CLAASP: a Cryptographic Library for the Automated Analysis of Symmetric Primitives

This paper introduces CLAASP, a Cryptographic Library for the Automated Analysis of Symmetric Primitives. The library is designed to be modular, extendable, easy to use, generic, efficient and fully automated. It is an extensive toolbox gathering state-of-the-art techniques aimed at simplifying the manual tasks of symmetric primitive designers and analysts. CLAASP is built on top of Sagemath and is open-source under the GPLv3 license. The central input of CLAASP is the description of a cryptographic primitive as a list of connected components in the form of a directed acyclic graph. From this representation, the library can automatically: (1) generate the Python or C code of the primitive evaluation function, (2) execute a wide range of statistical and avalanche tests on the primitive, (3) generate SAT, SMT, CP and MILP models to search, for example, differential and linear trails, (4) measure algebraic properties of the primitive, (5) test neural-based distinguishers. In this work, we also present a comprehensive survey and comparison of other software libraries aiming at similar goals as CLAASP

A Practical-Quantum Differential Attack on Block Ciphers

Differential attack is a basic cryptanalysis method for block ciphers that exploits the high probability relations between the input and output differences. The existing work in quantum differential cryptanalysis of block ciphers focuses on resource estimation to recover the last round subkeys on the basis of existing relations constructed on classical computers. To find such relations using quantum computer, we propose a method to search the high probability differential and impossible differential characteristics using quantum computer. The method explores all possible input and output difference pairs simultaneously using superposition of qubits. The proposed method is used to design the quantum circuit to search the differential characteristics for a toy cipher smallGIFT. The branch-and-bound based method is used to validate differential and impossible differential characteristics obtained using proposed method

SAND: an AND-RX Feistel lightweight block cipher supporting S-box-based security evaluations

We revisit designing AND-RX block ciphers, that is, the designs assembled with the most fundamental binary operations---AND, Rotation and XOR operations and do not rely on existing units. Likely, the most popular representative is the NSA cipher \texttt{SIMON}, which remains one of the most efficient designs, but suffers from difficulty in security evaluation. As our main contribution, we propose \texttt{SAND}, a new family of lightweight AND-RX block ciphers. To overcome the difficulty regarding security evaluation, \texttt{SAND} follows a novel design approach, the core idea of which is to restrain the AND-RX operations to be within nibbles. By this, \texttt{SAND} admits an equivalent representation based on a $4\times8$ \textit{synthetic S-box} ($SSb$). This enables the use of classical S-box-based security evaluation approaches. Consequently, for all versions of \texttt{SAND}, (a) we evaluated security bounds with respect to differential and linear attacks, and in both single-key and related-key scenarios; (b) we also evaluated security against impossible differential and zero-correlation linear attacks. This better understanding of the security enables the use of a relatively simple key schedule, which makes the ASIC round-based hardware implementation of \texttt{SAND} to be one of the state-of-art Feistel lightweight ciphers. As to software performance, due to the natural bitslice structure, \texttt{SAND} reaches the same level of performance as \texttt{SIMON} and is among the most software-efficient block ciphers

Searching for Subspace Trails and Truncated Differentials

Grassi et al. [Gra+16] introduced subspace trail cryptanalysis as a generalization of invariant subspaces and used it to give the first five round distinguisher for Aes. While it is a generic method, up to now it was only applied to the Aes and Prince. One problem for a broad adoption of the attack is a missing generic analysis algorithm. In this work we provide efficient and generic algorithms that allow to compute the provably best subspace trails for any substitution permutation cipher

Modeling Large S-box in MILP and a (Related-key) Differential Attack on Full Round PIPO-64/128

Mixed integer linear programming (MILP) based tools are used to estimate the strength of block ciphers against the cryptanalytic attacks. The existing tools use partial difference distribution table (p-DDT) approach to optimize the probability of differential characteristics for large (≥8-bit) S-box based ciphers. We propose to use the full difference distribution table (DDT) with the probability of each possible propagation for MILP modeling of large S-boxes. This requires more than 16 variables to represent the linear inequalities of each propagation and corresponding probabilities. The existing tools (viz. Logic Friday) cannot handle the linear inequalities in more than 16 variables. In this paper, we present a new tool (namely MILES) to minimize the linear inequalities in more than 16 variables. This tool reduces the number of inequalities by minimizing the truth table corresponding to the DDT of S-box. We use our tool to minimize the linear inequalities for 8-bit S-boxes (AES and SKINNY) and get better results than existing tools. We show the application of MILES on 8-bit S-box based lightweight block cipher PIPO. There are 20621 inequalities in 23 variables corresponding to the possible propagations in DDT and these are minimized to 6035 inequalities using MILES. MILP model based on these linear inequalities is used to optimizethe probability of differential characteristics for round-reduced PIPO. MILP model based on these inequalities is used to optimize the probability of differential and impossible differential characteristics for PIPO-64/128 reduced to 9 and 4 rounds respectively. We present an iterative 2-round related-key differential characteristic with the probability of 2^{-4} and that is used to construct a full round related-key differential distinguisher with the probability of 2^{-24}. We present a major collision in PIPO-64/128 which produces the same ciphertext (C) by encrypting the plaintext (P) under two different keys

