Improved Linear (hull) Cryptanalysis of Round-reduced Versions of KATAN

KATAN is a family of block ciphers published at CHES 2009. Based on the Mixed-integer linear programming (MILP) technique, we propose the first third-party linear cryptanalysis on KATAN. Furthermore, we evaluate the security of KATAN against the linear attack without ignoring the dependence of the input bits of the $2\times 1$ S-box(the AND operation). Note that in previous analysis, the dependence is not considered, and therefore the previous results are not accurate. Furthermore, the mounted 131/120-round attack on KATAN32/48 respectively by our 84/90-round linear hull is the best single-key known-plaintext attack. In addition, a best 94-round linear hull attack is mounted on KATAN64 by our 76-round linear hull

The Security of SIMON-like Ciphers Against Linear Cryptanalysis

In the present paper, we analyze the security of SIMON-like ciphers against linear cryptanalysis. First, an upper bound is derived on the squared correlation of SIMON-like round function. It is shown that the upper bound on the squared correlation of SIMON-like round function decreases with the Hamming weight of output mask increasing. Based on this, we derive an upper bound on the squared correlation of linear trails for SIMON and SIMECK, which is $2^{-2R+2}$ for any $R$-round linear trail. We also extend this upper bound to SIMON-like ciphers. Meanwhile, an automatic search algorithm is proposed, which can find the optimal linear trails in SIMON-like ciphers under the Markov assumption. With the proposed algorithm, we find the provably optimal linear trails for $12$, $16$, $19$, $28$ and $37$ rounds of SIMON$32/48/64/96/128$. To the best of our knowledge, it is the first time that the provably optimal linear trails for SIMON$64$, SIMON$96$ and SIMON$128$ are reported. The provably optimal linear trails for $13$, $19$ and $25$ rounds of SIMECK$32/48/64$ are also found respectively. Besides the optimal linear trails, we also find the $23$, $31$ and $41$-round linear hulls for SIMON$64/96/128$, and $13$, $21$ and $27$-round linear hulls for SIMECK$32/48/64$. As far as we know, these are the best linear hull distinguishers for SIMON and SIMECK so far. Compared with the approach based on SAT/SMT solvers in \cite{KolblLT15}, our search algorithm is more efficient and practical to evaluate the security against linear cryptanalysis in the design of SIMON-like ciphers

On Boomerang Attacks on Quadratic Feistel Ciphers

The recent introduction of the Boomerang Connectivity Table (BCT) at Eurocrypt 2018 revived interest in boomerang cryptanalysis and in the need to correctly build boomerang distinguishers. Several important advances have been made on this matter, with in particular the study of the extension of the BCT theory to multiple rounds and to different types of ciphers. In this paper, we pursue these investigations by studying the specific case of quadratic Feistel ciphers, motivated by the need to look at two particularly lightweight ciphers, KATAN and Simon. Our analysis shows that their light round function leads to an extreme case, as a one-round boomerang can only have a probability of 0 or 1. We identify six papers presenting boomerang analyses of KATAN or Simon and all use the naive approach to compute the distinguisher’s probability. We are able to prove that several results are theoretically incorrect and we run experiments to check the probability of the others. Many do not have the claimed probability: it fails distinguishing in some cases, but we also identify instances where the experimental probability turns out to be better than the claimed one. To address this shortfall, we propose an SMT model taking into account the boomerang constraints. We present several experimentally-verified related-key distinguishers obtained with our new technique: on KATAN32 a 151-round boomerang and on Simon-32/64 a 17-round boomerang, a 19-round rotational-xor boomerang and a 15-round rotational-xor-differential boomerang. Furthermore, we extend our 19-round distinguisher into a 25-round rotational-xor rectangle attack on Simon-32/64. To the best of our knowledge this attack reaches one more round than previously published results

