The research within the project-team is related to cryptography and more generally to protection of information, be it classical or quantum. In a nutshell, the overall goal within our project-team is to cover the following classical and quantum aspects of cryptology, together with the specific area of quantum codes:

Well-analyzed mathematical problems such as integer factorization or the discrete logarithm problem, that have been the foundations of asymmetric cryptographic for many years, were found to be easily solved with Shor's algorithm by a quantum computer. This has prompted the community to actively search for alternatives and the NIST to launch in 2017 a still ongoing competition aiming at standardizing the most suitable candidates. Even if the proposed solutions to this competition have good reasons to be believed resistant to a quantum computer, they often have a rich mathematical structure that makes them tantalizing targets for quantum speedups that go beyond the usual Grover/quantum-walk speedups. The recent work of Chen, Liu and Zhandry on solving LWE in superposition (Eurocrypt 2022) is a good illustration of this potential. It gives a quantum polynomial time algorithm of the Short Integer Solution (SIS) problem for some parameters seemingly unreachable for classical computers. The SIS problem appears in lattice-based cryptography and while this does not break current proposals for lattice-based cryptography, it shows that even computational assumptions believed to be secure against quantum computers are at risk with quantum algorithms going way beyond Shor's algorithm.

On the other hand, symmetric cryptography, essential for enabling secure communications, used to seem much less affected at first sight: the biggest known threat was Grover's algorithm, which allows exhaustive key searches in the square root of the normal complexity. Thus, it was believed that doubling key-lengths suffices to maintain an equivalent security in the post-quantum world, but this has changed since our project QUASYModo.

Indeed, our results have shown that both for symmetric and asymmetric cryptography, the impact of quantum computers goes well beyond Grover's and Shor's algorithms and has to be studied carefully in order to understand if a given cryptographic primitive is secure or not in a quantum world. To correctly evaluate the security of cryptographic primitives in the post-quantum world, it is really desirable to elaborate a quantum cryptanalysis toolbox. This whole thread of research, that needs to combine techniques from symmetric or asymmetric cryptanalysis together with quantum algorithmic tools, came naturally in our team which is composed of symmetric and asymmetric cryptologists as well as of experts in quantum computing. We have exploited this unique opportunity to become one of the leading research teams in the field. We have also managed to pass on the interest and the focus in this research direction to other international groups that have recently published some interesting new results on quantum cryptanalysis, like: G. Leander and A. May (U. Bochum), T. Iwata (U. Nagoya), Y. Sasaki and A. Hosoyamada (NTT), Xiaoyun Wang et al. (Tsinghua U, Beijing), Li Yang et al. (Chinese academy of science)...

Symmetric techniques are widely used because they are the only ones that can achieve some major features such as high-speed or low-cost encryption, fast authentication, and efficient hashing. It is a very active research area which is stimulated by a pressing industrial demand for low-cost implementations. Even if the block cipher standard AES remains unbroken 20 years after its design, it clearly appears that it cannot serve as a Swiss Army knife in all environments. In particular an important challenge raised by several new applications is the design of symmetric encryption schemes with some additional properties compared to the AES, either in terms of implementation performance (low-cost hardware implementation, low latency, resistance against side-channel attacks...) or in terms of functionalities. The past decade has then been characterized by a multiplicity of new proposals and evaluating their security has become a primordial task which requires the attention of the community.

This proliferation of symmetric primitives has been amplified by public competitions, including the recent NIST lightweight standardization effort, which have encouraged innovative but unconventional constructions in order to answer the harsh implementation constraints. These promising but new designs need to be carefully analyzed since they may introduce unexpected weaknesses in the ciphers. Our research work captures this conflict for all families of symmetric ciphers. It includes new attacks and the search for new building blocks which ensure both a high resistance to known attacks and a low implementation cost. This work, which combines cryptanalysis and the theoretical study of discrete mathematical objects, is essential to progress in the formal analysis of the security of symmetric systems.

Our specificity, compared to most groups in the area, is that our research work tackles all aspects of the problem, from the practical ones (new attacks, concrete constructions of primitives and low-cost building-blocks) to the most theoretical ones (study of the algebraic structure of underlying mathematical objects, definition of optimal objects). We study these aspects not separately but as several sides of the same domain.

