The Uber-Knowledge Assumption: A Bridge to the AGM
Authors
Balthazar Bauer, Pooya Farshim, Patrick Harasser, Markulf Kohlweiss
Balthazar Bauer
Université de Versailles Saint-Quentin-en-Yvelines, France
balthazar dot bauer at ens dot fr
balthazar dot bauer at ens dot fr
Pooya Farshim
IOG, Switzerland
Durham University, United Kingdom
pooya dot farshim at gmail dot com
Durham University, United Kingdom
pooya dot farshim at gmail dot com
Patrick Harasser
Technical University of Darmstadt, Germany
patrick dot harasser at tu-darmstadt dot de
patrick dot harasser at tu-darmstadt dot de
Markulf Kohlweiss
University of Edinburgh, United Kingdom
IOG, United Kingdom
mkohlwei at ed dot ac dot uk
IOG, United Kingdom
mkohlwei at ed dot ac dot uk
Keywords:
Knowledge assumption
Standard model
Generic-group model
Algebraic-group model
Groth16
KZG commitment
Abstract
The generic-group model (GGM) and the algebraic-group model (AGM) have been exceptionally successful in proving the security of many classical and modern cryptosystems. These models, however, come with standard-model uninstantiability results, raising the question of whether the schemes analyzed under them can be based on firmer standard-model footing.
We formulate the uber-knowledge (UK) assumption, a standard-model assumption that naturally extends the uber-assumption family to knowledge-type problems. We justify the soundness of UK in both the bilinear GGM and the bilinear AGM. Along the way we extend these models to account for hashing into groups, an adversarial capability that is available in many concrete groups—In contrast to standard assumptions, hashing may affect the validity of knowledge assumptions. These results, in turn, enable a modular approach to security in the GGM and the AGM.
As example applications, we use the UK assumption to prove knowledge soundness of Groth's zero-knowledge SNARK (EUROCRYPT 2016) and of KZG polynomial commitments (ASIACRYPT 2010) in the standard model, where for the former we reuse the existing proof in the AGM without hashing.
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History
Submitted: 2024-07-08
Accepted: 2024-09-02
Published: 2024-10-07
Accepted: 2024-09-02
Published: 2024-10-07
How to cite
Balthazar Bauer, Pooya Farshim, Patrick Harasser, and Markulf Kohlweiss, The Uber-Knowledge Assumption: A Bridge to the AGM. IACR Communications in Cryptology, vol. 1, no. 3, Oct 07, 2024, doi: 10.62056/anr-zoja5.
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