Cryptographie

The security of modern cryptosystems relies on computational assumptions, which may be challenged by the advent of large-scale quantum computing devices. While Shor's algorithm is known to break today's most popular public-key schemes, secret-key cryptosystems are generally expected to retain half of their pre-quantum bits of security. However, the precise advantage of quantum attacks cannot be determined without a dedicated analysis. In this talk, we will focus on key-recovery attacks against block ciphers. These attacks are often categorized in two scenarios, depending on the type of black-box access allowed to the adversary: either a classical query access, or a "quantum" query access where the black-box is part of the adversary's quantum algorithm. Attacks with classical queries, which are deemed more realistic, have so far complied with the rule of halving security levels. On the contrary, attacks with quantum queries can break some classically secure designs which exhibit a strong algebraic structure (Kuwakado & Morii, ISIT 2010). Exploiting this structure with classical queries only was the goal of the offline-Simon algorithm of Bonnetain et al. (ASIACRYPT 2019). In the final part of this talk, we will show that this algorithm allows to reach a more than quadratic speedup against some specific block cipher constructions. This is joint work with Xavier Bonnetain and Ferdinand Sibleyras.

Protocols for password-based authenticated key exchange (PAKE) allow two users sharing only a short, low-entropy password to establish a secure session with a cryptographically strong key. The challenge in designing such protocols is that they must resist offline dictionary attacks in which an attacker exhaustively enumerates the dictionary of likely passwords in an attempt to match the used password. In this paper, we study the resilience of one particular PAKE against these attacks. Indeed, we focus on the Secure Remote Password (SRP) protocol that was designed by T. Wu in 1998. Despite its lack of formal security proof, SRP has become a de-facto standard. For more than 20 years, many projects have turned towards SRP for their authentication solution, thanks to the availability of open-source implementations with no restrictive licenses. Of particular interest, we mention the Stanford reference implementation (in C and Java) and the OpenSSL one (in C). In this work, we analyze the security of the SRP implementation inside the OpenSSL library. In particular, we identify that this implementation is vulnerable to offline dictionary attacks. Indeed, we exploit a call for a function computing modular exponentiation of big numbers in OpenSSL. In the SRP protocol, this function leads to the call of a non-constant time function, thereby leaking some information about the used password when leveraging cache-based Flush+Reload timing attack. Then, we show that our attack is practical, since it only requires one single trace, despite the noise of cache measurements. In addition, the attack is quite efficient as the reduction of some common dictionaries is very fast using modern resources at negligible cost. We also prove that the scope of our vulnerability is not only limited to OpenSSL, since many other projects, including Stanford's, ProtonMail and Apple Homekit, rely on OpenSSL, which makes them vulnerable. We find that our flaw might also impact projects written in Python, Erlang, JavaScript and Ruby, as long as they load the OpenSSL dynamic library for their big number operations. We disclosed our attack to OpenSSL who acknowledged the attack and timely fixed the vulnerability.

Many attribute-based anonymous credential (ABC) schemes have been proposed allowing a user to prove the possession of some attributes, anonymously. They became more and more practical with, for the most recent papers, a constant-size credential to show a subset of attributes issued by a unique credential issuer. However, proving possession of attributes coming from K different credential issuers usually requires K independent credentials to be shown. Only attribute-based credential schemes from aggregatable signatures can overcome this issue. In this paper, we propose new ABC schemes from aggregatable signatures with randomizable tags. We consider malicious credential issuers, with adaptive corruptions and collusions with malicious users. Whereas our constructions only support selective disclosures of attributes, to remain compact, our approach significantly improves the complexity in both time and memory of the showing of multiple attributes: for the first time, the cost for the prover is (almost) independent of the number of attributes and the number of credential issuers. Whereas anonymous credentials require privacy of the user, we propose the first schemes allowing traceability. We formally define an aggregatable signature scheme with (traceable) randomizable tags, which is of independent interest. We build concrete schemes from the recent linearly homomorphic signature scheme of PKC 20. As all the recent ABC schemes, our construction relies on signatures which unforgeability is proven in the bilinear generic group model.