GIFT: A Small Present Towards Reaching the Limit of Lightweight Encryption

In this article, we revisit the design strategy of PRESENT, leveraging all the advances provided by the research community in construction and cryptanalysis since its publication, to push the design up to its limits. We obtain an improved version, named GIFT, that provides a much increased efficiency in all domains (smaller and faster), while correcting the well-known weakness of PRESENT with regards to linear hulls. GIFT is a very simple and clean design that outperforms even SIMON or SKINNY for round-based implementations, making it one of the most energy efficient ciphers as of today. It reaches a point where almost the entire implementation area is taken by the storage and the Sboxes, where any cheaper choice of Sbox would lead to a very weak proposal. In essence, GIFT is composed of only Sbox and bit-wiring, but its natural bitslice data flow ensures excellent performances in all scenarios, from area-optimised hardware implementations to very fast software implementation on high-end platforms. We conducted a thorough analysis of our design with regards to state-of-the-art cryptanalysis, and we provide trong bounds with regards to differential/linear attacks

MILP Modeling for (Large) S-boxes to Optimize Probability of Differential Characteristics

Current Mixed Integer Linear Programming (MILP)-based search against symmetric-key primitives with 8-bit S-boxes can only build word-wise model to search for truncated differential characteristics. In such a model, the properties of the Differential Distribution Table (DDT) are not considered. To take these properties into account, a bit-wise model is necessary, which can be generated by the H-representation of the convex hull or the logical condition modeling. However, the complexity of both approaches becomes impractical when the size of the S-box exceeds 5 bits. In this paper, we propose a new modeling for large (8-bit or more) S-boxes. In particular, we first propose an algorithm to generate a bit-wise model of the DDT for large S-boxes. We observe that the problem of generating constraints in logical condition modeling can be converted into the problem of minimizing the product-of-sum of Boolean functions, which is a well-studied problem. Hence, classical off-the-shelf solutions such as the Quine-McCluskey algorithm or the Espresso algorithm can be utilized, which makes building a bit-wise model, for 8-bit or larger S-boxes, practical. Then this model is further extended to search for the best differential characteristic by considering the probabilities of each propagation in the DDT, which is a much harder problem than searching for the lower bound on the number of active S-boxes. Our idea is to separate the DDT into multiple tables for each probability and add conditional constraints to control the behavior of these multiple tables. The proposed modeling is first applied to SKINNY-128 to find that there is no differential characteristic having probability higher than 2−128 for 14 rounds, while the designers originally expected that 15 rounds were required. We also applied the proposed modeling to two, arbitrarily selected, constructions of the seven AES round function based constructions proposed in FSE 2016 and managed to improve the lower bound on the number of the active S-boxes in one construction and the upper bound on the differential characteristic for the other

DEFAULT : cipher level resistance against differential fault attack

Differential Fault Analysis (DFA) is a well known cryptanalytic tech- nique that exploits faulty outputs of an encryption device. Despite its popularity and similarity with the classical Differential Analysis (DA), a thorough analysis explaining DFA from a designer’s point-of-view is missing in the literature. To the best of our knowledge, no DFA immune block cipher at an algorithmic level has been proposed so far. Furthermore, all known DFA countermeasures somehow depend on the device/protocol or on the implementation such as duplication/comparison. As all of these are outside the scope of the cipher designer, we focus on designing a primitive which can protect from DFA on its own. We present the first concept of cipher level DFA resistance which does not rely on any device/protocol related assumption, nor does it depend on any form of duplication. Our construction is simple, software/hardware friendly and DFA security scales up with the state size. It can be plugged before and/or after (almost) any symmetric key cipher and will ensure a non-trivial search complexity against DFA. One key component in our DFA protection layer is an SBox with linear structures. Such SBoxes have never been used in cipher design as they generally perform poorly against differential attacks. We argue that they in fact represent an interesting trade-off between good cryptographic properties and DFA resistance. As a proof of concept, we construct a DFA protecting layer, named DEFAULT-LAYER, as well as a full-fledged block cipher DEFAULT. Our solutions compare favorably to the state-of-the-art, offering advantages over the sophisticated duplication based solutions like impeccable circuits/CRAFT or infective countermeasures