## CryptoDB

### Siwei Sun

#### Affiliation: Chinese Academy of Sciences, China

#### Publications

**Year**

**Venue**

**Title**

2020

TOSC

Lightweight Iterative MDS Matrices: How Small Can We Go?
📺
Abstract

As perfect building blocks for the diffusion layers of many symmetric-key primitives, the construction of MDS matrices with lightweight circuits has received much attention from the symmetric-key community. One promising way of realizing low-cost MDS matrices is based on the iterative construction: a low-cost matrix becomes MDS after rising it to a certain power. To be more specific, if At is MDS, then one can implement A instead of At to achieve the MDS property at the expense of an increased latency with t clock cycles. In this work, we identify the exact lower bound of the number of nonzero blocks for a 4 × 4 block matrix to be potentially iterative-MDS. Subsequently, we show that the theoretically lightest 4 × 4 iterative MDS block matrix (whose entries or blocks are 4 × 4 binary matrices) with minimal nonzero blocks costs at least 3 XOR gates, and a concrete example achieving the 3-XOR bound is provided. Moreover, we prove that there is no hope for previous constructions (GFS, LFS, DSI, and spares DSI) to beat this bound. Since the circuit latency is another important factor, we also consider the lower bound of the number of iterations for certain iterative MDS matrices. Guided by these bounds and based on the ideas employed to identify them, we explore the design space of lightweight iterative MDS matrices with other dimensions and report on improved results. Whenever we are unable to find better results, we try to determine the bound of the optimal solution. As a result, the optimality of some previous results is proved.

2020

TOSC

Differential Attacks on CRAFT Exploiting the Involutory S-boxes and Tweak Additions
📺
Abstract

CRAFT is a lightweight tweakable block cipher proposed at FSE 2019, which allows countermeasures against Differential Fault Attacks to be integrated into the cipher at the algorithmic level with ease. CRAFT employs a lightweight and involutory S-box and linear layer, such that the encryption function can be turned into decryption at a low cost. Besides, the tweakey schedule algorithm of CRAFT is extremely simple, where four 64-bit round tweakeys are generated and repeatedly used. Due to a combination of these features which makes CRAFT exceedingly lightweight, we find that some input difference at a particular position can be preserved through any number of rounds if the input pair follows certain truncated differential trails. Interestingly, in contrast to traditional differential analysis, the validity of this invariant property is affected by the positions where the constant additions take place. We use this property to construct “weak-tweakey” truncated differential distinguishers of CRAFT in the single-key model. Subsequently, we show how the tweak additions allow us to convert these weak-tweakey distinguishers into ordinary secret-key distinguishers based on which key-recovery attacks can be performed. Moreover, we show how to construct MILP models to search for truncated differential distinguishers exploiting this invariant property. As a result, we find a 15-round truncated differential distinguisher of CRAFT and extend it to a 19-round key-recovery attack with 260.99 data, 268 memory, 294.59 time complexity, and success probability 80.66%. Also, we find a 14-round distinguisher with probability 2−43 (experimentally verified), a 16-round distinguisher with probability 2−55, and a 20-round weak-key distinguisher (2118 weak keys) with probability 2−63. Experiments on round-reduced versions of the distinguishers show that the experimental probabilities are sometimes higher than predicted. Finally, we note that our result is far from threatening the security of the full CRAFT.

2020

TOSC

On the Security Margin of TinyJAMBU with Refined Differential and Linear Cryptanalysis
📺
Abstract

This paper presents the first third-party security analysis of TinyJAMBU, which is one of 32 second-round candidates in NIST’s lightweight cryptography standardization process. TinyJAMBU adopts an NLFSR based keyed-permutation that computes only a single NAND gate as a non-linear component per round. The designers evaluated the minimum number of active AND gates, however such a counting method neglects the dependency between multiple AND gates. There also exist previous works considering such dependencies with stricter models, however those are known to be too slow. In this paper, we present a new model that provides a good balance of efficiency and accuracy by only taking into account the first-order correlation of AND gates that frequently occurs in TinyJAMBU. With the refined model, we show a 338-round differential with probability 2−62.68 that leads to a forgery attack breaking 64-bit security. This implies that the security margin of TinyJAMBU with respect to the number of unattacked rounds is approximately 12%. We also show a differential on full 384 rounds with probability 2−70.64, thus the security margin of full rounds with respect to the data complexity, namely the gap between the claimed security bits and the attack complexity, is less than 8 bits. Our attacks also point out structural weaknesses of the mode that essentially come from the minimal state size to be lightweight.