Current public-key cryptography is particularly threatened by quantum computers, since almost all cryptosystems used in practice rely on related number-theoretic security problems that can be easily solved on a quantum computer as shown by Shor in 1994. This very worrisome situation has prompted NIST to launch a standardization process in 2017 for quantum-resistant alternatives to those cryptosystems. This concerns all three major asymmetric primitives, namely public-key encryption schemes, key-exchange protocols and digital signatures. The NIST has made it clear that for each primitive there will be several selected candidates relying on different security assumptions. It publicly admits that the evaluation process for these post-quantum cryptosystems is significantly more complex than the evaluation of the SHA-3 and AES candidates for instance.

There were 69 (valid) submissions to this call in November 2017, with numerous lattice-based, code-based and multivariate-cryptography submissions and some submissions based either on hashing or on supersingular elliptic curve isogenies. In January 2019, 26 of these submissions were selected for the second round and 7 of them are code-based submissions. In July 2020, 15 schemes were selected as third round finalists/alternate candidates, 3 of them are code-based. NIST has anounced in 2021 that this call for postquantum primitives would be extended specifically for digital signatures based on techniques other than lattices. This new call should be released in the first quarter of 2022.

The research of the project-team in this field is focused on the design and cryptanalysis of cryptosystems making use of coding theory and we have proposed code-based candidates to the NIST call for the first two types of primitives, namely public-key encryption and key-exchange protocols and have two candidates among the finalists/alternate candidates. We are also preparing to submit Wave to the new code-based signature whose deadline is June 1, 2023.

The field of quantum information and computation aims at exploiting the laws of quantum physics to manipulate information in radically novel ways. There are two main applications:

Our team deals with quantum coding theoretic issues related to building a large quantum computer and with quantum cryptography. If these two questions may seem at first sight quite distinct, they are in fact closely related in the sense that they both concern the protection of (quantum) information either against an adversary in the case of quantum cryptography or against the environment in the case of quantum error-correction. This connection is actually quite deep since an adversary in quantum cryptography is typically modeled by a party having access to the entire environment. The goals of both topics are then roughly to be able to measure how much information has leaked to the environment for cryptography and to devise mechanisms that prevent information from leaking to the environment in the context of error correction.

While quantum cryptography is already getting out of the labs, this is not yet the case of quantum computing, with large quantum computers capable of breaking RSA with Shor's algorithms maybe still decades away. The situation is evolving very quickly, however, notably thanks to massive public investments in the past couple of years and all the major software or hardware companies starting to develop their own quantum computers. One of the main obstacles towards building a quantum computer is the fragility of quantum information: any unwanted interaction with the environment gives rise to the phenomenon of decoherence which prevents any quantum speedup from occurring. In practice, all the hardware of the quantum computer is intrinsically faulty: the qubits themselves, the logical gates and the measurement devices. To address this issue, one must resort to quantum fault-tolerance techniques which in turn rely on the existence of good families of quantum error-correcting codes that can be decoded efficiently. Our expertise in this area lies in the study of a particularly important class of quantum codes called quantum low-density parity-check (LDPC) codes. The LDPC property, which is well-known in the classical context where it allows for very efficient decoding algorithms, is even more crucial in the quantum case since enforcing interactions between a large number of qubits is very challenging. Quantum LDPC codes solve this issue by requiring each qubit to only interact with a constant number of other qubits.

The research community is strongly involved in the
development and evolution of cryptographic standards. Many standards
are developed through open competitions (e.g. AES, SHA-3) where
multiple teams propose new designs, and a joint cryptanalysis effort
allows to select the most suitable proposals. The analysis of
established standards is also an important work, in order to depreciate
weak algorithms before they can be exploited. Several members of the
team have been involved in this type of effort and we plan to continue
this work to ensure that secure algorithms are widely available. We
believe that good cryptographic standards have a large socio-economic
impact, and we are active in proposing schemes to future
competitions, and in analyzing schemes proposed to current or future
competitions, as well as widely-used algorithms and standards.

At the moment, we are involved in the two standardization efforts run by NIST for post-quantum cryptography and lightweight cryptography. We have also uncovered potential backdoors in two algorithms from the Russian Federation (Streebog and Kuznyechik), and successfully presented the standardization of the latter by ISO. We have also implemented practical attacks against SHA-1 to speed-up its deprecation.

