## CryptoDB

### Papers from Transaction on Symmetric Cryptology 2019

**Year**

**Venue**

**Title**

2019

TOSC

A General Proof Framework for Recent AES Distinguishers
📺 Abstract

In this paper, a new framework is developed for proving and adapting the recently proposed multiple-of-8 property and mixture-differential distinguishers. The above properties are formulated as immediate consequences of an equivalence relation on the input pairs, under which the difference at the output of the round function is invariant. This approach provides a further understanding of these newly developed distinguishers. For example, it clearly shows that the branch number of the linear layer does not influence the validity of the property, on the contrary of what was previously believed. We further provide an extension of the mixture-differential distinguishers and multiple-of-8 property to any SPN and to a larger class of subspaces. These adapted properties can then be exhibited in a systematic way for other ciphers than the AES. We illustrate this with the examples of Midori, Klein, LED and Skinny.

2019

TOSC

A new SNOW stream cipher called SNOW-V
📺 Abstract

In this paper we are proposing a new member in the SNOW family of stream ciphers, called SNOW-V. The motivation is to meet an industry demand of very high speed encryption in a virtualized environment, something that can be expected to be relevant in a future 5G mobile communication system. We are revising the SNOW 3G architecture to be competitive in such a pure software environment, making use of both existing acceleration instructions for the AES encryption round function as well as the ability of modern CPUs to handle large vectors of integers (e.g. SIMD instructions). We have kept the general design from SNOW 3G, in terms of linear feedback shift register (LFSR) and Finite State Machine (FSM), but both entities are updated to better align with vectorized implementations. The LFSR part is new and operates 8 times the speed of the FSM. We have furthermore increased the total state size by using 128-bit registers in the FSM, we use the full AES encryption round function in the FSM update, and, finally, the initialization phase includes a masking with key bits at its end. The result is an algorithm generally much faster than AES-256 and with expected security not worse than AES-256.

2019

TOSC

Boomerang Connectivity Table Revisited. Application to SKINNY and AES
📺 Abstract

The boomerang attack is a variant of differential cryptanalysis which regards a block cipher E as the composition of two sub-ciphers, i.e., E = E1 o E0, and which constructs distinguishers for E with probability p2q2 by combining differential trails for E0 and E1 with probability p and q respectively. However, the validity of this attack relies on the dependency between the two differential trails. Murphy has shown cases where probabilities calculated by p2q2 turn out to be zero, while techniques such as boomerang switches proposed by Biryukov and Khovratovich give rise to probabilities greater than p2q2. To formalize such dependency to obtain a more accurate estimation of the probability of the distinguisher, Dunkelman et al. proposed the sandwich framework that regards E as Ẽ1 o Em o Ẽ0, where the dependency between the two differential trails is handled by a careful analysis of the probability of the middle part Em. Recently, Cid et al. proposed the Boomerang Connectivity Table (BCT) which unifies the previous switch techniques and incompatibility together and evaluates the probability of Em theoretically when Em is composed of a single S-box layer. In this paper, we revisit the BCT and propose a generalized framework which is able to identify the actual boundaries of Em which contains dependency of the two differential trails and systematically evaluate the probability of Em with any number of rounds. To demonstrate the power of this new framework, we apply it to two block ciphers SKINNY and AES. In the application to SKINNY, the probabilities of four boomerang distinguishers are re-evaluated. It turns out that Em involves5 or 6 rounds and the probabilities of the full distinguishers are much higher than previously evaluated. In the application to AES, the new framework is used to exclude incompatibility and find high probability distinguishers of AES-128 under the related-subkey setting. As a result, a 6-round distinguisher with probability 2−109.42 is constructed. Lastly, we discuss the relation between the dependency of two differential trails in boomerang distinguishers and the properties of components of the cipher.

2019

TOSC

Boomerang Switch in Multiple Rounds. Application to AES Variants and Deoxys
📺 Abstract

The boomerang attack is a cryptanalysis technique that allows an attacker to concatenate two short differential characteristics. Several research results (ladder switch, S-box switch, sandwich attack, Boomerang Connectivity Table (BCT), ...) showed that the dependency between these two characteristics at the switching round can have a significant impact on the complexity of the attack, or even potentially invalidate it. In this paper, we revisit the issue of boomerang switching effect, and exploit it in the case where multiple rounds are involved. To support our analysis, we propose a tool called Boomerang Difference Table (BDT), which can be seen as an improvement of the BCT and allows a systematic evaluation of the boomerang switch through multiple rounds. In order to illustrate the power of this technique, we propose a new related-key attack on 10-round AES-256 which requires only 2 simple related-keys and 275 computations. This is a much more realistic scenario than the state-of-the-art 10-round AES-256 attacks, where subkey oracles, or several related-keys and high computational power is needed. Furthermore, we also provide improved attacks against full AES-192 and reduced-round Deoxys.

