A 2^{70} Attack on the Full MISTY1

MISTY1 is a block cipher designed by Matsui in 1997. It is widely deployed in Japan, and is recognized internationally as a European NESSIE-recommended cipher and an ISO standard. After almost 20 years of unsuccessful cryptanalytic attempts, a first attack on the full MISTY1 was presented at CRYPTO 2015 by Todo. The attack, using a new technique called {\it division property}, requires almost the full codebook and has time complexity of 2^{107.3} encryptions. In this paper we present a new attack on the full MISTY1. It is based on a modified variant of Todo\u27s division property, along with a variety of refined key-recovery techniques. Our attack requires the full codebook, but allows to retrieve 49 bits of the secret key in time complexity of only 2^{64} encryptions, and the full key in time complexity of 2^{69.5} encryptions. While our attack is clearly impractical due to its large data complexity, it shows that MISTY1 provides security of only 2^{70} --- significantly less than what was considered before

SoK: Security Evaluation of SBox-Based Block Ciphers

Cryptanalysis of block ciphers is an active and important research area with an extensive volume of literature. For this work, we focus on SBox-based ciphers, as they are widely used and cover a large class of block ciphers. While there have been prior works that have consolidated attacks on block ciphers, they usually focus on describing and listing the attacks. Moreover, the methods for evaluating a cipher\u27s security are often ad hoc, differing from cipher to cipher, as attacks and evaluation techniques are developed along the way. As such, we aim to organise the attack literature, as well as the work on security evaluation. In this work, we present a systematization of cryptanalysis of SBox-based block ciphers focusing on three main areas: (1) Evaluation of block ciphers against standard cryptanalytic attacks; (2) Organisation and relationships between various attacks; (3) Comparison of the evaluation and attacks on existing ciphers

Partial Sums Meet FFT: Improved Attack on 6-Round AES

The partial sums cryptanalytic technique was introduced in 2000 by Ferguson et al., who used it to break 6-round AES with time complexity of $2^{52}$ S-box computations -- a record that has not been beaten ever since. In 2014, Todo and Aoki showed that for 6-round AES, partial sums can be replaced by a technique based on the Fast Fourier Transform (FFT), leading to an attack with a comparable complexity. In this paper we show that the partial sums technique can be combined with an FFT-based technique, to get the best of the two worlds. Using our combined technique, we obtain an attack on 6-round AES with complexity of about $2^{46.4}$ additions. We fully implemented the attack experimentally, along with the partial sums attack and the Todo-Aoki attack, and confirmed that our attack improves the best known attack on 6-round AES by a factor of more than 32. We expect that our technique can be used to significantly enhance numerous attacks that exploit the partial sums technique. To demonstrate this, we use our technique to improve the best known attack on 7-round Kuznyechik by a factor of more than 80, and to reduce the complexity of the best known attack on the full MISTY1 from $2^{69.5}$ to $2^{67}$

Integral Attack on the Full FUTURE Block Cipher

FUTURE is a recently proposed lightweight block cipher that achieved a remarkable hardware performance due to careful design decisions. FUTURE is an Advanced Encryption Standard (AES)-like Substitution-Permutation Network (SPN) with 10 rounds, whose round function consists of four components, i.e., SubCell, MixColumn, ShiftRow and AddRoundKey. Unlike AES, it is a 64-bit-size block cipher with a 128-bit secret key, and the state can be arranged into 16 cells. Therefore, the operations of FUTURE including its S-box is defined over $\mathbb{F}_2^4$. The previous studies have shown that the integral properties of 4-bit S-boxes are usually weaker than larger-size S-boxes, thus the number of rounds of FUTURE, i.e., 10 rounds only, might be too aggressive to provide enough resistance against integral cryptanalysis. In this paper, we mount the integral cryptanalysis on FUTURE. With state-of-the-art detection techniques, we identify several integral distinguishers of 7 rounds of FUTURE. By extending this 7-round distinguisher by 3 forward rounds, we manage to recover all the 128 bits secret keys from the full FUTURE cipher without the full codebook for the first time. To further achieve better time complexity, we also present a key recovery attack on full FUTURE with full codebook. Both attacks have better time complexity than existing results

