Meet-in-the-Middle Attacks on Classes of Contracting and Expanding Feistel Constructions

We show generic attacks on unbalanced Feistel ciphers based on the meet-in-the-middle technique. We analyze two general classes of unbalanced Feistel structures, namely contracting Feistels and expanding Feistels. In both of the cases, we consider the practical scenario where the round functions are keyless and known to the adversary. In the case of contracting Feistels with 4 branches, we show attacks on 16 rounds when the key length k (in bits) is as large as the block length n (in bits), and up to 24 rounds when k = 2n. In the case of expanding Feistels, we consider two scenarios: one, where different nonlinear functions without particular structures are used in the round function, and a more practical one, where a single nonlinear is used but different linear functions are introduced in the state update. In the former case, we propose generic attacks on 13 rounds when k = n, and up to 21 rounds when k = 2n. In the latter case, 16 rounds can be attacked for k = n, and 24 rounds for k = 2n

SoK: Security Evaluation of SBox-Based Block Ciphers

Cryptanalysis of block ciphers is an active and important research area with an extensive volume of literature. For this work, we focus on SBox-based ciphers, as they are widely used and cover a large class of block ciphers. While there have been prior works that have consolidated attacks on block ciphers, they usually focus on describing and listing the attacks. Moreover, the methods for evaluating a cipher\u27s security are often ad hoc, differing from cipher to cipher, as attacks and evaluation techniques are developed along the way. As such, we aim to organise the attack literature, as well as the work on security evaluation. In this work, we present a systematization of cryptanalysis of SBox-based block ciphers focusing on three main areas: (1) Evaluation of block ciphers against standard cryptanalytic attacks; (2) Organisation and relationships between various attacks; (3) Comparison of the evaluation and attacks on existing ciphers

Horst Meets Fluid-SPN: Griffin for Zero-Knowledge Applications

Zero-knowledge (ZK) applications form a large group of use cases in modern cryptography, and recently gained in popularity due to novel proof systems. For many of these applications, cryptographic hash functions are used as the main building blocks, and they often dominate the overall performance and cost of these approaches. Therefore, in the last years several new hash functions were built in order to reduce the cost in these scenarios, including Poseidon and Rescue among others. These hash functions often look very different from more classical designs such as AES or SHA-2. For example, they work natively over prime fields rather than binary ones. At the same time, for example Poseidon and Rescue share some common features, such as being SPN schemes and instantiating the nonlinear layer with invertible power maps. While this allows the designers to provide simple and strong arguments for establishing their security, it also introduces crucial limitations in the design, which may affect the performance in the target applications. In this paper, we propose the Horst construction, in which the addition in a Feistel scheme (x, y) -> (y + F(x), x) is extended via a multiplication, i.e., (x, y) -> (y * G(x) + F(x), x). By carefully analyzing the performance metrics in SNARK and STARK protocols, we show how to combine an expanding Horst scheme with a Rescue-like SPN scheme in order to provide security and better efficiency in the target applications. We provide an extensive security analysis for our new design Griffin and a comparison with all current competitors

Programming the Demirci-Selçuk Meet-in-the-Middle Attack with Constraints

International audienceCryptanalysis with SAT/SMT, MILP and CP has increased in popularity among symmetric-key cryptanalysts and designers due to its high degree of automation. So far, this approach covers differential, linear, impossible differential, zero-correlation, and integral cryptanaly-sis. However, the Demirci-Selçuk meet-in-the-middle (DS-MITM) attack is one of the most sophisticated techniques that has not been automated with this approach. By an in-depth study of Derbez and Fouque's work on DS-MITM analysis with dedicated search algorithms, we identify the crux of the problem and present a method for automatic DS-MITM attack based on general constraint programming, which allows the crypt-analysts to state the problem at a high level without having to say how it should be solved. Our method is not only able to enumerate distin-guishers but can also partly automate the key-recovery process. This approach makes the DS-MITM cryptanalysis more straightforward and easier to follow, since the resolution of the problem is delegated to off-the-shelf constraint solvers and therefore decoupled from its formulation. We apply the method to SKINNY, TWINE, and LBlock, and we get the currently known best DS-MITM attacks on these ciphers. Moreover, to demonstrate the usefulness of our tool for the block cipher designers, we exhaustively evaluate the security of 8! = 40320 versions of LBlock instantiated with different words permutations in the F functions. It turns out that the permutation used in the original LBlock is one of the 64 permutations showing the strongest resistance against the DS-MITM attack. The whole process is accomplished on a PC in less than 2 hours. The same process is applied to TWINE, and similar results are obtained

