Parallelizing the Camellia and SMS4 Block Ciphers - Extended version

The n-cell GF-NLFSR (Generalized Feistel-NonLinear Feedback Shift Register) structure [8] is a generalized unbalanced Feistel network that can be considered as a generalization of the outer function FO of the KASUMI block cipher. An advantage of this cipher over other n-cell generalized Feistel networks, e.g. SMS4 [11] and Camellia [5], is that it is parallelizable for up to n rounds. In hardware implementations, the benefits translate to speeding up encryption by up to n times while consuming similar area and significantly less power. At the same time n-cell GF-NLFSR structures offer similar proofs of security against differential cryptanalysis as conventional n-cell Feistel structures. We also ensure that parallelized versions of Camellia and SMS4 are resistant against other block cipher attacks such as linear, boomerang, integral, impossible differential, higher order differential,interpolation, slide, XSL and related-key differential attacks

Meet-in-the-Middle Attacks on Classes of Contracting and Expanding Feistel Constructions

We show generic attacks on unbalanced Feistel ciphers based on the meet-in-the-middle technique. We analyze two general classes of unbalanced Feistel structures, namely contracting Feistels and expanding Feistels. In both of the cases, we consider the practical scenario where the round functions are keyless and known to the adversary. In the case of contracting Feistels with 4 branches, we show attacks on 16 rounds when the key length k (in bits) is as large as the block length n (in bits), and up to 24 rounds when k = 2n. In the case of expanding Feistels, we consider two scenarios: one, where different nonlinear functions without particular structures are used in the round function, and a more practical one, where a single nonlinear is used but different linear functions are introduced in the state update. In the former case, we propose generic attacks on 13 rounds when k = n, and up to 21 rounds when k = 2n. In the latter case, 16 rounds can be attacked for k = n, and 24 rounds for k = 2n

Cryptanalysis of a Type of White-Box Implementations of the SM4 Block Cipher

The SM4 block cipher was first released in 2006 as SMS4 used in the Chinese national standard WAPI, and became a Chinese national standard in 2016 and an ISO international standard in 2021. White-box cryptography aims primarily to protect the secret key used in a cryptographic software implementation in the white-box scenario that assumes an attacker to have full access to the execution environment and execution details of an implementation. Since white-box cryptography has many real-life applications nowadays, a few white-box implementations of the SM4 block cipher has been proposed with its increasingly wide use, among which a type of constructions is dominated, that use an affine diagonal block encoding to protect the original XOR sum of the three branches entering the S-box layer of a round and use its inverse to protect the original input of the S-box layer, such as Xiao and Lai\u27s implementation in 2009, Shang\u27s implementation in 2016 and Yao and Chen\u27s implementation in 2020. In this paper, we show that this type of white-box SM4 constructions can be somewhat equivalent to a plain implementation mostly with Boolean masks from a security viewpoint, by devising collision-based attacks on Xiao and Lai\u27s, Shang\u27s and Yao and Chen\u27s implementations with a time complexity of respectively about $2^{22}$, $2^{39}$ and $2^{22}$ to peel off most white-box operations until only Boolean masks remain. Besides, we present a collision-based attack on a white-box SM4 implementation with a time complexity of about $2^{17.1}$ to recover an original round key, which uses a linear diagonal block encoding instead of an affine diagonal block encoding. Our results show that generating such a white-box SM4 implementation with affine encodings can be simplified into generating a plain implementation with Boolean masks (if its security expectation is beyond the above-mentioned complexity), and the effect of an affine encoding is significantly better than the effect of a linear encoding in the sense of our cryptanalysis results

Improvements for Finding Impossible Differentials of Block Cipher Structures

We improve Wu and Wang’s method for finding impossible differentials of block cipher structures. This improvement is more general than Wu and Wang’s method where it can find more impossible differentials with less time. We apply it on Gen-CAST256, Misty, Gen-Skipjack, Four-Cell, Gen-MARS, SMS4, MIBS, Camellia⁎, LBlock, E2, and SNAKE block ciphers. All impossible differentials discovered by the algorithm are the same as Wu’s method. Besides, for the 8-round MIBS block cipher, we find 4 new impossible differentials, which are not listed in Wu and Wang’s results. The experiment results show that the improved algorithm can not only find more impossible differentials, but also largely reduce the search time

Cryptoraptor : high throughput reconfigurable cryptographic processor for symmetric key encryption and cryptographic hash functions

textIn cryptographic processor design, the selection of functional primitives and connection structures between these primitives are extremely crucial to maximize throughput and flexibility. Hence, detailed analysis on the specifications and requirements of existing crypto-systems plays a crucial role in cryptographic processor design. This thesis provides the most comprehensive literature review that we are aware of on the widest range of existing cryptographic algorithms, their specifications, requirements, and hardware structures. In the light of this analysis, it also describes a high performance, low power, and highly flexible cryptographic processor, Cryptoraptor, that is designed to support both today's and tomorrow's encryption standards. To the best of our knowledge, the proposed cryptographic processor supports the widest range of cryptographic algorithms compared to other solutions in the literature and is the only crypto-specific processor targeting the future standards as well. Unlike previous work, we aim for maximum throughput for all known encryption standards, and to support future standards as well. Our 1GHz design achieves a peak throughput of 128Gbps for AES-128 which is competitive with ASIC designs and has 25X and 160X higher throughput per area than CPU and GPU solutions, respectively.Electrical and Computer Engineerin