2019

TOSC

Classification of Balanced Quadratic Functions
📺 Abstract

S-boxes, typically the only nonlinear part of a block cipher, are the heart of symmetric cryptographic primitives. They significantly impact the cryptographic strength and the implementation characteristics of an algorithm. Due to their simplicity, quadratic vectorial Boolean functions are preferred when efficient implementations for a variety of applications are of concern. Many characteristics of a function stay invariant under affine equivalence. So far, all 6-bit Boolean functions, 3- and 4-bit permutations have been classified up to affine equivalence. At FSE 2017, Bozoliv et al. presented the first classification of 5-bit quadratic permutations. In this work, we propose an adaptation of their work resulting in a highly efficient algorithm to classify n x m functions for n ≥ m. Our algorithm enables for the first time a complete classification of 6-bit quadratic permutations as well as all balanced quadratic functions for n ≤ 6. These functions can be valuable for new cryptographic algorithm designs with efficient multi-party computation or side-channel analysis resistance as goal. In addition, we provide a second tool for finding decompositions of length two. We demonstrate its use by decomposing existing higher degree S-boxes and constructing new S-boxes with good cryptographic and implementation properties.

2019

TOSC

Constructing Low-latency Involutory MDS Matrices with Lightweight Circuits
📺 Abstract

MDS matrices are important building blocks providing diffusion functionality for the design of many symmetric-key primitives. In recent years, continuous efforts are made on the construction of MDS matrices with small area footprints in the context of lightweight cryptography. Just recently, Duval and Leurent (ToSC 2018/FSE 2019) reported some 32 × 32 binary MDS matrices with branch number 5, which can be implemented with only 67 XOR gates, whereas the previously known lightest ones of the same size cost 72 XOR gates.In this article, we focus on the construction of lightweight involutory MDS matrices, which are even more desirable than ordinary MDS matrices, since the same circuit can be reused when the inverse is required. In particular, we identify some involutory MDS matrices which can be realized with only 78 XOR gates with depth 4, whereas the previously known lightest involutory MDS matrices cost 84 XOR gates with the same depth. Notably, the involutory MDS matrix we find is much smaller than the AES MixColumns operation, which requires 97 XOR gates with depth 8 when implemented as a block of combinatorial logic that can be computed in one clock cycle. However, with respect to latency, the AES MixColumns operation is superior to our 78-XOR involutory matrices, since the AES MixColumns can be implemented with depth 3 by using more XOR gates.We prove that the depth of a 32 × 32 MDS matrix with branch number 5 (e.g., the AES MixColumns operation) is at least 3. Then, we enhance Boyar’s SLP-heuristic algorithm with circuit depth awareness, such that the depth of its output circuit is limited. Along the way, we give a formula for computing the minimum achievable depth of a circuit implementing the summation of a set of signals with given depths, which is of independent interest. We apply the new SLP heuristic to a large set of lightweight involutory MDS matrices, and we identify a depth 3 involutory MDS matrix whose implementation costs 88 XOR gates, which is superior to the AES MixColumns operation with respect to both lightweightness and latency, and enjoys the extra involution property.

2019

TOSC

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

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.

2019

TOSC

Cryptanalysis of Plantlet
📺 Abstract

Plantlet is a lightweight stream cipher designed by Mikhalev, Armknecht and Müller in IACR ToSC 2017. It has a Grain-like structure with two state registers of size 40 and 61 bits. In spite of this, the cipher does not seem to lose in security against generic Time-Memory-Data Tradeoff attacks due to the novelty of its design. The cipher uses a 80-bit secret key and a 90-bit IV. In this paper, we first present a key recovery attack on Plantlet that requires around 276.26 Plantlet encryptions. The attack leverages the fact that two internal states of Plantlet that differ in the 43rd LFSR location are guaranteed to produce keystream that are either equal or unequal in 45 locations with probability 1. Thus an attacker can with some probability guess that when 2 segments of keystream blocks possess the 45 bit difference just mentioned, they have been produced by two internal states that differ only in the 43rd LFSR location. Thereafter by solving a system of polynomial equations representing the keystream bits, the attacker can find the secret key if his guess was indeed correct, or reach some kind of contradiction if his guess was incorrect. In the latter event, he would repeat the procedure for other keystream blocks with the given difference. We show that the process when repeated a finite number of times, does indeed yield the value of the secret key.
In the second part of the paper, we observe that the previous attack was limited to internal state differences that occurred at time instances that were congruent to 0 mod 80. We further observe that by generalizing the attack to include internal state differences that are congruent to all equivalence classed modulo 80, we lower the total number of keystream bits required to perform the attack and in the process reduce the attack complexity to 269.98 Plantlet encryptions.