A Salad of Block Ciphers

This book is a survey on the state of the art in block cipher design and analysis. It is work in progress, and it has been for the good part of the last three years -- sadly, for various reasons no significant change has been made during the last twelve months. However, it is also in a self-contained, useable, and relatively polished state, and for this reason I have decided to release this \textit{snapshot} onto the public as a service to the cryptographic community, both in order to obtain feedback, and also as a means to give something back to the community from which I have learned much. At some point I will produce a final version -- whatever being a ``final version\u27\u27 means in the constantly evolving field of block cipher design -- and I will publish it. In the meantime I hope the material contained here will be useful to other people

Cryptanalysis, Reverse-Engineering and Design of Symmetric Cryptographic Algorithms

In this thesis, I present the research I did with my co-authors on several aspects of symmetric cryptography from May 2013 to December 2016, that is, when I was a PhD student at the university of Luxembourg under the supervision of Alex Biryukov. My research has spanned three different areas of symmetric cryptography. In Part I of this thesis, I present my work on lightweight cryptography. This field of study investigates the cryptographic algorithms that are suitable for very constrained devices with little computing power such as RFID tags and small embedded processors such as those used in sensor networks. Many such algorithms have been proposed recently, as evidenced by the survey I co-authored on this topic. I present this survey along with attacks against three of those algorithms, namely GLUON, PRINCE and TWINE. I also introduce a new lightweight block cipher called SPARX which was designed using a new method to justify its security: the Long Trail Strategy. Part II is devoted to S-Box reverse-engineering, a field of study investigating the methods recovering the hidden structure or the design criteria used to build an S-Box. I co-invented several such methods: a statistical analysis of the differential and linear properties which was applied successfully to the S-Box of the NSA block cipher Skipjack, a structural attack against Feistel networks called the yoyo game and the TU-decomposition. This last technique allowed us to decompose the S-Box of the last Russian standard block cipher and hash function as well as the only known solution to the APN problem, a long-standing open question in mathematics. Finally, Part III presents a unifying view of several fields of symmetric cryptography by interpreting them as purposefully hard. Indeed, several cryptographic algorithms are designed so as to maximize the code size, RAM consumption or time taken by their implementations. By providing a unique framework describing all such design goals, we could design modes of operations for building any symmetric primitive with any form of hardness by combining secure cryptographic building blocks with simple functions with the desired form of hardness called plugs. Alex Biryukov and I also showed that it is possible to build plugs with an asymmetric hardness whereby the knowledge of a secret key allows the privileged user to bypass the hardness of the primitive

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

The IPBES regional assessment report on biodiversity and ecosystem services for Europe and Central Asia

The Regional Assessment Report on Biodiversity and Ecosystem Services for Europe and Central Asia produced by the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES) provides a critical analysis of the state of knowledge regarding the importance, status, and trends of biodiversity and nature’s contributions to people. The assessment analyses the direct and underlying causes for the observed changes in biodiversity and in nature’s contributions to people, and the impact that these changes have on the quality of life of people. The assessment, finally, identifies a mix of governance options, policies and management practices that are currently available to reduce the loss of biodiversity and of nature’s contributions to people in that region. The assessment addresses terrestrial, freshwater, and coastal biodiversity and covers current status and trends, going back in time several decades, and future projections, with a focus on the 2020-2050 period