2020

ASIACRYPT

Quantum Collision Attacks on AES-like Hashing with Low Quantum Random Access Memories
📺
Abstract

At EUROCRYPT 2020, Hosoyamada and Sasaki proposed the first dedicated quantum attack on hash functions -- a quantum version of the rebound attack exploiting differentials whose probabilities are too low to be useful in the classical setting. This work opens up a new perspective toward the security of hash functions against quantum attacks. In particular, it tells us that the search for differentials should not stop at the classical birthday bound. Despite these interesting and promising implications, the concrete attacks described by Hosoyamada and Sasaki make use of large quantum random access memories (qRAMs), a resource whose availability in the foreseeable future is controversial even in the quantum computation community. Without large qRAMs, these attacks incur significant increases in time complexities. In this work, we reduce or even avoid the use of qRAMs by performing a quantum rebound attack based on differentials with non-full-active super S-boxes. Along the way, an MILP-based method is proposed to systematically explore the search space of useful truncated differentials with respect to rebound attacks. As a result, we obtain improved attacks on \aes-\texttt{MMO}, \aes-\texttt{MP}, and the first classical collision attacks on 4- and 5-round \grostl-\texttt{512}.
Interestingly, the use of non-full-active super S-box differentials in the analysis of \aes-\texttt{MMO} gives rise to new difficulties in collecting enough starting points. To overcome this issue, we consider attacks involving two message blocks to gain more degrees of freedom, and we successfully compress the qRAM demand of the collision attacks on \texttt{AES}-\texttt{MMO} and \texttt{AES}-\texttt{MP} (EUROCRYPT 2020) from $2^{48}$ to a range from $2^{16}$ to $0$, while still maintaining a comparable time complexity.
To the best of our knowledge, these are the first dedicated quantum attacks on hash functions that slightly outperform Chailloux, Naya-Plasencia, and Schrottenloher's generic quantum collision attack (ASIACRYPT 2017) in a model where large qRAMs are not available. This work demonstrates again how a clever combination of classical cryptanalytic technique and quantum computation leads to improved attacks, and shows that the direction pointed out by Hosoyamada and Sasaki deserves further investigation.

2020

ASIACRYPT

An Algebraic Formulation of the Division Property: Revisiting Degree Evaluations, Cube Attacks, and Key-Independent Sums
📺
Abstract

Since it was proposed in 2015 as a generalization
of integral properties, the division property has
evolved into a powerful tool for probing the
structures of Boolean functions whose
algebraic normal forms are not available.
We capture the most essential elements for the detection of division properties
from a pure algebraic perspective, proposing a technique named as {\it monomial prediction}, which
can be employed to determine the presence or absence of a
monomial in the product of the coordinate functions of a vectorial
Boolean function $\bs f$ by counting the number of the so-called {\it monomial trails}
across a sequence of simpler functions whose composition is $\bs f$.
Under the framework of the monomial prediction, we formally prove that
most algorithms for detecting division properties in previous literature
raise no false alarms but may miss.
We also establish the equivalence between the monomial prediction and
the three-subset bit-based division property without unknown subset presented at EUROCRYPT 2020,
and show that these two techniques are perfectly accurate.
This algebraic formulation gives more insights into division properties
and inspires new search strategies. With the monomial prediction,
we obtain the {\it exact} algebraic degrees of \TRIVIUM up
to 834 rounds for the first time. In the context of cube attacks,
we are able to explore a larger search space in limited time and
recover the exact algebraic normal forms of complex superpolies
with the help of a divide-and-conquer strategy. As a result,
we identify more cubes with smaller dimensions, leading
to improvements of some near-optimal attacks against 840-, 841-
and 842-round \TRIVIUM.

