Cryptanalysis of Symmetric Cryptographic Primitives

Symmetric key cryptographic primitives are the essential building blocks in modern information security systems. The overall security of such systems is crucially dependent on these mathematical functions, which makes the analysis of symmetric key primitives a goal of critical importance. The security argument for the majority of such primitives in use is only a heuristic one and therefore their respective security evaluation continually remains an open question. In this thesis, we provide cryptanalytic results for several relevant cryptographic hash functions and stream ciphers. First, we provide results concerning two hash functions: HAS-160 and SM3. In particular, we develop a new heuristic for finding compatible differential paths and apply it to the the Korean hash function standard HAS-160. Our heuristic leads to a practical second order collision attack over all of the HAS-160 function steps, which is the first practical-complexity distinguisher on this function. An example of a colliding quartet is provided. In case of SM3, which is a design that builds upon the SHA-2 hash and is published by the Chinese Commercial Cryptography Administration Office for the use in the electronic authentication service system, we study second order collision attacks over reduced-round versions and point out a structural slide-rotational property that exists in the function. Next, we examine the security of the following three stream ciphers: Loiss, SNOW 3G and SNOW 2.0. Loiss stream cipher is designed by Dengguo Feng et al. aiming to be implemented in byte-oriented processors. By exploiting some differential properties of a particular component utilized in the cipher, we provide an attack of a practical complexity on Loiss in the related-key model. As confirmed by our experimental results, our attack recovers 92 bits of the 128-bit key in less than one hour on a PC with 3 GHz Intel Pentium 4 processor. SNOW 3G stream cipher is used in 3rd Generation Partnership Project (3GPP) and the SNOW 2.0 cipher is an ISO/IEC standard (IS 18033-4). For both of these two ciphers, we show that the initialization procedure admits a sliding property, resulting in several sets of related-key pairs. In addition to allowing related-key key recovery attacks against SNOW 2.0 with 256-bit keys, the presented properties reveal non-random behavior of the primitives, yield related-key distinguishers for the two ciphers and question the validity of the security proofs of protocols based on the assumption that these ciphers behave like perfect random functions of the key-IV. Finally, we provide differential fault analysis attacks against two stream ciphers, namely, HC-128 and Rabbit. In this type of attacks, the attacker is assumed to have physical influence over the device that performs the encryption and is able to introduce random faults into the computational process. In case of HC-128, the fault model in which we analyze the cipher is the one in which the attacker is able to fault a random word of the inner state of the cipher but cannot control its exact location nor its new faulted value. Our attack requires about 7968 faults and recovers the complete internal state of HC-128 by solving a set of 32 systems of linear equations over Z2 in 1024 variables. In case of Rabbit stream cipher, the fault model in which the cipher is analyzed is the one in which a random bit of the internal state of the cipher is faulted, however, without control over the location of the injected fault. Our attack requires around 128 − 256 faults, precomputed table of size 2^41.6 bytes and recovers the complete internal state of Rabbit in about 2^38 steps

Cryptanalysis of symmetric key primitives

Block ciphers and stream ciphers are essential building blocks that are used to construct computing systems which have to satisfy several security objectives. Since the security of these systems depends on the security of its parts, the analysis of these symmetric key primitives has been a goal of critical importance. In this thesis we provide cryptanalytic results for some recently proposed block and stream ciphers. First, we consider two light-weight block ciphers, TREYFER and PIFEA-M. While TREYFER was designed to be very compact in order to fit into constrained environments such as smart cards and RFIDs, PIFEA-M was designed to be very fast in order to be used for the encryption of multimedia data. We provide a related-key attack on TREYFER which recovers the secret key given around 2 11 encryptions and negligible computational effort. As for PIFEA-M, we provide evidence that it does not fulfill its design goal, which was to defend from certain implementation dependant differential attacks possible on previous versions of the cipher. Next. we consider the NGG stream cipher, whose design is based on RC4 and aims to increase throughput by operating with 32-bit or 64-bit values instead of with 8-bit values. We provide a distinguishing attack on NGG which requires just one keystream word. We also show that the first few kilobytes of the keystream may leak information about the secret key which allows the cryptanalyst to recover the secret key in an efficient way. Finally, we consider GGHN, another RC4-like cipher that operates with 32-bit words. We assess different variants of GGHN-Iike algorithms with respect to weak states, in which all internal state words and output elements are even. Once GGHN is absorbed in such a weak state, the least significant bit of the plaintext words will be revealed only by looking at the ciphertext. By modelling the algorithm by a Markov chain and calculating the chain absorption time, we show that the average number of steps required by these algorithms to enter this weak state can be lower than expected at first glance and hence caution should be exercised when estimating this numbe