NIST post-quantum competition.

The NIST post-quantum competition1 aims at standardizing quantum-safe public-key
primitives. It is really about offering a credible quantum-safe alternative for the schemes based on number theory which are severely threatened by the advent of quantum computers.
It is expected to have a huge and long-term impact on all public-key cryptography. It has received 69 proposals in November 2017, among which five have been co-designed by the project-team.
Four of them have made it to the second round in January 2019. One of them was chosen in July 2020 for the third round and another one was chosen as an alternate third round finalist.
We have also broken two first round candidates Edon-K90
and RankSign
89,
and have devised a partial break of the RLCE encryption scheme
88.
In 2020, we obtained a significant breakthrough in solving more efficiently the MinRank problem and the decoding problem in the rank metric
86, 87
by using algebraic techniques. This had several consequences: all second round rank metric candidates were dismissed from the third round (including our own candidate) and it was later found out that this algebraic algorithm could also be used to attack the third round multivariate finalist, namely Rainbow and the alternate third round finalist GeMSS.

NIST competition on lightweight symmetric encryption.

The NIST lightweight cryptography standardization process2 is an initiative to develop and standardize new authenticated encryption algorithms suitable for constrained devices. As explained in Subsection 3.2, there is a real need for new standards in lightweight cryptography, and the selected algorithms are expected to be widely deployed within the Internet of Things, as well as on more constrained devices such as contactless smart cards, or medical implants. The NIST received 56 submissions in February 2019, three of which have been co-designed by members of the team. Furthermore, one of the 10 finalists was co-designed by a member of the team.

Monitoring Current Standards

While we are very involved in the design phase of new cryptographic standards (see above), we also monitor the algorithms that are already standardized. In practice, this work has two sides.

First, we work towards the deprecation of algorithms known to be unsage. Unfortunately, even when this fact is known in the academic community, standardizing bodies can be slow to implement the required changes to their standards. This prompted for example G. Leurent to implement even better attacks against SHA-1 to illustrate its very practical weakness, and L. Perrin and X. Bonnetain (then a COSMIQ member) to find simple arguments proving that a subfunction used by the current Russian standards was not generated randomly, despite the claims of its authors.

Second, it also means that we participate to the relevant ISO meetings discussing the standardization of cryptographic primitives (JC27/WG2), and that we follow the discussions of the IETF and IRTF on RFCs. We have also provided technical assistance to members of other standardizing bodies such as the ETSI.

Major academic and industrial efforts are currently underway to implement quantum key distribution at large scale by integrating this technology within existing telecommunication networks. Colossal investments have already taken place in China to develop a large network of several thousand kilometers secured by quantum cryptography, and there is little doubt that Europe will follow the same strategy, as testified by the current European projects CiViQ (in which we are involved), OpenQKD and the future initiative Euro-QCI (Quantum Communication Infrastructure). While the main objectives of these actions are to develop better systems at lower cost and are mainly engineering problems, it is crucial to note that the security of the quantum key distribution protocols to be deployed remains far from being completely understood. For instance, while the asymptotic regime of these protocols (where one assumes a perfect knowledge of the quantum channel for instance) has been thoroughly studied in the literature, it is not the case of the much more relevant finite-size regime accounting for various sources of statistical uncertainties for instance. Another issue is that compliance with the standards of the telecommunication industry requires much improved performances compared to the current state-of-the-art, and this can only be achieved by significantly tweaking the original protocols. It is therefore rather urgent to better understand whether these more efficient protocols remain as secure as the previous ones. Our work in this area is to build upon our own expertise in continuous-variable quantum key distribution, for which we have developed the most advanced security proofs, to give security proofs for the protocols used in this kind of quantum networks.

Anne Canteaut was awarded by the French Academy of Sciences the "Female Scientist of the Year" prize. This prize distinguishes one senior woman scientist per year among all disciplines.

Clémence Bouvier, 2023,

Clémence Bouvier, Cryptanalysis and design of symmetric primitives defined over large finite fields, Sorbonne Université, 2023

We have kept on working on symmetric quantum cryptanalysis and generic quantum algorithms related to cryptanalysis, and in addition, started looking at some asymmetric cryptanalysis problems in lattice based cryptography or isogeny based cryptography.