2019

TOSC

DoveMAC: A TBC-based PRF with Smaller State, Full Security, and High Rate
📺 Abstract

Recent parallelizable message authentication codes (MACs) have demonstrated the benefit of tweakable block ciphers (TBCs) for authentication with high security guarantees. With ZMAC, Iwata et al. extended this line of research by showing that TBCs can simultaneously increase the number of message bits that are processed per primitive call. However, ZMAC and previous TBC-based MACs needed more memory than sequential constructions. While this aspect is less an issue on desktop processors, it can be unfavorable on resource-constrained platforms. In contrast, existing sequential MACs limit the number of message bits to the block length of the primitive n or below.This work proposes DoveMAC, a TBC-based PRF that reduces the memory of ZMAC-based MACs to 2n+ 2t+2k bits, where n is the state size, t the tweak length, and k the key length of the underlying primitive. DoveMAC provides (n+min(n+t))/2 bits of security, and processes n+t bits per primitive call. Our construction is the first sequential MAC that combines beyond-birthday-bound security with a rate above n bits per call. By reserving a single tweak bit for domain separation, we derive a single-key variant DoveMAC1k.

2019

TOSC

Efficient Search for Optimal Diffusion Layers of Generalized Feistel Networks
📺 Abstract

The Feistel construction is one of the most studied ways of building block ciphers. Several generalizations were then proposed in the literature, leading to the Generalized Feistel Network, where the round function first applies a classical Feistel operation in parallel on an even number of blocks, and then a permutation is applied to this set of blocks. In 2010 at FSE, Suzaki and Minematsu studied the diffusion of such construction, raising the question of how many rounds are required so that each block of the ciphertext depends on all blocks of the plaintext. They thus gave some optimal permutations, with respect to this diffusion criteria, for a Generalized Feistel Network consisting of 2 to 16 blocks, as well as giving a good candidate for 32 blocks. Later at FSE’19, Cauchois et al. went further and were able to propose optimal even-odd permutations for up to 26 blocks.In this paper, we complete the literature by building optimal even-odd permutations for 28, 30, 32, 36 blocks which to the best of our knowledge were unknown until now. The main idea behind our constructions and impossibility proof is a new characterization of the total diffusion of a permutation after a given number of rounds. In fact, we propose an efficient algorithm based on this new characterization which constructs all optimal even-odd permutations for the 28, 30, 32, 36 blocks cases and proves a better lower bound for the 34, 38, 40 and 42 blocks cases. In particular, we improve the 32 blocks case by exhibiting optimal even-odd permutations with diffusion round of 9. The existence of such a permutation was an open problem for almost 10 years and the best known permutation in the literature had a diffusion round of 10. Moreover, our characterization can be implemented very efficiently and allows us to easily re-find all optimal even-odd permutations for up to 26 blocks with a basic exhaustive search

2019

TOSC

Exhaustive Search for Various Types of MDS Matrices
📺 Abstract

MDS matrices are used in the design of diffusion layers in many block ciphers and hash functions due to their optimal branch number. But MDS matrices, in general, have costly implementations. So in search for efficiently implementable MDS matrices, there have been many proposals. In particular, circulant, Hadamard, and recursive MDS matrices from companion matrices have been widely studied. In a recent work, recursive MDS matrices from sparse DSI matrices are studied, which are of interest due to their low fixed cost in hardware implementation. In this paper, we present results on the exhaustive search for (recursive) MDS matrices over GL(4, F2). Specifically, circulant MDS matrices of order 4, 5, 6, 7, 8; Hadamard MDS matrices of order 4, 8; recursive MDS matrices from companion matrices of order 4; recursive MDS matrices from sparse DSI matrices of order 4, 5, 6, 7, 8 are considered. It is to be noted that the exhaustive search is impractical with a naive approach. We first use some linear algebra tools to restrict the search to a smaller domain and then apply some space-time trade-off techniques to get the solutions. From the set of solutions in the restricted domain, one can easily generate all the solutions in the full domain. From the experimental results, we can see the (non) existence of (involutory) MDS matrices for the choices mentioned above. In particular, over GL(4, F2), we provide companion matrices of order 4 that yield involutory MDS matrices, circulant MDS matrices of order 8, and establish the nonexistence of involutory circulant MDS matrices of order 6, 8, circulant MDS matrices of order 7, sparse DSI matrices of order 4 that yield involutory MDS matrices, and sparse DSI matrices of order 5, 6, 7, 8 that yield MDS matrices. To the best of our knowledge, these results were not known before. For the choices mentioned above, if such MDS matrices exist, we provide base sets of MDS matrices, from which all the MDS matrices with the least cost (with respect to d-XOR and s-XOR counts) can be obtained. We also take this opportunity to present some results on the search for sparse DSI matrices over finite fields that yield MDS matrices. We establish that there is no sparse DSI matrix S of order 8 over F28 such that S8 is MDS.