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

Boomerang and Slide-Rotational Analysis of the SM3 Hash Function

SM3 is a hash function designed by Xiaoyun Wang et al., and published by the Chinese Commercial Cryptography Administration Office for the use of electronic authentication service system. The design of SM3 builds upon the design of the SHA-2 hash function, but introduces additional strengthening features. In this paper, using a higher order differential cryptanalysis approach, we present a practical 4-sum distinguisher against the compression function of SM3 reduced to 32 rounds. In addition, we point out a slide-rotational property of SM3-XOR, which exists due to the fact that constants used in the rounds are not independent

Rebound attacks on stribog

Abstract. In August 2012, the Stribog hash function was selected as the new Russian hash standard (GOST R 34.11-2012). Stribog is an AES-based primitive and is considered as an asymmetric reply to the new SHA-3. In this paper we investigate the collision resistance of the Stribog compression function and its internal cipher. Specifically, we present a message differential path for the internal block cipher that allows us to efficiently obtain a 5-round free-start collision and a 7.75 free-start near collision for the internal cipher with complexities 2 8 and 2 40 , respectively. Finally, the compression function is analyzed and a 7.75 round semi freestart collision, 8.75 and 9.75 round semi free-start near collisions are presented along with an example for 4.75 round 50 out of 64 bytes near colliding message pair

Cryptanalysis of the Loiss Stream Cipher

Loiss is a byte-oriented stream cipher designed by Dengguo Feng et al. Its design builds upon the design of the SNOW family of ciphers. The algorithm consists of a linear feedback shift register (LFSR) and a non-linear finite state machine (FSM). Loiss utilizes a structure called Byte-Oriented Mixer with Memory (BOMM) in its filter generator, which aims to improve resistance against algebraic attacks, linear distinguishing attacks and fast correlation attacks. In this paper, by exploiting some differential properties of the BOMM structure during the cipher initialization phase, we provide an attack of a practical complexity on Loiss in the related-key model. As confirmed by our experimental results, our attack recovers 92 bits of the 128-bit key in less than one hour on a PC with 3 GHz Intel Pentium 4 processor. The possibility of extending the attack to a resynchronization attack in a single-key model is discussed. We also show that Loiss is not resistant to slide attacks

boomerang and slide-rotational analysis of the sm3 hash function

SM3 is a hash function, designed by Xiaoyun Wang et al. and published by the Chinese Commercial Cryptography Administration Office for the use of electronic authentication service system. The design of SM3 builds upon the design of the SHA-2 hash function, but introduces additional strengthening features. In this paper, we present boomerang distinguishers for the SM3 compression function reduced to 32 steps out of 64 steps with complexity 2 14.4, 33 steps with complexity 232.4, 34 steps with complexity 253.1 and 35 steps with complexity 2117.1. Examples of zero-sum quartets for the 32-step and 33-step SM3 compression function are provided. We also point out a slide-rotational property of SM3-XOR, which exists due to the fact that constants used in the steps are not independent. © 2013 Springer-Verlag Berlin Heidelberg.Department of Electrical and Computer Engineering; Faculty of Engineering; Office of Vice President - Research, University of WindsorSM3 is a hash function, designed by Xiaoyun Wang et al. and published by the Chinese Commercial Cryptography Administration Office for the use of electronic authentication service system. The design of SM3 builds upon the design of the SHA-2 hash function, but introduces additional strengthening features. In this paper, we present boomerang distinguishers for the SM3 compression function reduced to 32 steps out of 64 steps with complexity 2 14.4, 33 steps with complexity 232.4, 34 steps with complexity 253.1 and 35 steps with complexity 2117.1. Examples of zero-sum quartets for the 32-step and 33-step SM3 compression function are provided. We also point out a slide-rotational property of SM3-XOR, which exists due to the fact that constants used in the steps are not independent. © 2013 Springer-Verlag Berlin Heidelberg