# Information Security and Cryptography Research Group

## Generalized Proofs of Knowledge with Fully Dynamic Setup

### Christian Badertscher, Daniel Jost, and Ueli Maurer

Theory of Cryptography – TCC 2021, LNCS, Springer International Publishing, vol. 13042, pp. 499–528, Nov 2021.

Proofs of knowledge (PoK) are one of the most fundamental notions in cryptography. The appeal of this notion is that it provides a general template that an application can suitably instantiate by choosing a specific relation. Nonetheless, several important applications have been brought to light, including proofs-of-ownership of files or two-factor authentication, which do not fit the PoK template but naturally appear to be special cases of a more general notion of proofs of knowledge or possession. One would thus expect that their security properties, in particular privacy and soundness, are simply derived as concrete instantiation of a common generalized PoK concept with well understood security semantics. Unfortunately, such a notion does not exist, resulting in a variety of tailor-made security definitions whose plausibility must be checked on a case-by-case basis.

In this work, we close this gap by providing the theoretical foundations of a generalized notion of PoK that encompasses dynamic and setup-dependent relations as well as interactive statement derivations. This novel combination enables an application to directly specify relations that depend on an assumed setup, such as a random oracle, a database or ledger, and to have statements be agreed upon interactively and dynamically between parties based on the state of the setup. Our new notion is called agree-and-prove and provides clear semantics of correctness, soundness, and zero-knowledge in the above generalized scenario.

As an application, we first consider proofs-of-ownership of files for client-side file deduplication. We cast the problem and some of its prominent schemes in our agree-and-prove framework and formally analyze their security. Leveraging our generic zero-knowledge formalization, we then devise a novel scheme that is provably the privacy-preserving analogue of the well-known Merkle-Tree based protocol. As a second application, we consider two-factor entity authentication to showcase how the agree-and-prove notion encompasses proofs of ability, such as proving the correct usage of an abstract hardware token.

## BibTeX Citation

@inproceedings{BJM21,
author       = {Christian Badertscher, Daniel Jost, and Ueli Maurer},
title        = {Generalized Proofs of Knowledge with Fully Dynamic Setup},
editor       = {Nissim, Kobbi and Waters, Brent},
booktitle    = {Theory of Cryptography -- TCC 2021},
pages        = 499--528,
series       = {LNCS},
volume       = 13042,
year         = 2021,
month        = 11,