2019

TOSC

General Diffusion Analysis: How to Find Optimal Permutations for Generalized Type-II Feistel Schemes
📺 Abstract

Type-II Generalized Feistel Schemes are one of the most popular versions of Generalized Feistel Schemes. Their round function consists in applying a classical Feistel transformation to p sub-blocks of two consecutive words and then shifting the k = 2p words cyclically. The low implementation costs it offers are balanced by a low diffusion, limiting its efficiency. Diffusion of such structures may however be improved by replacing the cyclic shift with a different permutation without any additional implementation cost. In this paper, we study ways to determine permutations with the fastest diffusion called optimal permutations.To do so, two ideas are used. First, we study the natural equivalence classes of permutations that preserve cryptographic properties; second, we use the representation of permutations as coloured trees.For both heuristic and historical reasons, we focus first on even-odd permutations, that is, those permutations for which images of even numbers are odd. We derive from their structure an upper bound on the number of their equivalence classes together with a strategy to perform exhaustive searches on classes. We performed those exhaustive searches for sizes k ≤ 24, while previous exhaustive searches on all permutations were limited to k ≤ 16. For sizes beyond the reach of this method, we use tree representations to find permutations with good intermediate diffusion properties. This heuristic leads to an optimal even-odd permutation for k = 26 and best-known results for sizes k = 64 and k = 128.Finally, we transpose these methods to all permutations. Using a new strategy to exhaust equivalence classes, we perform exhaustive searches on classes for sizes k ≤ 20 whose results confirmed the initial heuristic: there always exist optimal permutations that are even-odd and furthermore for k = 18 all optimal permutations are even-odd permutations.

2019

TOSC

libInterMAC: Beyond Confidentiality and Integrity in Practice
📺 Abstract

Boldyreva et al. (Eurocrypt 2012) defined a fine-grained security model capturing ciphertext fragmentation attacks against symmetric encryption schemes. The model was extended by Albrecht et al. (CCS 2016) to include an integrity notion. The extended security model encompasses important security goals of SSH that go beyond confidentiality and integrity to include length hiding and denial-of-service resistance properties. Boldyreva et al. also defined and analysed the InterMAC scheme, while Albrecht et al. showed that InterMAC satisfies stronger security notions than all currently available SSH encryption schemes. In this work, we take the InterMAC scheme and make it fully ready for use in practice. This involves several steps. First, we modify the InterMAC scheme to support encryption of arbitrary length plaintexts and we replace the use of Encrypt-then-MAC in InterMAC with modern noncebased authenticated encryption. Second, we describe a reference implementation of the modified InterMAC scheme in the form of the library libInterMAC. We give a performance analysis of libInterMAC. Third, to test the practical performance of libInterMAC, we implement several InterMAC-based encryption schemes in OpenSSH and carry out a performance analysis for the use-case of file transfer using SCP. We measure the data throughput and the data overhead of using InterMAC-based schemes compared to existing schemes in OpenSSH. Our analysis shows that, for some network set-ups, using InterMAC-based schemes in OpenSSH only moderately affects performance whilst providing stronger security guarantees compared to existing schemes.

2019

TOSC

New Conditional Cube Attack on Keccak Keyed Modes
📺 Abstract

The conditional cube attack on round-reduced Keccak keyed modes was proposed by Huang et al. at EUROCRYPT 2017. In their attack, a conditional cube variable was introduced, whose diffusion was significantly reduced by certain key bit conditions. The attack requires a set of cube variables which are not multiplied in the first round while the conditional cube variable is not multiplied with other cube variables (called ordinary cube variables) in the first two rounds. This has an impact on the degree of the output of Keccak and hence gives a distinguisher. Later, the MILP method was applied to find ordinary cube variables. However, for some Keccak based versions with few degrees of freedom, one could not find enough ordinary cube variables, which weakens or even invalidates the conditional cube attack.In this paper, a new conditional cube attack on Keccak is proposed. We remove the limitation that no cube variables multiply with each other in the first round. As a result, some quadratic terms may appear in the first round. We make use of some new bit conditions to prevent the quadratic terms from multiplying with other cube variables in the second round, so that there will be no cubic terms in the first two rounds. Furthermore, we introduce the kernel quadratic term and construct a 6-2-2 pattern to reduce the diffusion of quadratic terms significantly, where the Θ operation even in the second round becomes an identity transformation (CP-kernel property) for the kernel quadratic term. Previous conditional cube attacks on Keccak only explored the CP-kernel property of Θ operation in the first round. Therefore, more degrees of freedom are available for ordinary cube variables and fewer bit conditions are used to remove the cubic terms in the second round, which plays a key role in the conditional cube attack on versions with very few degrees of freedom. We also use the MILP method in the search of cube variables and give key-recovery attacks on round-reduced Keccak keyed modes.As a result, we reduce the time complexity of key-recovery attacks on 7-round Keccak-MAC-512 and 7-round Ketje Sr v2 from 2111, 299 to 272, 277, respectively. Additionally, we have reduced the time complexity of attacks on 9-round KMAC256 and 7-round Ketje Sr v1. Besides, practical attacks on 6-round Ketje Sr v1 and v2 are also given in this paper for the first time.

