Cryptographic algorithms are the equivalent of locks, seals, and identification documents over the Internet. They are essential to protect our online bank transactions, medical and personal information, and to support e-commerce and e-government. They come in different flavors. Encryption algorithms are necessary to protect sensitive information from prying eyes. Digital signature algorithms (in combination with hash functions) and MAC algorithms replace hand-written signatures in electronic transactions. Identification protocols allow to securely verify the identity of a remote party. As a whole, cryptology is a research area with a high strategic impact in industry, for individuals, and for society. The research activity of project-team CASCADE addresses the following topics, which cover most of the areas that are currently active in the international cryptographic community, with a focus on public-key algorithms:
Since the beginning of public-key cryptography, with the seminal Diffie-Hellman paper, many suitable algorithmic problems for cryptography have been proposed and many cryptographic schemes have been designed, together with more or less heuristic proofs of their security relative to the intractability of the underlying problems. However, many of those schemes have thereafter been broken. The simple fact that a cryptographic algorithm withstood cryptanalytic attacks for several years has often been considered as a kind of validation procedure, but schemes may take a long time before being broken. As a consequence, the lack of attacks at some time should never be considered as a full security validation of the proposal.
A completely different paradigm is provided by the concept of “provable” security. A significant line of research has tried to provide proofs in the framework of computational complexity theory (a.k.a. “reductionist” security proofs): the proofs provide reductions from a well-studied problem (factoring, RSA or the discrete logarithm) to an attack against a cryptographic protocol.
At the beginning, researchers just tried to define the security notions required by actual cryptographic schemes, and then to design protocols which could achieve these notions. The techniques were directly derived from complexity theory, providing polynomial reductions. However, their aim was essentially theoretical. They were indeed trying to minimize the required assumptions on the primitives (one-way functions or permutations, possibly trapdoor, etc), without considering practicality. Therefore, they just needed to design a scheme with polynomial-time algorithms, and to exhibit polynomial reductions from the basic mathematical assumption on the hardness of the underlying problem to an attack of the security notion, in an asymptotic way. However, such a result has no practical impact on actual security. For many years, more efficient reductions have been expected, under the denomination of either “exact security" or “concrete security”, which provide more practical security results, with concrete efficiency properties.
To this aim, a cryptographer has to deal with the following four important steps, which are all main goals of ours:
But, some schemes are still published without complete security proofs, hence their security requires further analysis, and attacks may be found. And even for provably secure schemes, attacks are not excluded, and may appear at several levels:
The security of almost all public-key cryptographic protocols in use today relies on the presumed hardness of problems from number theory such as factoring and computing discrete logarithms. This is problematic because these problems have very similar underlying structure, and its unforeseen exploit can render all currently used public-key cryptography insecure. This structure was in fact exploited by Shor to construct efficient quantum algorithms that break all hardness assumptions from number theory that are currently in use. And so naturally, an important area of research is to build provably secure protocols based on mathematical problems that are unrelated to factoring and discrete log. One of the most promising directions in this line of research is using lattice problems as a source of computational hardness, which also offer features that other alternative public-key cryptosystems (such as MQ-based, code-based, isogeny-based or hash-based schemes) cannot provide. The ERC Advanced Grant PARQ aims at evaluating the security of lattice-based cryptography, with respect to the most powerful adversaries, such as quantum computers and large-scale parallel computers.
In the meantime, although a universal quantum computer may be some decades in the future, quantum communication and quantum error correcting codes are beginning to become concretely available. It is already possible to prepare, manipulate and precisely control systems involving a few quantum information bits (qubits). Such quantum technologies could help improve the efficiency and security of concrete cryptographic protocols. The ANR JCJC project CryptiQ aims at considering three possible scenarios (first, the simple existence of a quantum attacker, then the access to quantum communication for anyone, and finally a complete quantum world) and studies the consequences on the cryptographic protocols currently available. This implies elaborating adversarial models and designing or analyzing concrete protocols with formal security proofs, in order to get ready as soon as one of these scenarios becomes the new reality.
In the area of computations on encrypted data, there are three main families of approaches:
Many companies have already started the migration to the Cloud and many individuals share their personal informations on social networks.
