Mind the Gap - A Closer Look at the Security of Block Ciphers against Differential Cryptanalysis

Resistance against differential cryptanalysis is an important design criteria for any modern block cipher and most designs rely on finding some upper bound on probability of single differential characteristics. However, already at EUROCRYPT'91, Lai et al. comprehended that differential cryptanalysis rather uses differentials instead of single characteristics. In this paper, we consider exactly the gap between these two approaches and investigate this gap in the context of recent lightweight cryptographic primitives. This shows that for many recent designs like Midori, Skinny or Sparx one has to be careful as bounds from counting the number of active S-boxes only give an inaccurate evaluation of the best differential distinguishers. For several designs we found new differential distinguishers and show how this gap evolves. We found an 8-round differential distinguisher for Skinny-64 with a probability of 2−56.932−56.93, while the best single characteristic only suggests a probability of 2−722−72. Our approach is integrated into publicly available tools and can easily be used when developing new cryptographic primitives. Moreover, as differential cryptanalysis is critically dependent on the distribution over the keys for the probability of differentials, we provide experiments for some of these new differentials found, in order to confirm that our estimates for the probability are correct. While for Skinny-64 the distribution over the keys follows a Poisson distribution, as one would expect, we noticed that Speck-64 follows a bimodal distribution, and the distribution of Midori-64 suggests a large class of weak keys

On the Key Schedule of Lightweight Block Ciphers

Key schedules in lightweight block ciphers are often highly simplified, which causes weakness that can be exploited in many attacks. Today it remains an open problem on how to use limited operations to guarantee enough diffusion of key bits in lightweight key schedules. Also, there are few tools special for detecting weakness in the key schedule. In 2013 Huang et al. pointed out that insufficient actual key information (AKI) in computation chains is responsible for many attacks especially the meet-in-the-middle (MITM) attacks. Motivated by this fact, in this paper we develop an efficient (with polynomial time complexity) and effective tool to search the computation chains which involve insufficient AKI for iterated key schedules of lightweight ciphers. The effectiveness of this tool is shown by an application on TWINE-80. Then, we formulate the cause of key bits leakage phenomenon, where the knowledge of subkey bits is leaked or overlapped by other subkey bits in the same computation chain. Based on the interaction of diffusion performed by the key schedule and by the round function, a necessary condition is thus given on how to avoid key bits leakage. Therefore, our work sheds light on the design of lightweight key schedules by guiding how to quickly rule out unreasonable key schedules and maximize the security under limited diffusion

Differential Cryptanalysis of WARP

WARP is an energy-efficient lightweight block cipher that is currently the smallest 128-bit block cipher in terms of hardware. It was proposed by Banik et al. in SAC 2020 as a lightweight replacement for AES-128 without changing the mode of operation. This paper proposes key-recovery attacks on WARP based on differential cryptanalysis in single and related-key settings. We searched for differential trails for up to 20 rounds of WARP, with the first 19 having optimal differential probabilities. We also found that the cipher has a strong differential effect, whereby 16 to 20-round differentials have substantially higher probabilities than their corresponding individual trails. A 23-round key-recovery attack was then realized using an 18-round differential distinguisher. Next, we formulated an automatic boomerang search using SMT that relies on the Feistel Boomerang Connectivity Table to identify valid switches. We designed the search as an add-on to the CryptoSMT tool, making it applicable to other Feistel-like ciphers such as TWINE and LBlock-s. For WARP, we found a 21-round boomerang distinguisher which was used in a 24-round rectangle attack. In the related-key setting, we describe a family of 2-round iterative differential trails, which we used in a practical related-key attack on the full 41-round WARP

SAND: an AND-RX Feistel lightweight block cipher supporting S-box-based security evaluations

We revisit designing AND-RX block ciphers, that is, the designs assembled with the most fundamental binary operations---AND, Rotation and XOR operations and do not rely on existing units. Likely, the most popular representative is the NSA cipher \texttt{SIMON}, which remains one of the most efficient designs, but suffers from difficulty in security evaluation. As our main contribution, we propose \texttt{SAND}, a new family of lightweight AND-RX block ciphers. To overcome the difficulty regarding security evaluation, \texttt{SAND} follows a novel design approach, the core idea of which is to restrain the AND-RX operations to be within nibbles. By this, \texttt{SAND} admits an equivalent representation based on a $4\times8$ \textit{synthetic S-box} ($SSb$). This enables the use of classical S-box-based security evaluation approaches. Consequently, for all versions of \texttt{SAND}, (a) we evaluated security bounds with respect to differential and linear attacks, and in both single-key and related-key scenarios; (b) we also evaluated security against impossible differential and zero-correlation linear attacks. This better understanding of the security enables the use of a relatively simple key schedule, which makes the ASIC round-based hardware implementation of \texttt{SAND} to be one of the state-of-art Feistel lightweight ciphers. As to software performance, due to the natural bitslice structure, \texttt{SAND} reaches the same level of performance as \texttt{SIMON} and is among the most software-efficient block ciphers

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

Applying MILP Method to Searching Integral Distinguishers Based on Division Property for 6 Lightweight Block Ciphers

Division property is a generalized integral property proposed by Todo at EUROCRYPT 2015, and very recently, Todo et al. proposed bit-based division property and applied to SIMON32 at FSE 2016. However, this technique can only be applied to block ciphers with block size no larger than 32 due to its high time and memory complexity. In this paper, we extend Mixed Integer Linear Programming (MILP) method, which is used to search differential characteristics and linear trails of block ciphers, to search integral distinguishers of block ciphers based on division property with block size larger than 32. Firstly, we study how to model division property propagations of three basic operations (copy, bitwise AND, XOR) and an Sbox operation by linear inequalities, based on which we are able to construct a linear inequality system which can accurately describe the division property propagations of a block cipher given an initial division property. Secondly, by choosing an appropriate objective function, we convert a search algorithm under Todo\u27s framework into an MILP problem, and we use this MILP problem appropriately to search integral distinguishers. As an application of our technique, we have searched integral distinguishers for SIMON, SIMECK, PRESENT, RECTANGLE, LBlock and TWINE. Our results show that we can find 14-, 16-, 18-, 22- and 26-round integral distinguishers for SIMON32, 48, 64, 96 and 128 respectively. Moreover, for two SP-network lightweight block ciphers PRESENT and RECTANGLE, we found 9-round integral distinguishers for both ciphers which are two more rounds than the best integral distinguishers in the literature. For LBlock and TWINE, our results are consistent with the best known ones with respect to the longest distinguishers