opposite rankings have the same expectation values but respond very differently to noise. Taken together, these two components connect the abstract QMR constitution to concrete implementations on noisy intermediate-scale quantum (NISQ) devices and highlight design considerations for future quantum voting protocols.