Automatic Generation of Declarative Models For Differential Cryptanalysis

When designing a new symmetric block cipher, it is necessary to evaluate its robustness against differential attacks. This is done by computing Truncated Differential Characteristics (TDCs) that provide bounds on the complexity of these attacks. TDCs are often computed by using declarative approaches such as CP (Constraint Programming), SAT, or ILP (Integer Linear Programming). However, designing accurate and efficient models for these solvers is a difficult, error-prone and time-consuming task, and it requires advanced skills on both symmetric cryptography and solvers. In this paper, we describe a tool for automatically generating these models, called Tagada (Tool for Automatic Generation of Abstraction-based Differential Attacks). The input of Tagada is an operational description of the cipher by means of black-box operators and bipartite Directed Acyclic Graphs (DAGs). Given this description, we show how to automatically generate constraints that model operator semantics, and how to generate MiniZinc models. We experimentally evaluate our approach on two different kinds of differential attacks (e.g., single-key and related-key) and four different symmetric block ciphers (e.g., the AES (Advanced Encryption Standard), Craft, Midori, and Skinny). We show that our automatically generated models are competitive with state-of-the-art approaches. These automatically generated models constitute a new benchmark composed of eight optimization problems and eight enumeration problems, with instances of increasing size in each problem. We experimentally compare CP, SAT, and ILP solvers on this new benchmark

Constraint Based Compiler Optimization for Energy Harvesting Applications

We propose a method for optimizing the energy efficiency of software code running on small computing devices in the Internet of Things (IoT) that are powered exclusively by electricity harvested from ambient energy in the environment. Due to the weak and unstable nature of the energy source, it is challenging for developers to manually optimize the software code to deal with mismatch between the intermittent power supply and the computation demand. Our method overcomes the challenge by using a combination of three techniques. First, we use static program analysis to automatically identify opportunities for precomputation, i.e., computation that may be performed ahead of time as opposed to just in time. Second, we optimize the precomputation policy, i.e., a way to split and reorder steps of a computation task in the original software to match the intermittent power supply while satisfying a variety of system requirements; this is accomplished by formulating energy optimization as a constraint satisfiability problem and then solving the problem using an off-the-shelf SMT solver. Third, we use a state-of-the-art compiler platform (LLVM) to automate the program transformation to ensure that the optimized software code is correct by construction. We have evaluated our method on a large number of benchmark programs, which are C programs implementing secure communication protocols that are popular for energy-harvesting IoT devices. Our experimental results show that the method is efficient in optimizing all benchmark programs. Furthermore, the optimized programs significantly outperform the original programs in terms of energy efficiency and latency, and the overall improvement ranges from 2.3X to 36.7X

abstractXOR: A global constraint dedicated to differential cryptanalysis

International audienceConstraint Programming models have been recently proposed to solve cryptanalysis problems for symmetric block ciphers such as AES. These models are more efficient than dedicated approaches but their design is difficult: straightforward models do not scale well and it is necessary to add advanced constraints derived from cryptographic properties. We introduce a global constraint which simplifies the modelling step and improves efficiency. We study its complexity, introduce propagators and experimentally evaluate them on two cryptanalysis problems (single-key and related-key) for two block ciphers (AES and Midori)

Related-Key Differential Analysis of the AES

The Advanced Encryption Standard (AES) is considered to be the most important and widely deployed symmetric primitive. While the cipher was designed to be immune against differential and other classical attacks, this immunity does not hold in the related-key setting, and various related-key attacks have appeared over time. This work presents tools and algorithms to search for related-key distinguishers and attacks of differential nature against the AES. First, we propose two entirely different approaches to find optimal truncated differential characteristics and bounds on the minimum number of active S-boxes for all variants of the AES. In the first approach, we propose a simple MILP model that handles better linear inconsistencies with respect to the AES system of equations and that compares particularly well to previous tool-based approaches to solve this problem. The main advantage of this tool is that it can easily be used as the core algorithm to search for any attack on AES exploiting related-key differentials. Then, we design a fast and low-memory algorithm based on dynamic programming that has a very simple to understand complexity analysis and does not depend on any generic solver. This second algorithm provides us useful insight on the related-key differential search problem for AES and shows that the search space is not as big as one would expect. Finally, we build on the top of our MILP model a fully automated tool to search for the best differential MITM attacks against the AES. We apply our tool on AES-256 and find an attack on 13 rounds with only two related keys. This attack can be seen as the best known cryptanalysis against this variant if only 2 related keys are permitted

