The research work within the project-team is mostly devoted to the design and analysis of cryptographic algorithms, in the classical or in the quantum setting. It is especially motivated by the fact that the current situation of cryptography is rather fragile: many of the available symmetric and asymmetric primitives have been either threatened by recent progress in cryptanalysis or by the possible invention of a large quantum computer. Most of our work mixes fundamental aspects and practical aspects of information protection (cryptanalysis, design of algorithms, implementations). In particular we devise

work on practical aspects in cryptography, e.g. lightweight constructions and implementation, but also on more fundamental issues, either on discrete mathematics or on quantum information.

The current state-of-the-art asymmetric cryptography would become insecure in a post-quantum world, and the community is actively searching for alternatives. 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 search space. Thus, it was believed that doubling key-lengths suffices to maintain an equivalent security in the post-quantum world. This conventional wisdom was contradicted by Kuwakado and Morii in 2012 when they proposed for the first time to use Simon's algorithm in symmetric cryptanalysis 61, proving the popular Even-Mansour construction to be insecure in a strong security model called the superposition model.

This model allows an attacker to query quantumly the block cipher. Simon's algorithm 63 contrarily to Grover's algorithm gives an exponential speedup and can therefore be devastating in this setting.

In the framework of our ERC QUASYModo, we studied in detail this algorithm and possible applications,
and we were able to show that Simon's algorithm applies to other schemes as well, such as for instance
to the CAESAR candidate AEZ 57. It also allows
to break some well-known modes of operation for MACs and authenticated encryption
and provides devastating quantum slide attacks 9. Other quantum algorithms turned out be useful in this model, such as for instance
Kuperberg's algorithm 60.
It allowed to break a
tweak 52
to counter the previous attack of 9 or to devise a quantum attack in the superposition model on the Poly1305 MAC primitive 56,
which is largely used and claimed to be quantumly secure.

All these results show that in 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 is precisely the first objective of the ERC QUASYModo regarding symmetric cryptanalysis.
We plan in the coming years to continue to actively contribute to this toolbox. This goes together
with improving or finding new quantum algorithms for cryptanalysis, possibly adapted to some particular situations or scenarios that have not been studied before, like the

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-K 62 and RankSign 59, and have devised a partial break of the RLCE encryption scheme 58. In 2020, we obtained a significant breakthrough in solving more efficiently the MinRank problem and the decoding problem in the rank metric 53, 54 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.

Our cryptanalysis results on SHA-1 10 and GEA 55 have helped convince users and industry to deprecate those obsolete standards. Publication of those attacks and discussion with industry has resulted in concrete actions to reduce usage of those ciphers. Leo Perrin participates to the ISO/IEC working group on cryptographic primitives.

Our project is also involved in two NIST competitions: the competition for lightweight cryptography and the competition for standardizing quantum safe cryptosystems. In the first competition, our team has still one candidate among the finalists of the competition, while in the second competition we have two candidates that are fourth round finalists. The outcome of these two competitions will have a strong impact since the standardized solutions will likely replace large parts of the world’s infrastructure underpinning secure global communication.

The work of the team was affected by several problems:

Furthermore, our team has been directly impacted in the following ways:

The Ethereum Foundation has launched a series of bounties to cryptanalyze hash functions optimized for Zero-Knowledge proofs.

Augustin Bariant, Clémence Bouvier, Gaëtan Leurent and Léo Perrin have solved 7 of the challenges, on three different hash functions: Feistel-MIMC, Poseidon, and Rescue Prime 15

Léo Perrin has obtained a European Research Concil Grant for Starting Researchers called REinventing Symmetric Cryptography for Arithmetization over Large fiElds.

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

In order to alleviate this bottleneck, it is necessary to devise symmetric algorithms that are natively described in

The aim of this project bring symmetric cryptography into

María Naya-Plasencia has given a Keynote talk on Symmetric Cryptography for Long Term Security the 2nd June 2022 in Trodheim, Norway, at the flagship cryptography conference, Eurocrypt 2022. video

Symmetric cryptography has made important advances in recent years, in part due to new challenges that have appeared, requiring some new developments. During this talk we will discuss these advances and developments, with a particular emphasis on quantum-safe symmetric cryptography and latest results, providing the details of some particularly interesting cases. We will also discuss some related open problems.

