Analysis of Boomerang Differential Trails via a SAT-Based Constraint Solver URSA

In order to obtain differential patterns over many rounds of a cryptographic primitive, the cryptanalyst often needs to work on local differential trail analysis. Examples include merging two differential trail parts into one or, in the case of boomerang and rectangle attacks, connecting two short trails within the quartet boomerang setting. In the latter case, as shown by Murphy in 2011, caution should be exercised as there is increased chance of running into contradictions in the middle rounds of the primitive. In this paper, we propose the use of a SAT-based constraint solver URSA as aid in analysis of differential trails and find that previous rectangle/boomerang attacks on XTEA and SHACAL-1 block ciphers and SM3 hash function are based on incompatible trails. Given the C specification of the cryptographic primitive, verifying differential trail portions requires minimal work on the side of the cryptanalyst

The (related-key) impossible boomerang attack and its application to the AES block cipher

The Advanced Encryption Standard (AES) is a 128-bit block cipher with a user key of 128, 192 or 256 bits, released by NIST in 2001 as the next-generation data encryption standard for use in the USA. It was adopted as an ISO international standard in 2005. Impossible differential cryptanalysis and the boomerang attack are powerful variants of differential cryptanalysis for analysing the security of a block cipher. In this paper, building on the notions of impossible differential cryptanalysis and the boomerang attack, we propose a new cryptanalytic technique, which we call the impossible boomerang attack, and then describe an extension of this attack which applies in a related-key attack scenario. Finally, we apply the impossible boomerang attack to break 6-round AES with 128 key bits and 7-round AES with 192/256 key bits, and using two related keys we apply the related-key impossible boomerang attack to break 8-round AES with 192 key bits and 9-round AES with 256 key bits. In the two-key related-key attack scenario, our results, which were the first to achieve this amount of attacked rounds, match the best currently known results for AES with 192/256 key bits in terms of the numbers of attacked rounds. The (related-key) impossible boomerang attack is a general cryptanalytic technique, and can potentially be used to cryptanalyse other block ciphers

A Bit-Vector Differential Model for the Modular Addition by a Constant and its Applications to Differential and Impossible-Differential Cryptanalysis

ARX algorithms are a class of symmetric-key algorithms constructed by Addition, Rotation, and XOR. To evaluate the resistance of an ARX cipher against differential and impossible-differential cryptanalysis, the recent automated methods employ constraint satisfaction solvers to search for optimal characteristics or impossible differentials. The main difficulty in formulating this search is finding the differential models of the non-linear operations. While an efficient bit-vector differential model was obtained for the modular addition with two variable inputs, no differential model for the modular addition by a constant has been proposed so far, preventing ARX ciphers including this operation from being evaluated with automated methods. In this paper, we present the first bit-vector differential model for the $n$-bit modular addition by a constant input. Our model contains $O(\log_2(n))$ basic bit-vector constraints and describes the binary logarithm of the differential probability. We describe an SMT-based automated method that includes our model to search for differential characteristics of ARX ciphers including constant additions. We also introduce a new automated method for obtaining impossible differentials where we do not search over a small pre-defined set of differences, such as low-weight differences, but let the SMT solver search through the space of differences. Moreover, we implement both methods in our open-source tool \texttt{ArxPy} to find characteristics and impossible differentials of ARX ciphers with constant additions in a fully automated way. As some examples, we provide related-key impossible differentials and differential characteristics of TEA, XTEA, HIGHT, LEA, SHACAL-1, and SHACAL-2, which achieve better results compared to previous works

HUC-HISF: A Hybrid Intelligent Security Framework for Human-centric Ubiquitous Computing

制度:新 ; 報告番号:乙2336号 ; 学位の種類:博士(人間科学) ; 授与年月日:2012/1/18 ; 早大学位記番号:新584

Cryptanalysis of Block Ciphers

The block cipher is one of the most important primitives in modern cryptography, information and network security; one of the primary purposes of such ciphers is to provide confidentiality for data transmitted in insecure communication environments. To ensure that confidentiality is robustly provided, it is essential to investigate the security of a block cipher against a variety of cryptanalytic attacks. In this thesis, we propose a new extension of differential cryptanalysis, which we call the impossible boomerang attack. We describe the early abort technique for (related-key) impossible differential cryptanalysis and rectangle attacks. Finally, we analyse the security of a number of block ciphers that are currently being widely used or have recently been proposed for use in emerging cryptographic applications; our main cryptanalytic results are as follows. An impossible differential attack on 7-round AES when used with 128 or 192 key bits, and an impossible differential attack on 8-round AES when used with 256 key bits. An impossible boomerang attack on 6-round AES when used with 128 key bits, and an impossible boomerang attack on 7-round AES when used with 192 or 256 key bits. A related-key impossible boomerang attack on 8-round AES when used with 192 key bits, and a related-key impossible boomerang attack on 9-round AES when used with 256 key bits, both using two keys. An impossible differential attack on 11-round reduced Camellia when used with 128 key bits, an impossible differential attack on 12-round reduced Camellia when used with 192 key bits, and an impossible differential attack on 13-round reduced Camellia when used with 256 key bits. A related-key rectangle attack on the full Cobra-F64a, and a related-key differential attack on the full Cobra-F64b. A related-key rectangle attack on 44-round SHACAL-2. A related-key rectangle attack on 36-round XTEA. An impossible differential attack on 25-round reduced HIGHT, a related-key rectangle attack on 26-round reduced HIGHT, and a related-key impossible differential attack on 28-round reduced HIGHT. In terms of either the attack complexity or the numbers of attacked rounds, the attacks presented in the thesis are better than any previously published cryptanalytic results for the block ciphers concerned, except in the case of AES; for AES, the presented impossible differential attacks on 7-round AES used with 128 key bits and 8-round AES used with 256 key bits are the best currently published results on AES in a single key attack scenario, and the presented related-key impossible boomerang attacks on 8-round AES used with 192 key bits and 9-round AES used with 256 key bits are the best currently published results on AES in a related-key attack scenario involving two keys

Cryptanalysis and Design of Symmetric Primitives

Der Schwerpunkt dieser Dissertation liegt in der Analyse und dem Design von Block- chiffren und Hashfunktionen. Die Arbeit beginnt mit einer Einführung in Techniken zur Kryptoanalyse von Blockchiffren. Wir beschreiben diese Methoden und zeigen wie man daraus neue Techniken entwickeln kann, welche zu staerkeren Angriffen fuehren. Im zweiten Teil der Arbeit stellen wir eine Reihe von Angriffen auf eine Vielzahl von Blockchiffren dar. Wir haben dabei Angriffe auf reduzierte Versionen von ARIA und dem AES entwickelt. Darueber hinaus praesentieren wir im dritten Teil Angriffe auf interne Blockchiffren von Hashfunktionen. Wir entwickeln Angriffe, welche die inter- nen Blockchiffren von Tiger und HAS-160 auf volle Rundenanzahl brechen. Die hier vorgestellten Angriffe sind die ersten dieser Art. Ein Angriff auf eine reduzierte Ver- sion von SHACAL-2 welcher fast keinen Speicherbedarf hat, wird ebenfalls vorgestellt. Der vierte Teil der Arbeit befasst sich mit den Design und der Analyse von kryp- tographischen Hashfunktionen. Wir habe einen Slide Angriff, eine Technik welche aus der Analyse von Blockchiffren bekannt ist, im Kontext von Hashfunktionen zur Anwendung gebracht. Dabei praesentieren wir verschiedene Angriffe auf GRINDAHL und RADIOGATUN. Aufbauend auf den Angriffen des zweiten und dritten Teils dieser Arbeit stellen wir eine neue Hashfunktion vor, welche wir TWISTER nennen. TWISTER wurde fuer den SHA-3 Wettbewerb entwickelt und ist bereits zur ersten Runde angenommen.This thesis focuses on the cryptanalysis and the design of block ciphers and hash func- tions. The thesis starts with an overview of methods for cryptanalysis of block ciphers which are based on differential cryptanalysis. We explain these concepts and also sev- eral combinations of these attacks. We propose new attacks on reduced versions of ARIA and AES. Furthermore, we analyze the strength of the internal block ciphers of hash functions. We propose the first attacks that break the internal block ciphers of Tiger, HAS-160, and a reduced round version of SHACAL-2. The last part of the thesis is concerned with the analysis and the design of cryptographic hash functions. We adopt a block cipher attack called slide attack into the scenario of hash function cryptanalysis. We then use this new method to attack different variants of GRINDAHL and RADIOGATUN. Finally, we propose a new hash function called TWISTER which was designed and pro- posed for the SHA-3 competition. TWISTER was accepted for round one of this com- petition. Our approach follows a new strategy to design a cryptographic hash function. We also describe several attacks on TWISTER and discuss the security issues concern- ing these attack on TWISTER

Related-Key Boomerang and Rectangle Attacks

This paper introduces the related-key boomerang and the related-key rectangle attacks. These new attacks can expand the cryptanalytic toolbox, and can be applied to many block ciphers. The main advantage of these new attacks, is the ability to exploit the related-key model twice. Hence, even ciphers which were considered resistant to either boomerang or related-key differential attacks may be broken using the new techniques. In this paper we present a rigorous treatment of the related-key boomerang and the related-key rectangle distinguishers. Following this treatment, we devise optimal distinguishing algorithms using the LLR (Logarithmic Likelihood Ratio) statistics. We then analyze the success probability under reasonable independence assumptions, and verify the computation experimentally by implementing an actual attack on a 6-round variant of KASUMI. The paper ends with a demonstration of the strength of our new proposed techniques with attacks on 10-round AES-192 and the full KASUMI

Higher-Order Differential Attack on Reduced SHA-256

In this work, we study the application of higher-order differential attacks on hash functions. We show a second-order differential attack on the SHA-256 compression function reduced to 46 out of 64 steps. We implemented the attack and give the result in Table 1. The best attack so far (in a different attack model) with practical complexity was for 33 steps of the compression function