2019

TOSC

New Related-Tweakey Boomerang and Rectangle Attacks on Deoxys-BC Including BDT Effect
📺 Abstract

In the CAESAR competition, Deoxys-I and Deoxys-II are two important authenticated encryption schemes submitted by Jean et al. Recently, Deoxys-II together with Ascon, ACORN, AEGIS-128, OCB and COLM have been selected as the final CAESAR portfolio. Notably, Deoxys-II is also the primary choice for the use case “Defense in depth”. However, Deoxys-I remains to be one of the third-round candidates of the CAESAR competition. Both Deoxys-I and Deoxys-II adopt Deoxys-BC-256 and Deoxys-BC-384 as their internal tweakable block ciphers.In this paper, we investigate the security of round-reduced Deoxys-BC-256/-384 and Deoxys-I against the related-tweakey boomerang and rectangle attacks with some new boomerang distinguishers. For Deoxys-BC-256, we present 10-round related-tweakey boomerang and rectangle attacks for the popular setting (|tweak|, |key|) = (128, 128), which reach one more round than the previous attacks in this setting. Moreover, an 11-round related-tweakey rectangle attack on Deoxys-BC-256 is given for the first time. We also put forward a 13-round related-tweakey boomerang attack in the popular setting (|tweak|, |key|) = (128, 256) for Deoxys-BC-384, while the previous attacks in this setting only work for 12 rounds at most. In addition, the first 14-round relatedtweakey rectangle attack on Deoxys-BC-384 is given when (|tweak| < 98, |key| > 286), that attacks one more round than before. Besides, we give the first 10-round rectangle attack on the authenticated encryption mode Deoxys-I-128-128 with one more round than before, and we also reduce the complexity of the related-tweakey rectangle attack on 12-round Deoxys-I-256-128 by a factor of 228. Our attacks can not be applied to (round-reduced) Deoxys-II.

2019

TOSC

New Semi-Free-Start Collision Attack Framework for Reduced RIPEMD-160
📺 Abstract

RIPEMD-160 is a hash function published in 1996, which shares similarities with other hash functions designed in this time-period like MD4, MD5 and SHA-1. However, for RIPEMD-160, no (semi-free-start) collision attacks on the full number of steps are known. Hence, it is still used, e.g., to generate Bitcoin addresses together with SHA-256, and is an ISO/IEC standard. Due to its dual-stream structure, even semifree- start collision attacks starting from the first step only reach 36 steps, which were firstly shown by Mendel et al. at Asiacrypt 2013 and later improved by Liu, Mendel and Wang at Asiacrypt 2017. Both of the attacks are based on a similar freedom degree utilization technique as proposed by Landelle and Peyrin at Eurocrypt 2013. However, the best known semi-free-start collision attack on 36 steps of RIPEMD-160 presented at Asiacrypt 2017 still requires 255.1 time and 232 memory. Consequently, a practical semi-free-start collision attack for the first 36 steps of RIPEMD-160 still requires a significant amount of resources. Considering the structure of these previous semi-free-start collision attacks for 36 steps of RIPEMD-160, it seems hard to extend it to more steps. Thus, we develop a different semi-free-start collision attack framework for reduced RIPEMD-160 by carefully investigating the message expansion of RIPEMD-160. Our new framework has several advantages. First of all, it allows to extend the attacks to more steps. Second, the memory complexity of the attacks is negligible. Hence, we were able to mount semi-free-start collision attacks on 36 and 37 steps of RIPEMD-160 with practical time complexity 241 and 249 respectively. Additionally, we describe semi-free-start collision attacks on 38 and 40 (out of 80) steps of RIPEMD-160 with time complexity 252 and 274.6, respectively. To the best of our knowledge, these are the best semi-free-start collision attacks for RIPEMD-160 starting from the first step with respect to the number of steps, including the first practical colliding message pairs for 36 and 37 steps of RIPEMD-160.

2019

TOSC

On Beyond-Birthday-Bound Security: Revisiting the Development of ISO/IEC 9797-1 MACs
📺 Abstract

★ Best Paper FSE 2020

ISO/IEC 9797-1 is an international standard for block-cipher-based Message Authentication Code (MAC). The current version ISO/IEC 9797-1:2011 specifies six single-pass CBC-like MAC structures that are capped at the birthday bound security. For a higher security that is beyond-birthday bound, it recommends to use the concatenation combiner of two single-pass MACs. In this paper, we reveal the invalidity of the suggestion, by presenting a birthday bound forgery attack on the concatenation combiner, which is essentially based on Joux’s multi-collision. Notably, our new forgery attack for the concatenation of two MAC Algorithm 1 with padding scheme 2 only requires 3 queries. Moreover, we look for patches by revisiting the development of ISO/IEC 9797-1 with respect to the beyond-birthday bound security. More specifically, we evaluate the XOR combiner of single-pass CBC-like MACs, which was used in previous version of ISO/IEC 9797-1.