Our recent results in symmetric cryptography concern either the security analysis of existing primitives, or the design of new primitives. This second topic includes some work on the construction and properties of suitable building-blocks for these primitives, e.g. on the search of highly nonlinear functions.

Our work in this area is mainly focused on code-based cryptography, but some of our contributions, namely algebraic attacks, have applications in multivariate cryptography or in algebraic coding theory. Many contributions relate to the NIST call for postquantum primitives, either cryptanalysis or design.

We have also been organizing since 2015 a working group held every month or every two months on code-based cryptography that structures the French efforts on this topic: every meeting is attended by most of the groups working in France on this topic (project-team GRACE, University of Bordeaux, University of Limoges, University of Rennes and University of Rouen).

Most of our work in quantum information deals with either quantum algorithms, quantum error correction or cryptography.

Bull-ATOS (07/2020 -> 06/2023)
Funding for the supervision of Maxime Rémaud's PhD.

60 kEuros.

Thalès (11/2020 -> 10/2023)
Funding for the supervision of Loïc Demange's PhD.

45 kEuros.

Associate team between COSMIQ and Simula UiB (Bergen, Norway).

The aim of the team is to investigate the design and analysis of symmetric primitives operating over large and/or prime fields.

ReSCALE project on cordis.europa.eu

"Symmetric cryptography is finding new uses because of the emergence of novel and more complex (e.g. distributed) computing environments.

These are based on sophisticated zero-knowledge and Multi-Party Computation (MPC) protocols, and they aim to provide strong security guarantees of types that were unthinkable before. In particular, they make it theoretically possible to prove that a computation was done as claimed by those performing it without revealing its inputs or outputs. This would make it possible e.g. for e-governance algorithms to prove that they are run honestly; and overall would increase the trust we can have in various automated processes.

The security techniques providing these guarantees are sequences of operations in a large finite field GF(q), where typically q>24. However, these procedures also rely on hash functions and other ""symmetric"" cryptographic algorithms that are defined over GF(2}={0,1}. But encoding GF(2) operations using GF(q) operations is very costly: relying on standard hash functions leads to significant performance overhead, to the point were the protocols mentioned before are unusable in practice.

In order to alleviate this bottleneck, it is necessary to devise symmetric algorithms that are natively described in GF(q). This change requires great care: some hash functions described in GF(q) have already been presented, and subsequently exhibited significant flaws. The inherent structural differences between GF(2) and GF(q) are the cause behind these problems: our understanding of the construction of symmetric primitives in GF(2) does not carry over to GF(q).

With this project, I will bring symmetric cryptography into GF(q) in a safe and efficient way. To this end, I will rebuild the analysis tools and methods that are used both by designers and attackers. This project will naturally lead to the design of new algorithms whose adoption will be simplified by the efficient and easy-to-use software libraries we will provide."

ERC QUASYModo

QuantERA QUANTAGENOMICS

ANR SWAP (02/22→01/26)

Sboxes for Symmetric-Key Primitives

ANR Program: AAP Générique 2021

Partners: UVSQ (coordinateur), Inria COSMIQ, ANSSI, CryptoExperts, Univ. of Rouen, Univ. of Toulon.

172 kEuros

Sboxes are small nonlinear functions that are crucial components of most symmetric-key designs and their properties are highly related to the security of the overall construction. The development of new attacks has given rise to many Sbox design criteria. However, the emerge of new contexts, applications and environments requires the development of new design criteria and strategies. The SWAP project aims first at investigating such criteria for emerging use cases like whitebox cryptography, fully homomorphic encryption and side-channel resistance. Then, we wish for analyzing the impact of these particular designs on cryptanalysis and see how the use of Sboxes with some special mathematical structures can accelerate some known attacks or introduce new ones. Finally, we aim at studying Sboxes from a mathematical point of view and provide new directions to the Big APN problem, an old conjecture on the existence of a particular type of optimal permutations.