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.

Orange Labs Caen (11/2019 -> 11/2022)
Funding for the supervision of Paul Frixon's PhD.

30 kEuros.

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.

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."

EQUALITY project on cordis.europa.eu

QIA-Phase1 project on cordis.europa.eu

The mission of the Quantum Internet Alliance (QIA) is to build a global Quantum Internet made in Europe – by developing a full-stack prototype network, and by driving an innovative European Quantum Internet ecosystem capable of scaling the network to worldleading European technology. Building on its proven track record in teamwork, which has already resulted in world first Quantum Internet technology, QIA advances this mission in two complementary objectives: The first is the realization of a full-stack prototype network able to distribute entanglement between two metropolitan-scale networks via a long-distance backbone (>500 km) using quantum repeaters. The second is the establishment of a European platform for Quantum Internet development, which will act as a catalyst for a European Quantum Internet Ecosystem including actors all along the value chain.

QIA’s network will enable advanced quantum-network applications and prepare the ground for secure quantum computing in the cloud, thanks to our new generation of end nodes including both processing nodes and low-cost photonic client devices. Nodes in the metropolitan network will be interconnected via hubs that allow the scalable connection of hundreds of end nodes, paving the way for early adopters. The long-distance backbone will be realized using fully functional quantum repeaters unlocking Pan-European end-to-end quantum communication. QIA’s prototype network will operate on standard optical fibers and serves to validate all key sub-systems, ready to be scaled by European industry.

In this first SGA we will advance towards the long-term objectives set up in the FPA project. Here we present in detail how work will be implemented during this first phase of the SGA.

HPCQS project on cordis.europa.eu

ANR DEREC (10/16→03/22)

Relativistic cryptography

ANR Program: jeunes chercheurs

244 kEuros

The goal of project DEREC is to demonstrate the feasibility of guaranteeing the security of some cryptographic protocols using the relativistic paradigm, which states that information propagation is limited by the speed of light. We plan to study some two party primitives such as bit commitment and their security against classical and quantum adversaries in this model. We then plan to the integration of those primitives into larger cryptosystems. Finally, we plan on performing a demonstration of those systems in real life conditions.

ANR CBCRYPT (10/17→03/22)

Code-based cryptography

ANR Program: AAP Générique 2017

Partners: Inria COSMIQ (coordinator), XLIM, Univ. Rouen, Univ. Bordeaux.

197 kEuros

The goal of CBCRYPT is to propose code-based candidates to the NIST call aiming at standardizing public-key primitives which resist to quantum attacks. These proposals are based either on code-based schemes relying on the usual Hamming metric or on the rank metric. The project does not deal solely with the NIST call. We also develop some other code-based solutions: these are either primitives that are not mature enough to be proposed in the first NIST call or whose functionalities are not covered by the NIST call, such as identity-based encryption, broadcast encryption, attribute based encryption or functional encryption. A third goal of this project is of a more fundamental nature: namely to lay firm foundations for code-based cryptography by developing thorough and rigorous security proofs together with a set of algorithmic tools for assessing the security of code-based cryptography.

ANR quBIC (10/17→03/22)

Quantum Banknotes and Information-Theoretic Credit Cards

ANR Program: AAP Générique 2017

Partners: Univ. Paris-Diderot (coordinator), Inria COSMIQ, UPMC (LIP6), CNRS (Laboratoire Kastler Brossel)

87 kEuros

For a quantum-safe future, classical security systems as well as quantum protocols that guarantee security against all adversaries must be deployed. Here, we will study and implement one of the most promising quantum applications, namely unforgeable quantum money. A money scheme enables a secure transaction between a client, a vendor and a bank via the use of a credit card or via the use of banknotes, with maximal security guarantees. Our objectives are to perform a theoretical analysis of quantum money schemes, in realistic conditions and for encodings in both discrete and continuous variables, and to demonstrate experimentally these protocols using state-of-the-art quantum memories and integrated detection devices.

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.

As Head of Inria Evaluation Committee, A. Canteaut has been invited to give a presentation or to participate to a panel discussion to the following events: