How to Delete Without a Trace: Certified Deniability in a Quantum World

TL;DR

This paper introduces the concept of certified deniability in quantum cryptography, enabling complete deletion of information without leaving any trace, and constructs primitives like signatures and NIZKs satisfying this property.

Contribution

It formalizes certified deniability in the quantum setting and constructs non-interactive primitives in the quantum random oracle model that achieve this strong form of deletion.

Findings

Certified deniability ensures no trace remains after deletion.

Constructed quantum signatures and NIZKs with certified deniability.

Quantum phenomena enable bypassing classical impossibility results.

Abstract

Is it possible to comprehensively destroy a piece of quantum information, so that nothing is left behind except the memory of whether one had it at one point? For example, various works, most recently Morimae, Poremba, and Yamakawa (TQC 2024), show how to construct a signature scheme with certified deletion where a user who deletes a signature on m cannot later produce a signature for m. However, in all of the existing schemes, even after deletion the user is still able keep irrefutable evidence that m was signed, and thus they do not fully capture the spirit of deletion. In this work, we initiate the study of certified deniability in order to obtain a more comprehensive notion of deletion. Certified deniability uses a simulation-based security definition, ensuring that any information the user has kept after deletion could have been learned without being given the deleteable object to begin with; meaning that deletion leaves no trace behind! We define and construct two non-interactive primitives that satisfy certified deniability in the quantum random oracle model: signatures and non-interactive zero-knowledge arguments (NIZKs). As a consequence, for example, it is not possible to delete a signature/NIZK and later provide convincing evidence that it used to exist. Notably, our results utilize uniquely quantum phenomena to bypass the celebrated result of Pass (CRYPTO, 2003) showing that deniable NIZKs are impossible even in the random oracle model.