Cryptographic Properties and Application of a Generalized Unbalanced Feistel Network Structure (Revised Version)

In this paper, we study GF-NLFSR, a Generalized Unbalanced Feis- tel Network (GUFN) which can be considered as an extension of the outer function FO of the KASUMI block cipher. We show that the differential and linear probabilities of any n + 1 rounds of an n-cell GF-NLFSR are both bounded by p^2, where the corresponding probability of the round function is p. Besides analyzing security against differential and linear cryptanalysis, we provide a frequency distribution for upper bounds on the true differential and linear hull probabilities. From the frequency distribution, we deduce that the proportion of input-output differences/mask values with probability bounded by p^n is close to 1 whereas only a negligible proportion has probability bounded by p^2. We also recall an n^2-round integral attack distinguisher and (n^2+n-2)-round impossible impossible differential distinguisher on the n-cell GF-NLFSR by Li et al. and Wu et al. As an application, we design a new 30-round block cipher Four-Cell+ based on a 4-cell GF-NLFSR. We prove the security of Four-Cell+ against differential, linear, and boomerang attack. Four-Cell+ also resists existing key recovery attacks based on the 16-round integral attack distinguisher and 18-round impossible differential distinguisher. Furthermore, Four-Cell+ can be shown to be secure against other attacks such as higher order differential attack, cube attack, interpolation attack, XSL attack and slide attack

Optimization of SM4 Encryption Algorithm for Power Metering Data Transmission

This study focuses on enhancing the security of the SM4 encryption algorithm for power metering data transmission by employing hybrid algorithms to optimize its substitution box (S-box). A multi-objective fitness function is constructed to evaluate the S-box structure, aiming to identify design solutions that satisfy differential probability, linear probability, and non-linearity balance. To achieve global optimization and local search for the S-box, a hybrid algorithm model that combines genetic algorithm and simulated annealing is introduced. This approach yields significant improvements in optimization effects and increased non-linearity. Experimental results demonstrate that the optimized S-box significantly reduces differential probability and linear probability while increasing non-linearity to 112. Furthermore, a comparison of the ciphertext entropy demonstrates enhanced encryption security with the optimized S-box. This research provides an effective method for improving the performance of the SM4 encryption algorithm

Improving Key-Recovery in Linear Attacks: Application to 28-Round PRESENT

International audienceLinear cryptanalysis is one of the most important tools in usefor the security evaluation of symmetric primitives. Many improvementsand refinements have been published since its introduction, and manyapplications on different ciphers have been found. Among these upgrades,Collard et al. proposed in 2007 an acceleration of the key-recovery partof Algorithm 2 for last-round attacks based on the FFT.In this paper we present a generalized, matrix-based version of the pre-vious algorithm which easily allows us to take into consideration an ar-bitrary number of key-recovery rounds. We also provide efficient variantsthat exploit the key-schedule relations and that can be combined withmultiple linear attacks.Using our algorithms we provide some new cryptanalysis on PRESENT,including, to the best of our knowledge, the first attack on 28 rounds

An Overview of Cryptography (Updated Version, 3 March 2016)

There are many aspects to security and many applications, ranging from secure commerce and payments to private communications and protecting passwords. One essential aspect for secure communications is that of cryptography...While cryptography is necessary for secure communications, it is not by itself sufficient. This paper describes the first of many steps necessary for better security in any number of situations. A much shorter, edited version of this paper appears in the 1999 edition of Handbook on Local Area Networks published by Auerbach in September 1998

Quantum Cryptanalysis on Contracting Feistel Structures and Observation on Related-key Settings

In this paper we show several quantum chosen-plaintext attacks (qCPAs) on contracting Feistel structures. In the classical setting, a $d$-branch $r$-round contracting Feistel structure can be shown to be PRP-secure when $d$ is even and $r \geq 2d-1$, meaning it is secure against polynomial-time chosen-plaintext attacks. We propose a polynomial-time qCPA distinguisher on the $d$-branch $(2d-1)$-round contracting Feistel structure, which solves an open problem by Dong et al. In addition, we show a polynomial-time qCPA that recovers the keys of the $d$-branch $r$-round contracting Feistel structure when each round function $F^{(i)}_{k_i}$ has the form $F^{(i)}_{k_i}(x) = F_i(x \oplus k_i)$ for a public random function $F_i$. This is applicable to the Chinese block cipher standard {\texttt{SM4}}, which is a special case where $d=4$. Finally, in addition to quantum attacks under single-key setting, we also show related-key quantum attacks on balanced Feistel structures in the model that adversaries can only control part of the key difference in quantum superposition. Our related-key attacks on balanced Feistel structures can easily be extended to ones on contracting Feistel structures