2019

TOSC

Partitions in the S-Box of Streebog and Kuznyechik
📺 Abstract

Streebog and Kuznyechik are the latest symmetric cryptographic primitives standardized by the Russian GOST. They share the same S-Box, π, whose design process was not described by its authors. In previous works, Biryukov, Perrin and Udovenko recovered two completely different decompositions of this S-Box.We revisit their results and identify a third decomposition of π. It is an instance of a fairly small family of permutations operating on 2m bits which we call TKlog and which is closely related to finite field logarithms. Its simplicity and the small number of components it uses lead us to claim that it has to be the structure intentionally used by the designers of Streebog and Kuznyechik.The 2m-bit permutations of this type have a very strong algebraic structure: they map multiplicative cosets of the subfield GF(2m)* to additive cosets of GF(2m)*. Furthermore, the function relating each multiplicative coset to the corresponding additive coset is always essentially the same. To the best of our knowledge, we are the first to expose this very strong algebraic structure.We also investigate other properties of the TKlog and show in particular that it can always be decomposed in a fashion similar to the first decomposition of Biryukov et al., thus explaining the relation between the two previous decompositions. It also means that it is always possible to implement a TKlog efficiently in hardware and that it always exhibits a visual pattern in its LAT similar to the one present in π. While we could not find attacks based on these new results, we discuss the impact of our work on the security of Streebog and Kuznyechik. To this end, we provide a new simpler representation of the linear layer of Streebog as a matrix multiplication in the exact same field as the one used to define π. We deduce that this matrix interacts in a non-trivial way with the partitions preserved by π.

2019

TOSC

PEIGEN – a Platform for Evaluation, Implementation, and Generation of S-boxes
📺 Abstract

In this paper, a platform named PEIGEN is presented to evaluate security, find efficient software/hardware implementations, and generate cryptographic S-boxes. Continuously developed for decades, S-boxes are constantly evolving in terms of the design criteria for both security requirements and software/hardware performances. PEIGEN is aimed to be a platform covering a comprehensive check-list of design criteria of S-boxes appearing in the literature. To do so, the security requirements are first intensively surveyed, existing tools of S-boxes are then comprehensively compared, and finally our platform PEIGEN is presented. The survey part is aimed to be a systematic reference for the theoretical study of S-boxes. The platform is aimed to be an assistant tool for the experimental study and practical use of S-boxes. PEIGEN not only integrates most of the features in existing tools, but also equips with functionalities to evaluate new security-related properties, improves the efficiency of the search algorithms for optimized implementations in several aspects. With the help of this powerful platform, many interesting observations are made in-between the security notations, as well as on the S-boxes used in the existing symmetrickey cryptographic primitives. PEIGEN will become an open platform and welcomes contributions from all parties to help the community to facilitate the research and use of S-boxes.

2019

TOSC

Quantum Security Analysis of AES
📺 Abstract

In this paper we analyze for the first time the post-quantum security of AES. AES is the most popular and widely used block cipher, established as the encryption standard by the NIST in 2001. We consider the secret key setting and, in particular, AES-256, the recommended primitive and one of the few existing ones that aims at providing a post-quantum security of 128 bits. In order to determine the new security margin, i.e., the lowest number of non-attacked rounds in time less than 2128 encryptions, we first provide generalized and quantized versions of the best known cryptanalysis on reduced-round AES, as well as a discussion on attacks that don’t seem to benefit from a significant quantum speed-up. We propose a new framework for structured search that encompasses both the classical and quantum attacks we present, and allows to efficiently compute their complexity. We believe this framework will be useful for future analysis.Our best attack is a quantum Demirci-Selçuk meet-in-the-middle attack. Unexpectedly, using the ideas underlying its design principle also enables us to obtain new, counter-intuitive classical TMD trade-offs. In particular, we can reduce the memory in some attacks against AES-256 and AES-128.One of the building blocks of our attacks is solving efficiently the AES S-Box differential equation, with respect to the quantum cost of a reversible S-Box. We believe that this generic quantum tool will be useful for future quantum differential attacks. Judging by the results obtained so far, AES seems a resistant primitive in the post-quantum world as well as in the classical one, with a bigger security margin with respect to quantum generic attacks.