Alternative Key Schedules for the AES

The AES block cipher is today the most important and analyzed symmetric algorithm. While all versions of the AES are known to be secure in the single-key setting, this is not the case in the related-key scenario. In this article we try to answer the question whether the AES would resist better differential-like related-key attacks if the key schedule was different. For this, we search for alternative permutation-based key schedules by extending the work of Khoo et al. at ToSC 2017 and Derbez et al. at SAC 2018. We first show that the model of Derbez et al. was flawed. Then, we develop different approaches together with MILP-based tools to find good permutations that could be used as the key schedule for AES-128, AES-192 and AES-256. Our methods permitted to find permutations that outperform the permutation exhibited by Khoo et al. for AES-128. Moreover, our new approach based on two MILP models that call one another allowed us to handle a larger search space and thus to search for alternative key schedules for the two bigger versions of AES. This method permitted us to find permutations for AES-192 and AES-256 that provide better resistance to related-key differential attacks. Most importantly, we showed that these variants can resist full-round boomerang attacks

NASA/ASEE Summer Faculty Fellowship Program, 1990, Volume 1

The 1990 Johnson Space Center (JSC) NASA/American Society for Engineering Education (ASEE) Summer Faculty Fellowship Program was conducted by the University of Houston-University Park and JSC. A compilation of the final reports on the research projects are presented. The topics covered include: the Space Station; the Space Shuttle; exobiology; cell biology; culture techniques; control systems design; laser induced fluorescence; spacecraft reliability analysis; reduced gravity; biotechnology; microgravity applications; regenerative life support systems; imaging techniques; cardiovascular system; physiological effects; extravehicular mobility units; mathematical models; bioreactors; computerized simulation; microgravity simulation; and dynamic structural analysis

Power analysis on smartcard algorithms using simulation

This paper presents the results from a power analysis of the AES and RSA algorithms by\ud simulation using the PINPAS tool. The PINPAS tool is capable of simulating the power\ud consumption of assembler programs implemented in, amongst others, Hitachi H8/300\ud assembler. The Hitachi H8/300 is a popular CPU for smartcards. Using the PINPAS tool, the\ud vulnerability for power analysis attacks of straightforward AES and RSA implementations is\ud examined. In case a vulnerability is found countermeasures are added to the implementation\ud that attempt to counter power analysis attacks. After these modifications the analysis is\ud performed again and the new results are compared to the original results

Finding Bit-Based Division Property for Ciphers with Complex Linear Layers

The bit-based division property (BDP) is the most effective technique for finding integral characteristics of symmetric ciphers. Recently, automatic search tools have become one of the most popular approaches to evaluating the security of designs against many attacks. Constraint-aided automatic tools for the BDP have been applied to many ciphers with simple linear layers like bit-permutation. Constructing models of complex linear layers accurately and efficiently remains hard. A straightforward method proposed by Sun et al. (called the S method), decomposes a complex linear layer into basic operations like COPY and XOR, then models them one by one. However, this method can easily insert invalid division trails into the solution pool, which results in a quicker loss of the balanced property than the cipher itself would. In order to solve this problem, Zhang and Rijmen propose the ZR method to link every valid trail with an invertible sub-matrix of the matrix corresponding to the linear layer, and then generate linear inequalities to represent all the invertible sub-matrices. Unfortunately, the ZR method is only applicable to invertible binary matrices (defined in Definition 3).To avoid generating a huge number of inequalities for all the sub-matrices, we build a new model that only includes that the sub-matrix corresponding to a valid trail should be invertible. The computing scale of our model can be tackled by most of SMT/SAT solvers, which makes our method practical. For applications, we improve the previous BDP for LED and MISTY1. We also give the 7-round BDP results for Camellia with FL/FL−1, which is the longest to date.Furthermore, we remove the restriction of the ZR method that the matrix has to be invertible, which provides more choices for future designs. Thanks to this, we also reproduce 5-round key-dependent integral distinguishers proposed at Crypto 2016 which cannot be obtained by either the S or ZR methods