While some of the data are public information, many of them are personal and even quite sensitive.
Unfortunately, the current access mode is purely right-based: the provider first authenticates the client, and grants him access, or not, according to his rights in the access-control list.
Therefore, the provider itself not only has total access to the data, but also knows which data are accessed, by whom, and how:
privacy, which includes secrecy of data (confidentiality), identities (anonymity), and requests (obliviousness), should be enforced.
Moreover, while high availability can easily be controlled, and thus any defect can immediately be detected, failures in privacy protection can remain hidden for a long time.
The industry of the Cloud introduces a new implicit trust requirement: nobody has any idea at all of where and how his data are stored and manipulated, but everybody should blindly trust the providers.
The providers will definitely do their best, but this is not enough.
Privacy-compliant procedures cannot be left to the responsibility of the provider: however strong the trustfulness of the provider may be, any system or human vulnerability can be exploited against privacy.
This presents too huge a threat to tolerate.
The distribution of the data and the secrecy of the actions must be given back to the users. It requires promoting privacy as a global security notion.
In order to protect the data, one needs to encrypt it. Unfortunately, traditional encryption systems are inadequate for most applications involving big, complex data. Recall that in traditional public key encryption, a party encrypts data to a single known user, which lacks the expressiveness needed for more advanced data sharing. In enterprise settings, a party will want to share data with groups of users based on their credentials. Similarly, individuals want to selectively grant access to their personal data on social networks as well as documents and spreadsheets on Google Docs. Moreover, the access policy may even refer to users who do not exist in the system at the time the data is encrypted. Solving this problem requires an entirely new way of encrypting data.
A first natural approach would be fully homomorphic encryption (FHE, see above), but a second one is also Functional Encryption (FE), that is an emerging paradigm for public-key encryption:
it enables more fine-grained access control to encrypted data, for instance, the ability to specify a decryption policy in the ciphertext so that only individuals who satisfy the policy can decrypt, or the ability to associate keywords to a secret key so that it can only decrypt documents containing the keyword.
Our work on functional encryption centers around two goals:
Another approach is secure multi-party computation protocols, where interactivity might provide privacy in a more efficient way, namely for machine learning techniques.
Machine learning makes an intensive use of comparisons, for the activation of neurons, and new approaches have been proposed for efficient comparisons with interactive protocols.
Searchable Encryption (SE) is another technique that aims to protect users' privacy with regard to data uploaded to the cloud. Searchable Encryption is equally concerned with scalability, with the aim to accomodate large real-world databases. As a concrete application, an email provider may wish to store its users’ emails in an encrypted form to provide privacy; but it is obviously highly desirable that users should still be able to search for emails that contain a given word, or whose date falls within a given range. Businesses may also want to outsource databases containing sensitive information, such as client data, for example to dispense with a costly dedicated IT department. To be usable at all, the outsourced encrypted database should still offer some form of search functionality. Failing that, the entire database must be downloaded to process each query to the database, defeating the purpose of cloud storage.
In many contexts, the amount of data outsourced by a client is large, and the overhead incurred by generic solutions such as FHE or FE becomes prohibitive. The goal of Searchable Encryption is to find practical trade-offs between privacy, functionality, and efficiency. Regarding functionality, the focus is mainly on privately searching over encrypted cloud data, altough many SE schemes also support simple forms of update operation. Regarding privacy, SE typically allows the server to learn some information on the encrypted data.
This information is formally captured by a leakage function. Security proofs show that the cloud server does not learn any more information about the client's data than what is expressed by the leakage function.
The additional flexibility afforded by allowing a controlled amount of leakage enables SE to offer highly efficient solutions, which can be deployed in practice on large datasets. The main goal of our research in this area is to analyze the precise privacy impact of different leakage functions; propose new techniques to reduce this leakage; as well as extend the range of functionality achieved by Searchable Encryption.