2019

TOSC

Reconstructing an S-box from its Difference Distribution Table
📺 Abstract

In this paper we study the problem of recovering a secret S-box from its difference distribution table (DDT). While being an interesting theoretical problem on its own, the ability to recover the S-box from the DDT of a secret S-box can be used in cryptanalytic attacks where the attacker can obtain the DDT (e.g., in Bar-On et al.’s attack on GOST), in supporting theoretical analysis of the properties of difference distribution tables (e.g., in Boura et al.’s work), or in some analysis of S-boxes with unknown design criteria (e.g., in Biryukov and Perrin’s analysis).We show that using the well established relation between the DDT and the linear approximation table (LAT), one can devise an algorithm different from the straightforward guess-and-determine (GD) algorithm proposed by Boura et al. Moreover, we show how to exploit this relation, and embed the knowledge obtained from it in the GD algorithm. We tested our new algorithm on random S-boxes of different sizes, and for random 14-bit bijective S-boxes, our results outperform the GD attack by several orders of magnitude.

2019

TOSC

Related-Tweak Statistical Saturation Cryptanalysis and Its Application on QARMA
📺 Abstract

Statistical saturation attack takes advantage of a set of plaintext with some bits fixed while the others vary randomly, and then track the evolution of a non-uniform plaintext distribution through the cipher. Previous statistical saturation attacks are all implemented under single-key setting, and there is no public attack models under related-key/tweak setting. In this paper, we propose a new cryptanalytic method which can be seen as related-key/tweak statistical saturation attack by revealing the link between the related-key/tweak statistical saturation distinguishers and KDIB (Key Difference Invariant Bias) / TDIB (Tweak Difference Invariant Bias) ones. KDIB cryptanalysis was proposed by Bogdanov et al. at ASIACRYPT’13 and utilizes the property that there can exist linear trails such that their biases are deterministically invariant under key difference. And this method can be easily extended to TDIB distinguishers if the tweak is also alternated. The link between them provides a new and more efficient way to find related-key/tweak statistical saturation distinguishers in ciphers. Thereafter, an automatic searching algorithm for KDIB/TDIB distinguishers is also given in this paper, which can be implemented to find word-level KDIB distinguishers for S-box based key-alternating ciphers. We apply this algorithm to QARMA-64 and give related-tweak statistical saturation attack for 10-round QARMA-64 with outer whitening key. Besides, an 11-round attack on QARMA-128 is also given based on the TDIB technique. Compared with previous public attacks on QARMA including outer whitening key, all attacks presented in this paper are the best ones in terms of the number of rounds.

2019

TOSC

Revisit Division Property Based Cube Attacks: Key-Recovery or Distinguishing Attacks?
📺 Abstract

Cube attacks are an important type of key recovery attacks against stream ciphers. In particular, they are shown to be powerful against Trivium-like ciphers. Traditional cube attacks are experimental attacks which could only exploit cubes of size less than 40. At CRYPTO 2017, division property based cube attacks were proposed by Todo et al., and an advantage of introducing the division property to cube attacks is that large cube sizes which are beyond the experimental range could be explored, and so powerful theoretical attacks were mounted on many lightweight stream ciphers.In this paper, we revisit the division property based cube attacks. There is an important assumption, called Weak Assumption, proposed in division property based cube attacks to support the effectiveness of key recovery. Todo et al. in CRYPTO 2017 said that the Weak Assumption was expected to hold for theoretically recovered superpolies of Trivium according to some experimental results on small cubes. In this paper, it is shown that the Weak Assumption often fails in cube attacks against Trivium, and moreover a new method to recover the exact superpoly of a given cube is developed based on the bit-based division property. With our method, for the cube I proposed by Todo et al. at CRYPTO 2017 to attack the 832-round Trivium, we recover its superpoly pI (x, v) = v68v78 · (x58⊕v70) · (x59x60⊕x34⊕x61). Furthermore, we prove that some best key recovery results given at CRYPTO 2018 on Trivium are actually distinguishing attacks. Hopefully this paper gives some new insights on accurately recovering the superpolies with the bit-based division property and also attract some attention on the validity of division property based cube attacks against stream ciphers.

2019

TOSC

Security of Symmetric Primitives against Key-Correlated Attacks
📺 Abstract

We study the security of symmetric primitives against key-correlated attacks (KCA), whereby an adversary can arbitrarily correlate keys, messages, and ciphertexts. Security against KCA is required whenever a primitive should securely encrypt key-dependent data, even when it is used under related keys. KCA is a strengthening of the previously considered notions of related-key attack (RKA) and key-dependent message (KDM) security. This strengthening is strict, as we show that 2-round Even–Mansour fails to be KCA secure even though it is both RKA and KDM secure. We provide feasibility results in the ideal-cipher model for KCAs and show that 3-round Even–Mansour is KCA secure under key offsets in the random-permutation model. We also give a natural transformation that converts any authenticated encryption scheme to a KCA-secure one in the random-oracle model. Conceptually, our results allow for a unified treatment of RKA and KDM security in idealized models of computation.

