Constructing Quantum Money from Abelian Group Actions

Core Concepts

The author presents a novel construction of public key quantum money and quantum lightning using abelian group actions, proving security under computational assumptions. This work introduces a new approach to quantum security in the generic group model.

Abstract

The content discusses the creation of public key quantum money and quantum lightning schemes based on abelian group actions. It explores the challenges in constructing secure quantum protocols and provides insights into the limitations of knowledge assumptions and algebraic group actions in the quantum setting. The work offers a detailed analysis of cryptographic group actions and their implications for post-quantum cryptography.

The author outlines the theoretical framework for implementing quantum money and lightning schemes, emphasizing the importance of computational assumptions for ensuring security. The discussion delves into the complexities of designing cryptosystems based on isogenies over elliptic curves and highlights the need for robust security proofs in the quantum generic group action model.

Key points include:

• Introduction to public key quantum money concept by Wiesner.
• Construction of public key quantum money from abelian group actions.
• Exploration of knowledge assumptions and algebraic group actions in the context of quantum cryptography.
• Analysis of cryptographic group actions' role in post-quantum security.
• Development of a new framework for proving quantum hardness results relative to generic group actions.

The content provides valuable insights into advancing secure communication protocols using innovative approaches grounded in mathematical principles.

Stats

We prove security under plausible computational assumption.
Our construction relies on suitable isogenies over elliptic curves.
We explore limitations of knowledge assumptions in the quantum setting.

Quotes

"Quantum money is envisioned as un-counterfeitable currency through banknotes as quantum states."
"Our construction introduces a novel approach using abelian group actions for solving classically-impossible cryptographic tasks."
"We propose that generic group actions are preferred over algebraic models for analyzing cryptosystems."

Key Insights Distilled From

Quantum Money from Abelian Group Actions

by Mark Zhandry at arxiv.org 03-11-2024

https://arxiv.org/pdf/2307.12120.pdf

Deeper Inquiries

How can non-uniform attackers with quantum advice impact the security of these schemes

Non-uniform attackers with quantum advice can impact the security of these schemes by potentially hard-coding information into their advice that allows them to break the scheme. In the context of quantum lightning, such attackers could have the serial number and banknote states hard-coded in their advice, making it easier for them to pass off invalid banknotes as valid ones. This limitation arises because non-uniform attackers with quantum advice have access to additional resources and information that uniform attackers do not possess, allowing them to exploit vulnerabilities in the scheme more effectively.

What are potential implications of recognizing set elements within a cryptographic group action

Recognizing set elements within a cryptographic group action can have significant implications for security and efficiency. By being able to efficiently recognize elements in Xλ, one can ensure that only valid elements are processed during operations like minting or verification. This recognition capability helps prevent attacks where adversaries try to introduce invalid or malicious elements into the system. Additionally, efficient recognition can enhance performance by streamlining processes and reducing computational overhead associated with handling irrelevant or incorrect data.

How might advancements in isogeny-based cryptography influence future developments in post-quantum security

Advancements in isogeny-based cryptography are expected to have a profound impact on future developments in post-quantum security. Isogenies offer unique properties that make them resistant against quantum attacks, providing a promising avenue for building secure cryptographic systems in a post-quantum world. As research progresses in this area, we may see new cryptographic protocols and algorithms based on isogenies being developed and standardized as part of post-quantum cryptography standards. These advancements could lead to stronger encryption schemes, digital signatures, key exchange protocols, and other essential components of secure communication systems that are resilient against quantum threats.