In recent years, there has been very significant investment on research on quantum computers – machines that exploit quantum mechanical phenomena to solve mathematical problems that are difficult or intractable for conventional computers. If large-scale quantum computers are ever built, they will be able to break many of the public-key cryptosystems currently in use. This would seriously compromise the confidentiality and integrity of digital communications on the Internet and elsewhere. The goal of post-quantum cryptography (also called quantum-resistant cryptography or quantum-safe cryptography) is to develop cryptographic systems that are secure against both quantum and classical computers, and can interoperate with existing communication protocols and networks.
In 2016, NIST initiated a process to solicit, evaluate, and standardize one or more quantum-resistant public-key cryptographic algorithms. The first selection of standards was announced in July 2022. Out of four standards, three are based on lattice problems: CRYSTALS-KYBER for encryption, CRYSTALS-DILITHIUM and FALCON for signature. We intend to study the best lattice algorithms in order to assess the security of the three NIST standards (and two other NIST finalists SABER and NTRU) based on the hardness of lattice problems.
With several initiatives such as the development of a 2,000 km quantum network in China, the access of IBM's quantum platform freely available and the efforts made in the EU for instance with the quantum internet alliance team, we can assume that in a further future, not only the adversary has potential access to a quantum computer, but everybody may have access to quantum channels, allowing honest parties to exchange quantum data up to a limited amount. Going one step further than post-quantum cryptography, it is therefore needed to carefully study the security models and properties of classical protocols or the soundness of classical theoretical results in such a setting. Some security notions have already been defined but others have to be extended, such as the formal treatment of superposition attacks initiated by Zhandry.
On the positive side, some quantum primitives which are already well-studied, unconditionally quantum secure and already deployed in practice (such as Quantum Key Distribution) allow for new security properties such as everlasting confidentiality for sensitive long-lived data (which holds even if an attacker stores encrypted data now and decrypts them later when a quantum computer becomes available). We intend to study to what extent allowing honest parties to have access to currently available (or near-term) quantum technologies allows to achieve quantum-enhanced protocols (for classical functionalities) with improved security or efficiency beyond what is possible classically.
Unfortunately, private computation is usually at a huge cost: it definitely costs more to compute on encrypted data than on clear inputs. However, our goal is definitely to reduce this cost, as it will improve the user experience at the same time, with shorter computation time.
Strong privacy for the Cloud would have a huge societal impact since it would revolutionize the trust model: users would be able to make safe use of outsourced storage, namely for personal, financial and medical data, without having to worry about failures or attacks of the server.
Both design of new primitives and study of the best attacks are essential for this goal.
All the results of the team have been published (see the list of publications). They are all related to the research program (see Section 3) and the research projects (see Sections 7 and 8):
While GDPR (General Data Protection Regulation) imposes some privacy constraints, growing threats against servers require traffic analysis to detect malicious behaviors. This analysis includes identification of illegitimate connections to mitigate denial of service attacks, content filtering to limit content exposition or content leakage, and log management for later forensic analysis. Security Information and Event Management (SIEM) that deals with internal and external threats should still remain effective under GDPR constraints. Data protection usually means encryption, which in turn heavily limits the traffic analysis capabilities.
The main goal of this project is to bridge the gap between these two security and privacy requirements, with advanced cryptographic tools (such as searchable encryption, functional encryption, fully homomorphic encryption, and multi-party computation) in order to provide privacy to the end-users while allowing traffic monitoring by the network security manager. While current tools already work on encrypted streams by analyzing the meta-data only, advanced encryption tools may enrich the analysis by specific researches in the encrypted payload.
Our research group believes that the development of Quantum Information Processing requires a holistic approach that integrates architectures, algorithms, and applications. We recognize that applications are crucial for end-users, but they cannot be achieved without the necessary enablers, which are algorithms and architectures. Moreover, the practical impact of this technology on current and future hardware depends on a constant interplay between these three topics, especially given the limited hardware resources available.
To this end, our research program is focused on developing advanced theoretical tools that can help us understand the capabilities of quantum computers, improve their design for specific algorithms, and unlock new functionalities using quantum information processing. By taking this integrated approach, we hope to advance the state-of-the-art in Quantum Information Processing and provide valuable insights for future developments.
In the collection SCIENCES – Cryptography, Data Security of ISTE Publishing Knowledge and Wiley: