Quantum And Relativistic Protocols For Secure Multi-Party Computation (0911.3814v2)

Abstract: After a general introduction, the thesis is divided into four parts. In the first, we discuss the task of coin tossing, principally in order to highlight the effect different physical theories have on security in a straightforward manner, but, also, to introduce a new protocol for non-relativistic strong coin tossing. This protocol matches the security of the best protocol known to date while using a conceptually different approach to achieve the task. In the second part variable bias coin tossing is introduced. This is a variant of coin tossing in which one party secretly chooses one of two biased coins to toss. It is shown that this can be achieved with unconditional security for a specified range of biases, and with cheat-evident security for any bias. We also discuss two further protocols which are conjectured to be unconditionally secure for any bias. The third section looks at other two-party secure computations for which, prior to our work, protocols and no-go theorems were unknown. We introduce a general model for such computations, and show that, within this model, a wide range of functions are impossible to compute securely. We give explicit cheating attacks for such functions. In the final chapter we discuss the task of expanding a private random string, while dropping the usual assumption that the protocol's user trusts her devices. Instead we assume that all quantum devices are supplied by an arbitrarily malicious adversary. We give two protocols that we conjecture securely perform this task. The first allows a private random string to be expanded by a finite amount, while the second generates an arbitrarily large expansion of such a string.

• The paper's main contribution is demonstrating how quantum and relativistic principles can achieve secure multi-party computation without computational assumptions.
• It introduces a novel quantum coin tossing protocol and variable bias coin tossing model that provide unconditional and cheat-evident security.
• The work explores secure two-party computations with relaxed device trust, paving the way for robust cryptographic applications in adversarial contexts.

Quantum and Relativistic Protocols for Secure Multi-Party Computation

Roger Colbeck's dissertation examines the challenges and possibilities within the domain of secure multi-party computation (MPC), leveraging principles from quantum mechanics and relativity to enhance security. This work addresses the fundamental problem of executing joint computations among distrustful parties while maintaining the confidentiality of individual inputs. The dissertation systematically explores the potential for achieving secure MPC without relying on computational assumptions, but rather on the laws of physics.

Overview and Structural Breakdown

The dissertation is organized into several thematic sections, each addressing a distinct aspect of secure MPC:

1. Introduction and Background: Colbeck begins with grounding concepts in secure multi-party computation, offering a primer on cryptographic primitives like coin tossing and oblivious transfer, and highlighting the scarcity of computations achievable with unconditional security. It delineates the potential of relativistic theories, which have been underexplored in cryptographic contexts.
2. Strong Coin Tossing Protocols: A significant portion of the thesis is devoted to secure protocols for coin tossing—a fundamental primitive in cryptography. Colbeck proposes a new protocol in the non-relativistic quantum setting that achieves a security bias equal to the best-known methods using an original approach involving entanglement. This protocol demonstrates how quantum properties can be harnessed to achieve enhanced security in a task as rudimentary as coin tossing.
3. Variable Bias Coin Tossing: This section introduces "Variable Bias Coin Tossing" (VBCT), which allows one party to confidentially determine the bias of a coin toss—useful for scenarios requiring controlled randomness. The thesis offers proofs of concept that this task can be achieved with unconditional security for specific bias ranges, and with cheat-evident security universally. The protocols presented underline how quantum-relativistic methods can overcome certain limitations of classical computations.
4. Secure Two-Party Computation Model: Colbeck's analysis extends to other two-party secure computations, systematically examining models where previous protocols and no-go theorems were insufficient. He provides models demonstrating the impossibility of a wide array of computation tasks, supported by explicit examples of cheating methods.
5. Relaxing Assumptions with Malicious Devices: In a more applied context, the thesis explores scenarios where assumptions about device trustworthiness are relaxed—namely, when quantum devices could be adversarially provided. Colbeck presents preliminary protocols conjectured to securely expand a private random string under such scenarios, positing that cryptographic tasks might still be secure even when devices are supplied by untrusted entities.

Implications and Future Directions

The dissertation ventures into uncharted territories by integrating quantum and relativistic theories to solve classical cryptographic problems. The protocols proposed are not merely theoretical; they have practical implications for secure communications and information processing in adversarial environments.

Colbeck's work implies that while quantum and relativistic principles provide a robust foundation for enhancing security, many areas remain challenging. Particularly, the impossibility results in two-party computations remind us of inherent limitations that persist even at the intersection of advanced physical theories.

Future advancements may involve tightening these conjectures into robust proofs and further exploring device-independent protocols, where security does not rely on assumptions about the origin of the hardware or its operational fidelity. This could spur novel quantum cryptographic primitives that reshape how security is conceived in the age of quantum technologies.

This dissertation serves as an insightful contribution to the ongoing dialogue between quantum mechanics and information security, ushering in possibilities for both theoretical exploration and practical implementation in secure communications.