On Some Symmetric Lightweight Cryptographic Designs

This dissertation presents cryptanalysis of several symmetric lightweight primitives, both stream ciphers and block ciphers. Further, some aspects of authentication in combination with a keystream generator is investigated, and a new member of the Grain family of stream ciphers, Grain-128a, with built-in support for authentication is presented. The first contribution is an investigation of how authentication can be provided at a low additional cost, assuming a synchronous stream cipher is already implemented and used for encryption. These findings are then used when presenting the latest addition to the Grain family of stream ciphers, Grain-128a. It uses a 128-bit key and a 96-bit initialization vector to generate keystream, and to possibly also authenticate the plaintext. Next, the stream cipher BEAN, superficially similar to Grain, but notably using a weak output function and two feedback with carry shift registers (FCSRs) rather than linear and (non-FCSR) nonlinear feedback shift registers, is cryptanalyzed. An efficient distinguisher and a state-recovery attack is given. It is shown how knowledge of the state can be used to recover the key in a straightforward way. The remainder of this dissertation then focuses on block ciphers. First, a related-key attack on KTANTAN is presented. The attack notably uses only a few related keys, runs in less than half a minute on a current computer, and directly contradicts the designers' claims. It is discussed why this is, and what can be learned from this. Next, PRINTcipher is subjected to linear cryptanalysis. Several weak key classes are identified and it is shown how several observations of the same statistical property can be made for each plaintext--ciphertext pair. Finally, the invariant subspace property, first observed for certain key classes in PRINTcipher, is investigated. In particular, its connection to large linear biases is studied through an eigenvector which arises inside the cipher and leads to trail clustering in the linear hull which, under reasonable assumptions, causes a significant number of large linear biases. Simulations on several versions of PRINTcipher are compared to the theoretical findings

The LED Block Cipher

Abstract. We present a new block cipher LED. While dedicated to compact hardware implementation, and offering the smallest silicon footprint among comparable block ciphers, the cipher has been designed to simultaneously tackle three additional goals. First, we explore the role of an ultra-light (in fact non-existent) key schedule. Second, we consider the resistance of ciphers, and LED in particular, to related-key attacks: we are able to derive simple yet interesting AES-like security proofs for LED regarding related- or single-key attacks. And third, while we provide a block cipher that is very compact in hardware, we aim to maintain a reasonable performance profile for software implementation. Key words: lightweight, block cipher, RFID tag, AES.

SIMON and SPECK: Block Ciphers for the Internet of Things

The U.S. National Security Agency (NSA) developed the SIMON and SPECK families of lightweight block ciphers as an aid for securing applications in very constrained environments where AES may not be suitable. This paper summarizes the algorithms, their design rationale, along with current cryptanalysis and implementation results

Notes on the design and analysis of SIMON and SPECK

We discuss the design rationale and analysis of the SIMON and SPECK lightweight block ciphers

CRAFT: Lightweight Tweakable Block Cipher with Efficient Protection Against DFA Attacks

Traditionally, countermeasures against physical attacks are integrated into the implementation of cryptographic primitives after the algorithms have been designed for achieving a certain level of cryptanalytic security. This picture has been changed by the introduction of PICARO, ZORRO, and FIDES, where efficient protection against Side-Channel Analysis (SCA) attacks has been considered in their design. In this work we present the tweakable block cipher CRAFT: the efficient protection of its implementations against Differential Fault Analysis (DFA) attacks has been one of the main design criteria, while we provide strong bounds for its security in the related-tweak model. Considering the area footprint of round-based hardware implementations, CRAFT outperforms the other lightweight ciphers with the same state and key size. This holds not only for unprotected implementations but also when fault-detection facilities, side-channel protection, and their combination are integrated into the implementation. In addition to supporting a 64-bit tweak, CRAFT has the additional property that the circuit realizing the encryption can support the decryption functionality as well with very little area overhead

Truncated Differential Based Known-Key Attacks on Round-Reduced Simon

At Crypto 2015, Blondeau, Peyrin and Wang proposed a truncated-differential-based known-key attack on full PRESENT, a nibble oriented lightweight blockcipher with a SPN structure. The truncated difference they used is derived from the existing multidimensional linear characteristics. An innovative technique of their work is the design of a MITM layer added before the characteristic that covers extra rounds with a complexity lower than that of a generic construction. We notice that there are good linear hulls for bit-oriented block cipher Simon corresponding to highly qualified truncated differential characteristics. Based on these characteristics, we propose known-key distinguishers on round-reduced Simon block cipher family, which is bit oriented and has a Feistel structure. Similar to the MITM layer, we design a specific start-from-the-middle method for pre-adding extra rounds with complexities lower than generic bounds. With these techniques, we launch basic known-key attacks on round-reduced Simon. We also involve some key guessing technique and further extend the basic attacks to more rounds. Our known-key attacks can reach as many as 29/32/38/48/63-rounds of Simon32/48/64/96/128, which comes quite close to the full number of rounds. To the best of our knowledge, these are the first known-key results on the block cipher Simon