2019

TOSC

Substitution Attacks against Message Authentication
📺 Abstract

This work introduces Algorithm Substitution Attacks (ASAs) on message authentication schemes. In light of revelations concerning mass surveillance, ASAs were initially introduced by Bellare, Paterson and Rogaway as a novel attack class against the confidentiality of encryption schemes. Such an attack replaces one or more of the regular scheme algorithms with a subverted version that aims to reveal information to an adversary (engaged in mass surveillance), while remaining undetected by users. While most prior work focused on subverting encryption systems, we study options to subvert symmetric message authentication protocols. In particular we provide powerful generic attacks that apply e.g. to HMAC or Carter–Wegman based schemes, inducing only a negligible implementation overhead. As subverted authentication can act as an enabler for subverted encryption (software updates can be manipulated to include replacements of encryption routines), we consider attacks of the new class highly impactful and dangerous.

2019

TOSC

The Exact Security of PMAC with Two Powering-Up Masks
📺 Abstract

PMAC is a rate-1, parallelizable, block-cipher-based message authentication code (MAC), proposed by Black and Rogaway (EUROCRYPT 2002). Improving the security bound is a main research topic for PMAC. In particular, showing a tight bound is the primary goal of the research, since Luykx et al.’s paper (EUROCRYPT 2016). Regarding the pseudo-random-function (PRF) security of PMAC, a collision of the hash function, or the difference between a random permutation and a random function offers the lower bound Ω(q2/2n) for q queries and the block cipher size n. Regarding the MAC security (unforgeability), a hash collision for MAC queries, or guessing a tag offers the lower bound Ω(q2m /2n + qv/2n) for qm MAC queries and qv verification queries (forgery attempts). The tight upper bound of the PRF-security O(q2/2n) of PMAC was given by Gaži et el. (ToSC 2017, Issue 1), but their proof requires a 4-wise independent masking scheme that uses 4 n-bit random values. Open problems from their work are: (1) find a masking scheme with three or less random values with which PMAC has the tight upper bound for PRF-security; (2) find a masking scheme with which PMAC has the tight upper bound for MAC-security.In this paper, we consider PMAC with two powering-up masks that uses two random values for the masking scheme. Using the structure of the powering-up masking scheme, we show that the PMAC has the tight upper bound O(q2/2n) for PRF-security, which answers the open problem (1), and the tight upper bound O(q2m /2n + qv/2n) for MAC-security, which answers the open problem (2). Note that these results deal with two-key PMACs, thus showing tight upper bounds of PMACs with single-key and/or with one powering-up mask are open problems.

2019

TOSC

Zero-Correlation Attacks on Tweakable Block Ciphers with Linear Tweakey Expansion
📺 Abstract

The design and analysis of dedicated tweakable block ciphers is a quite recent and very active research field that provides an ongoing stream of new insights. For instance, results of Kranz, Leander, and Wiemer from FSE 2017 show that the addition of a tweak using a linear tweak schedule does not introduce new linear characteristics. In this paper, we consider – to the best of our knowledge – for the first time the effect of the tweak on zero-correlation linear cryptanalysis for ciphers that have a linear tweak schedule. It turns out that the tweak can often be used to get zero-correlation linear hulls covering more rounds compared to just searching zero-correlation linear hulls on the data-path of a cipher. Moreover, this also implies the existence of integral distinguishers on the same number of rounds. We have applied our technique on round reduced versions of Qarma, Mantis, and Skinny. As a result, we can present – to the best of our knowledge – the best attack (with respect to number of rounds) on a round-reduced variant of Qarma.

2019

TOSC

ZOCB and ZOTR: Tweakable Blockcipher Modes for Authenticated Encryption with Full Absorption
📺 Abstract

We define ZOCB and ZOTR for nonce-based authenticated encryption with associated data, and analyze their provable security. These schemes use a tweakable blockcipher (TBC) as the underlying primitive, and fully utilize its input to process a plaintext and associated data (AD). This property is commonly referred to as full absorption, and this has been explored for schemes based on a permutation or a pseudorandom function (PRF). Our schemes improve the efficiency of TBC-based counterparts of OCB and OTR called OCB3 (Krovetz and Rogaway, FSE 2011) and OTR (Minematsu, EUROCRYPT 2014). Specifically, ΘCB3 and OTR have an independent part to process AD, and our schemes integrate this process into the encryption part of a plaintext by using the tweak input of the TBC. Up to a certain length of AD, ZOCB and ZOTR completely eliminate the independent process for it. Even for longer AD, our schemes process it efficiently by fully using the tweak input of the TBC. For this purpose, based on previous tweak extension schemes for TBCs, we introduce a scheme called XTX*. To our knowledge, ZOCB and ZOTR are the first efficiency improvement of ΘCB3 and OTR in terms of the number of TBC calls. Compared to Sponge-based and PRF-based schemes, ZOCB and ZOTR allow fully parallel computation of the underlying primitive, and have a unique design feature that an authentication tag is independent of a part of AD. We present experimental results illustrating the practical efficiency gain and clarifying the efficiency cost for it with a concrete instantiation. The results show that for long input data, our schemes have gains, while we have efficiency loss for short input data.