CRYPTANALYSE (10/23

Cryptanalysis of classical cryptographic primitives

ANR Program: AAP PEPR Cybersécurité

Partners: COSMIQ (coordinator), CARAMBA (coordinator), LFANT, LIRMM, IRISA, LMV, MIS, LIP6, LJK

605 kEuros (Total amount: 5 MEuros)

This is one of the ten projects within the Program on Cybersecurity(https://www.pepr-cybersecurite.fr), funded by the French investment plan, France 2030. This project brings together the main French research groups working on cryptanalysis. It will study simultaneously the most widely used cryptographic primitives, the more recent primitives which have been around for a shorter time or which are within the long process of academic approval or standardisation, and finally the project also studies specialized primitives which are designed for some specific application contexts. In all cases, the main goal is to provide accurate hardness estimations for the underlying problems and, ultimately, a good understanding of the security level, both for symmetric and for asymmetric primitives. Software tools, which will be made openly available when appropriate, are bound to play a key role in this work. This project will advance the state of the art in cryptanalysis, and eventually increase the security of primitives used today and in the future.

ANR EPIQ (01/22

Quantum Software - Study of the quantum stack: Algorithm, models, and simulation for quantum computing

ANR Program: PEPR on Quantum Technologies

Partners: MOCQA(coordinator), COSMIQ, CEA (LIST, IPHT,MEM), Inria (Paris, Bordeaux, Nancy, Lyon, Rennes, Saclay), University of Aix-Marseille (LIS), University of Bordeaux (LABRI), University of Bourgogne and Franche Comté (ICB), University of Grenoble (LPMMC,NEEL), University of Paris (IRIF), Sorbonne University (LIP6),

230 kEuros

The purpose of this project is (i) to understand the advantages and limits of quantum computing via both quantum complexity research and the discovery and enhancement of algorithms, (ii) to define the framework for quantum computation using high-level languages, comparison of computational models as well as using their relations for program optimization, (iii) develop simulation tools to anticipate the performances of algorithms on noisy quantum machines. We are involved in studying the limits of quantum algorithms in cryptanalysis.

ANR NISQ2LSQ (01/22

From NISQ to LSQ: Bosonic and LDPC codes

ANR Program: PEPR on Quantum Technologies

Partners: COSMIQ (coordinator), Inria (Paris, Nancy, Lyon, Saclay), SPEC/CEA Saclay, PHELIQS/ CEA Grenoble, LPMMC, ENS Lyon, LPTHE, Alice

420 kEuros

This project aims at accelerating the R

ANR TLS-PQ (01/22

Post-quantum padlock for web browser

ANR Program: PEPR on Quantum Technologies

Partners: CAPSULE(coordinator), COSMIQ, Inria (Paris, Bordeaux, Nancy, Lyon, Rennes, Saclay), CEA-LETI, University of Bordeaux (TDN), University of Caen (AMACC), University of Limoges (Cryptis), University of Rouen (CA), University of Saint-Etienne (SESAM), University of Versailles (Cryptis), ARCAD

430 kEuros

This integrated project aims to develop in 5 years post-quantum primitives in a prototype of « post-quantum lock » that will be implemented in an open-source browser. We are involved in developing code-based solutions and analyzing the security of the proposed algorithms.

A. Canteaut, G. Leurent, M. Naya Plasencia and L. Perrin have been asked to analyze the security of some primitives to be deployed by some blockchain providers.
Back in 2019 A. Canteaut brought together and led a group of several international researchers to compare the security levels offered by some STARK-friendly hash functions, as a consulting activity group for Starkware.
A similar study focusing on Rescue was then commissioned by the German compagny cryptosolutions.
In 2023, the Ethereum Fondation organized an event with a group of
international experts to analyze the candidate sequential function
MinRoot; they asked G. Leurent and M. Naya Plasencia to lead
one the groups, and also invited A. Canteaut, and L. Perrin to
participate 75.
In each case, our expertise was needed to choose the appropriate solutions for their products.

Anne Canteaut has written (in French): Peut-on rêver d’une écriture impénétrable ?, in : “Déchiffrement(s) : des hiéroglyphes
à l'ADN”, Colloque annuel du Collège de France, Odile Jacob, Sep. 2023 853
The members of the project-team have published several general-audience papers (in French):

Our research activities have received significant media attention, and raised several general-audience papers. A selection is given below: