## CryptoDB

### Julia Kastner

#### Publications

**Year**

**Venue**

**Title**

2022

PKC

On Pairing-Free Blind Signature Schemes in the Algebraic Group Model
📺
Abstract

Studying the security and efficiency of blind signatures is an
important goal for privacy sensitive applications. In particular, for large-
scale settings (e.g., cryptocurrency tumblers), it is important for schemes
to scale well with the number of users in the system. Unfortunately, all
practical schemes either 1) rely on (very strong) number theoretic hard-
ness assumptions and/or computationally expensive pairing operations
over bilinear groups, or 2) support only a polylogarithmic number of
concurrent (i.e., arbitrarily interleaved) signing sessions per public key.
In this work, we revisit the security of two pairing-free blind signature
schemes in the Algebraic Group Model (AGM) + Random Oracle Model
(ROM). Concretely,
1. We consider the security of Abe’s scheme (EUROCRYPT ‘01), which
is known to have a flawed proof in the plain ROM. We adapt the
scheme to allow a partially blind variant and give a proof of the new
scheme under the discrete logarithm assumption in the AGM+ROM,
even for (polynomially many) concurrent signing sessions.
2. We then prove that the popular blind Schnorr scheme is secure un-
der the one-more discrete logarithm assumption if the signatures
are issued sequentially. While the work of Fuchsbauer et al. (EURO-
CRYPT ‘20) proves the security of the blind Schnorr scheme for con-
current signing sessions in the AGM+ROM, its underlying assump-
tion, ROS, is proven false by Benhamouda et al. (EUROCRYPT
‘21) when more than polylogarithmically many signatures are issued.
Given the recent progress, we present the first security analysis of the
blind Schnorr scheme in the slightly weaker sequential setting. We
also show that our security proof reduces from the weakest possible
assumption, with respect to known reduction techniques.

2022

TCC

The Price of Verifiability: Lower Bounds for Verifiable Random Functions
Abstract

Verifiable random functions (VRFs) are a useful extension of pseudorandom functions for which it is possible to generate a proof that a certain image is indeed the correct function value (relative to a public verification key). Due to their strong soundness requirements on such proofs, VRFs are notoriously hard to construct, and existing constructions suffer either from complex proofs (for function images), or rely on complex and non-standard assumptions.
In this work, we attempt to explain this phenomenon. We show that for a large class of pairing-based VRFs, it is not possible to obtain short proofs and a reduction to a simple assumption simultaneously. Since the class of "consecutively verifiable" VRFs we consider contains in particular the VRF of Lysyanskaya and that of Dodis-Yampolskiy, our results explain the large proof size, resp. the complex assumption of these VRFs.

2022

ASIACRYPT

The Abe-Okamoto Partially Blind Signature Scheme Revisited
Abstract

Partially blind signatures, an extension of ordinary blind signatures, are a primitive with wide applications in e-cash and electronic voting. One of the most efficient schemes to date is the one by Abe and Okamoto (CRYPTO 2000), whose underlying idea - the OR-proof technique - has served as the basis for several works.
We point out several subtle flaws in the original proof of security, and provide a new detailed and rigorous proof, achieving similar bounds as the original work. We believe our insights on the proof strategy will find useful in the security analyses of other OR-proof-based schemes.

2020

EUROCRYPT

On Instantiating the Algebraic Group Model from Falsifiable Assumptions
📺
Abstract

We provide a standard-model implementation (of a relaxation) of the algebraic group model (AGM, [Fuchsbauer, Kiltz, Loss, CRYPTO 2018]). Specifically, we show that every algorithm that uses our group is algebraic, and hence "must know" a
representation of its output group elements in terms of its input group
elements. Here, "must know" means that a suitable extractor can extract such
a representation efficiently. We stress that our implementation relies only on
falsifiable assumptions in the standard model, and in particular does not use
any knowledge assumptions.
As a consequence, our group allows to transport a number of results obtained in
the AGM into the standard model, under falsifiable assumptions. For instance,
we show that in our group, several Diffie-Hellman-like assumptions (including
computational Diffie-Hellman) are equivalent to the discrete logarithm
assumption. Furthermore, we show that our group allows to prove the Schnorr
signature scheme tightly secure in the random oracle model.
Our construction relies on indistinguishability obfuscation, and hence should
not be considered as a practical group itself. However, our results show that
the AGM is a realistic computational model (since it can be instantiated in the
standard model), and that results obtained in the AGM are also possible with
standard-model groups.

#### Coauthors

- Thomas Agrikola (1)
- Nicholas Brandt (1)
- Yu-ichi Hayashi (1)
- Dennis Hofheinz (2)
- Alexander Koch (1)
- Julian Loss (2)
- Daiki Miyahara (1)
- Takaaki Mizuki (1)
- Hideaki Sone (1)
- Akin Ünal (1)
- Stefan Walzer (1)
- Jiayu Xu (2)