State of the Art in Lightweight Symmetric Cryptography

Lightweight cryptography has been one of the ``hot topics'' in symmetric cryptography in the recent years. A huge number of lightweight algorithms have been published, standardized and/or used in commercial products. In this paper, we discuss the different implementation constraints that a ``lightweight'' algorithm is usually designed to satisfy. We also present an extensive survey of all lightweight symmetric primitives we are aware of. It covers designs from the academic community, from government agencies and proprietary algorithms which were reverse-engineered or leaked. Relevant national (\nist{}...) and international (\textsc{iso/iec}...) standards are listed. We then discuss some trends we identified in the design of lightweight algorithms, namely the designers' preference for \arx{}-based and bitsliced-S-Box-based designs and simple key schedules. Finally, we argue that lightweight cryptography is too large a field and that it should be split into two related but distinct areas: \emph{ultra-lightweight} and \emph{IoT} cryptography. The former deals only with the smallest of devices for which a lower security level may be justified by the very harsh design constraints. The latter corresponds to low-power embedded processors for which the \aes{} and modern hash function are costly but which have to provide a high level security due to their greater connectivity

State of the Art in Lightweight Symmetric Cryptography

Lightweight cryptography has been one of the hot topics in symmetric cryptography in the recent years. A huge number of lightweight algorithms have been published, standardized and/or used in commercial products. In this paper, we discuss the different implementation constraints that a lightweight algorithm is usually designed to satisfy in both the software and the hardware case. We also present an extensive survey of all lightweight symmetric primitives we are aware of. It covers designs from the academic community, from government agencies and proprietary algorithms which were reverse-engineered or leaked. Relevant national (NIST...) and international (ISO/IEC...) standards are listed. We identified several trends in the design of lightweight algorithms, such as the designers\u27 preference for ARX-based and bitsliced-S-Box-based designs or simpler key schedules. We also discuss more general trade-offs facing the authors of such algorithms and suggest a clearer distinction between two subsets of lightweight cryptography. The first, ultra-lightweight cryptography, deals with primitives fulfilling a unique purpose while satisfying specific and narrow constraints. The second is ubiquitous cryptography and it encompasses more versatile algorithms both in terms of functionality and in terms of implementation trade-offs

Too Much Crypto

We show that many symmetric cryptography primitives would not be less safe with significantly fewer rounds. To support this claim, we review the cryptanalysis progress in the last 20 years, examine the reasons behind the current number of rounds, and analyze the risk of doing fewer rounds. Advocating a rational and scientific approach to round numbers selection, we propose revised number of rounds for AES, BLAKE2, ChaCha, and SHA-3, which offer more consistent security margins across primitives and make them much faster, without increasing the security risk

Links between Division Property and Other Cube Attack Variants

A theoretically reliable key-recovery attack should evaluate not only the non-randomness for the correct key guess but also the randomness for the wrong ones as well. The former has always been the main focus but the absence of the latter can also cause self-contradicted results. In fact, the theoretic discussion of wrong key guesses is overlooked in quite some existing key-recovery attacks, especially the previous cube attack variants based on pure experiments. In this paper, we draw links between the division property and several variants of the cube attack. In addition to the zero-sum property, we further prove that the bias phenomenon, the non-randomness widely utilized in dynamic cube attacks and cube testers, can also be reflected by the division property. Based on such links, we are able to provide several results: Firstly, we give a dynamic cube key-recovery attack on full Grain-128. Compared with Dinur et al.’s original one, this attack is supported by a theoretical analysis of the bias based on a more elaborate assumption. Our attack can recover 3 key bits with a complexity 297.86 and evaluated success probability 99.83%. Thus, the overall complexity for recovering full 128 key bits is 2125. Secondly, now that the bias phenomenon can be efficiently and elaborately evaluated, we further derive new secure bounds for Grain-like primitives (namely Grain-128, Grain-128a, Grain-V1, Plantlet) against both the zero-sum and bias cube testers. Our secure bounds indicate that 256 initialization rounds are not able to guarantee Grain-128 to resist bias-based cube testers. This is an efficient tool for newly designed stream ciphers for determining the number of initialization rounds. Thirdly, we improve Wang et al.’s relaxed term enumeration technique proposed in CRYPTO 2018 and extend their results on Kreyvium and ACORN by 1 and 13 rounds (reaching 892 and 763 rounds) with complexities 2121.19 and 2125.54 respectively. To our knowledge, our results are the current best key-recovery attacks on these two primitives

Impossible Differential Cryptanalysis of Reduced Round SIMON

Impossible differential is a useful method for cryptanalysis. SIMON is a light weight block cipher that has attracted lots of attention ever since its publication in 2013. In this paper we propose impossible differential attack on five versions of SIMON, using bit conditions to minimize key bits guessed. We calculate keybits and give the exact attack results