## CryptoDB

### Julien Devevey

#### Publications

**Year**

**Venue**

**Title**

2023

ASIACRYPT

G+G: A Fiat-Shamir Lattice Signature Based on Convolved Gaussians
Abstract

Abstract. We describe an adaptation of Schnorr’s signature to the lattice setting, which relies on Gaussian convolution rather than flooding or rejection sampling as previous approaches. It does not involve any abort, can be proved secure in the ROM and QROM using existing analyses of the Fiat-Shamir transfom, and enjoys smaller signature sizes (both asymptotically and for concrete security levels).

2023

CRYPTO

A Detailed Analysis of Fiat-Shamir with Aborts
Abstract

Lyubashevky’s signatures are based on the Fiat-Shamir with Aborts paradigm. It transforms an interactive identification protocol that has a non-negligible probability of aborting into a signature by repeating executions until a loop iteration does not trigger an abort. Interaction is removed by replacing the challenge of the verifier by the evaluation of a hash function, modeled as a random oracle in the analysis. The access to the random oracle is classical (ROM), resp. quantum (QROM), if one is interested in security against classical, resp. quantum, adversaries. Most analyses in the literature consider a setting with a bounded number of aborts (i.e., signing fails if no signature is output within a prescribed number of loop iterations), while practical instantiations (e.g., Dilithium) run until a signature is output (i.e., loop iterations are unbounded). In this work, we emphasize that combining random oracles with loop iterations induces numerous technicalities for analyzing correctness, runtime, and security of the resulting schemes, both in the bounded and unbounded case. As a first contribution, we put light on errors in all existing analyses. We then provide two detailed analyses in the QROM for the bounded case, adapted from Kiltz et al [EUROCRYPT’18] and Grilo et al [ASIACRYPT’21]. In the process, we prove the underlying Σ-protocol to achieve a stronger zero-knowledge property than usually considered for Σ-protocols with aborts, which enables a corrected analysis. A further contribution is a detailed analysis in the case of unbounded aborts, the latter inducing several additional subtleties.

2022

PKC

Rational Modular Encoding in the DCR Setting: Non-Interactive Range Proofs and Paillier-Based Naor-Yung in the Standard Model
📺
Abstract

Range proofs allow a sender to convince a verifier that committed integers belong to an interval without revealing anything else. So far, all known non-interactive range proofs in the standard model rely on groups endowed with a bilinear map. Moreover, they either require the group order to be larger than the range of any proven statement or they suffer from a wasteful rate. Recently (Eurocrypt'21), Couteau et al. introduced a new approach to efficiently prove range membership by encoding integers as a modular ratio between small integers. We show that their technique can be transposed in the standard model under the Composite Residuosity (DCR) assumption. Interestingly, with this modification, the size of ranges is not a priori restricted by the common reference string. It also gives a constant ratio between the size of ranges and proofs. Moreover, we show that their technique of encoding messages as bounded rationals provides a secure standard model instantiation of the Naor-Yung CCA2 encryption paradigm under the DCR assumption.
Keywords: Range proofs, NIZK, standard model, Naor-Yung.

2022

ASIACRYPT

On Rejection Sampling in Lyubashevsky's Signature Scheme
📺
Abstract

Lyubashevsky’s signatures are based on the Fiat-Shamir with
aborts paradigm, whose central ingredient is the use of rejection sampling
to transform secret-dependent signature samples into samples from (or
close to) a secret-independent target distribution. Several choices for the
underlying distributions and for the rejection sampling strategy can be
considered. In this work, we study Lyubashevsky’s signatures through
the lens of rejection sampling, and aim to minimize signature size given
signing runtime requirements. Several of our results concern rejection
sampling itself and could have other applications.
We prove lower bounds for compactness of signatures given signing run-
time requirements, and for expected runtime of perfect rejection sampling
strategies. We also propose a Rényi-divergence-based analysis of Lyuba-
shevsky’s signatures which allows for larger deviations from the target
distribution, and show hyperball uniforms to be a good choice of distri-
butions: they asymptotically reach our compactness lower bounds and
offer interesting features for practical deployment. Finally, we propose
a different rejection sampling strategy which circumvents the expected
runtime lower bound and provides a worst-case runtime guarantee.

2021

PKC

On the Integer Polynomial Learning with Errors Problem
📺
Abstract

Several recent proposals of efficient public-key encryption are based on variants of the polynomial learning with errors problem (\textsf{PLWE}$^f$) in which the underlying \emph{polynomial} ring $\mZ_q[x]/f$ is replaced with the (related) modular \emph{integer} ring $\mZ_{f(q)}$; the corresponding problem is known as \emph{Integer Polynomial Learning with Errors} (\textsf{I-PLWE}$^f$). Cryptosystems based on \textsf{I-PLWE}$^f$ and its variants can
exploit optimised big-integer arithmetic to achieve good practical performance, as exhibited by the \textsf{ThreeBears} cryptosystem.
Unfortunately, the average-case hardness of \textsf{I-PLWE}$^f$
and its relation to more established lattice problems have to date remained unclear.
We describe the first polynomial-time average-case reductions for the search variant of \textsf{I-PLWE}$^f$, proving its computational equivalence with the search variant of its counterpart problem \textsf{PLWE}$^f$. Our reductions apply to a large class of defining polynomials~$f$. To obtain our results, we employ a careful adaptation of R\'{e}nyi divergence analysis techniques to bound the impact of the integer ring arithmetic carries on the error distributions.
As an application, we present a deterministic public-key cryptosystem over integer rings. Our cryptosystem, which resembles \textsf{ThreeBears}, enjoys one-way (OW-CPA) security provably based on the search variant of~\textsf{I-PLWE}$^f$.

2021

PKC

Non-Interactive CCA2-Secure Threshold Cryptosystems: Achieving Adaptive Security in the Standard Model Without Pairings
📺
Abstract

We consider threshold public-key encryption, where the decryption servers distributively hold the private key shares, and we need a threshold of these servers to decrypt the message (while the system remains secure when less than the threshold is corrupt). We investigate the notion of chosen-ciphertext secure threshold systems which has been historically hard to achieve. We further require the systems to be, both, adaptively secure (i.e., secure against a strong adversary making corruption decisions dynamically during the protocol), and non-interactive (i.e., where decryption servers do not interact amongst themselves but rather efficiently contribute, each, a single message). To date, only pairing-based implementations were known to achieve security in the standard security model without relaxation (i.e., without assuming the random oracle idealization) under the above stringent requirements. Here, we investigate how to achieve the above using other assumptions (in order to understand what other algebraic building blocks and mathematical assumptions are needed to extend the domain of encryption methods achieving the above). Specifically, we show realizations under the Decision Composite Residuosity (DCR) and Learning-With-Errors (LWE) assumptions.

#### Coauthors

- Pouria Fallahpour (1)
- Omar Fawzi (1)
- Benoît Libert (2)
- Khoa Nguyen (1)
- Alain Passelègue (3)
- Thomas Peters (2)
- Amin Sakzad (1)
- Damien Stehlé (4)
- Ron Steinfeld (1)
- Moti Yung (1)