TU Darmstadt / ULB / TUbiblio

Beyond Uber: Instantiating Generic Groups via PGGs

Bauer, Balthazar ; Farshim, Pooya ; Harasser, Patrick ; O'Neill, Adam (2022)
Beyond Uber: Instantiating Generic Groups via PGGs.
20th Theory of Cryptography Conference (TCC 2022). Chicago, USA (07.-10.11.2022)
doi: 10.1007/978-3-031-22368-6_8
Conference or Workshop Item, Bibliographie

Abstract

The generic-group model (GGM) has been very successful in making the analyses of many cryptographic assumptions and protocols tractable. It is, however, well known that the GGM is “uninstantiable,” i.e., there are protocols secure in the GGM that are insecure when using any real-world group. This motivates the study of standard-model notions formalizing that a real-world group in some sense “looks generic.”

We introduce a standard-model definition called pseudo-generic group (PGG), where we require exponentiations with base an (initially) unknown group generator to result in random-looking group elements. In essence, our framework delicately lifts the influential notion of Universal Computational Extractors of Bellare, Hoang, and Keelveedhi (BHK, CRYPTO 2013) to a setting where the underlying ideal reference object is a generic group. The definition we obtain simultaneously generalizes the Uber assumption family, as group exponents no longer need to be polynomially induced. At the core of our definitional contribution is a new notion of algebraic unpredictability, which reinterprets the standard Schwartz–Zippel lemma as a restriction on sources. We prove the soundness of our definition in the GGM with auxiliary-input (AI-GGM).

Our remaining results focus on applications of PGGs. We first show that PGGs are indeed a generalization of Uber. We then present a number of applications in settings where exponents are not polynomially induced. In particular we prove that simple variants of ElGamal meet several advanced security goals previously achieved only by complex and inefficient schemes. We also show that PGGs imply UCEs for split sources, which in turn are sufficient in several applications. As corollaries of our AI-GGM feasibility, we obtain the security of all these applications in the presence of preprocessing attacks.

Some of our implications utilize a novel type of hash function, which we call linear-dependence destroyers (LDDs) and use to convert standard into algebraic unpredictability. We give an LDD for low-degree sources, and establish their plausibility for all sources by showing, via a compression argument, that random functions meet this definition.

Item Type: Conference or Workshop Item
Erschienen: 2022
Creators: Bauer, Balthazar ; Farshim, Pooya ; Harasser, Patrick ; O'Neill, Adam
Type of entry: Bibliographie
Title: Beyond Uber: Instantiating Generic Groups via PGGs
Language: English
Date: 21 December 2022
Publisher: Springer
Book Title: Theory of Cryptography
Series: Lecture Notes in Computer Science
Series Volume: 13749
Event Title: 20th Theory of Cryptography Conference (TCC 2022)
Event Location: Chicago, USA
Event Dates: 07.-10.11.2022
DOI: 10.1007/978-3-031-22368-6_8
URL / URN: https://link.springer.com/chapter/10.1007/978-3-031-22368-6_...
Corresponding Links:
Abstract:

The generic-group model (GGM) has been very successful in making the analyses of many cryptographic assumptions and protocols tractable. It is, however, well known that the GGM is “uninstantiable,” i.e., there are protocols secure in the GGM that are insecure when using any real-world group. This motivates the study of standard-model notions formalizing that a real-world group in some sense “looks generic.”

We introduce a standard-model definition called pseudo-generic group (PGG), where we require exponentiations with base an (initially) unknown group generator to result in random-looking group elements. In essence, our framework delicately lifts the influential notion of Universal Computational Extractors of Bellare, Hoang, and Keelveedhi (BHK, CRYPTO 2013) to a setting where the underlying ideal reference object is a generic group. The definition we obtain simultaneously generalizes the Uber assumption family, as group exponents no longer need to be polynomially induced. At the core of our definitional contribution is a new notion of algebraic unpredictability, which reinterprets the standard Schwartz–Zippel lemma as a restriction on sources. We prove the soundness of our definition in the GGM with auxiliary-input (AI-GGM).

Our remaining results focus on applications of PGGs. We first show that PGGs are indeed a generalization of Uber. We then present a number of applications in settings where exponents are not polynomially induced. In particular we prove that simple variants of ElGamal meet several advanced security goals previously achieved only by complex and inefficient schemes. We also show that PGGs imply UCEs for split sources, which in turn are sufficient in several applications. As corollaries of our AI-GGM feasibility, we obtain the security of all these applications in the presence of preprocessing attacks.

Some of our implications utilize a novel type of hash function, which we call linear-dependence destroyers (LDDs) and use to convert standard into algebraic unpredictability. We give an LDD for low-degree sources, and establish their plausibility for all sources by showing, via a compression argument, that random functions meet this definition.

Uncontrolled Keywords: Primitives, P2
Divisions: 20 Department of Computer Science
20 Department of Computer Science > Cryptography and Complexity Theory
DFG-Collaborative Research Centres (incl. Transregio)
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 1119: CROSSING – Cryptography-Based Security Solutions: Enabling Trust in New and Next Generation Computing Environments
Date Deposited: 21 Mar 2023 09:06
Last Modified: 17 Jul 2023 10:14
PPN: 509748260
Export:
Suche nach Titel in: TUfind oder in Google
Send an inquiry Send an inquiry

Options (only for editors)
Show editorial Details Show editorial Details