2020

ASIACRYPT

Quantum Circuit Implementations of AES with Fewer Qubits
📺
Abstract

We propose some quantum circuit implementations of AES with the following improvements. Firstly, we propose some quantum circuits of the AES S-box and S-box$^{-1}$,which require fewer qubits than prior work. Secondly, we reduce the
number of qubits in the zig-zag method by introducing the S-box$^{-1}$ operation
in our quantum circuits of AES. Thirdly, we present a method to reduce the number of qubits in the key schedule of AES. While the previous quantum circuits of AES-128, AES-192, and AES-256 need at least 864, 896, and 1232 qubits respectively,our quantum circuit implementations of AES-128, AES-192, and AES-256 only require 512, 640, and 768 qubits respectively, where the number of qubits is reduced by more than 30\%.

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

CRYPTO

Correlation of Quadratic Boolean Functions: Cryptanalysis of All Versions of Full $\mathsf {MORUS}$
📺
Abstract

We show that the correlation of any quadratic Boolean function can be read out from its so-called disjoint quadratic form. We further propose a polynomial-time algorithm that can transform an arbitrary quadratic Boolean function into its disjoint quadratic form. With this algorithm, the exact correlation of quadratic Boolean functions can be computed efficiently.We apply this method to analyze the linear trails of $$\mathsf {MORUS}$$ (one of the seven finalists of the CAESAR competition), which are found with the help of a generic model for linear trails of $$\mathsf {MORUS}$$-like key-stream generators. In our model, any tool for finding linear trails of block ciphers can be used to search for trails of $$\mathsf {MORUS}$$-like key-stream generators. As a result, a set of trails with correlation $$2^{-38}$$ is identified for all versions of full $$\mathsf {MORUS}$$, while the correlations of previously published best trails for $$\mathsf {MORUS}$$-640 and $$\mathsf {MORUS}$$-1280 are $$2^{-73}$$ and $$2^{-76}$$ respectively (ASIACRYPT 2018). This significantly improves the complexity of the attack on $$\mathsf {MORUS}$$-1280-256 from $$2^{152}$$ to $$2^{76}$$. These new trails also lead to the first distinguishing and message-recovery attacks on $$\mathsf {MORUS}$$-640-128 and $$\mathsf {MORUS}$$-1280-128 with surprisingly low complexities around $$2^{76}$$.Moreover, we observe that the condition for exploiting these trails in an attack can be more relaxed than previously thought, which shows that the new trails are superior to previously published ones in terms of both correlation and the number of ciphertext blocks involved.

2018

ASIACRYPT

Programming the Demirci-Selçuk Meet-in-the-Middle Attack with Constraints
Abstract

Cryptanalysis with SAT/SMT, MILP and CP has increased in popularity among symmetric-key cryptanalysts and designers due to its high degree of automation. So far, this approach covers differential, linear, impossible differential, zero-correlation, and integral cryptanalysis. However, the Demirci-Selçuk meet-in-the-middle ($$\mathcal {DS}$$-$$\mathsf {MITM}$$) attack is one of the most sophisticated techniques that has not been automated with this approach. By an in-depth study of Derbez and Fouque’s work on $$\mathcal {DS}$$-$$\mathsf {MITM}$$ analysis with dedicated search algorithms, we identify the crux of the problem and present a method for automatic $$\mathcal {DS}$$-$$\mathsf {MITM}$$ attack based on general constraint programming, which allows the cryptanalysts to state the problem at a high level without having to say how it should be solved. Our method is not only able to enumerate distinguishers but can also partly automate the key-recovery process. This approach makes the $$\mathcal {DS}$$-$$\mathsf {MITM}$$ cryptanalysis more straightforward and easier to follow, since the resolution of the problem is delegated to off-the-shelf constraint solvers and therefore decoupled from its formulation. We apply the method to SKINNY, TWINE, and LBlock, and we get the currently known best $$\mathcal {DS}$$-$$\mathsf {MITM}$$ attacks on these ciphers. Moreover, to demonstrate the usefulness of our tool for the block cipher designers, we exhaustively evaluate the security of $$8! = 40320$$ versions of LBlock instantiated with different words permutations in the F functions. It turns out that the permutation used in the original LBlock is one of the 64 permutations showing the strongest resistance against the $$\mathcal {DS}$$-$$\mathsf {MITM}$$ attack. The whole process is accomplished on a PC in less than 2 h. The same process is applied to TWINE, and similar results are obtained.

2018

TOSC

Cryptanalysis of AES-PRF and Its Dual
📺
Abstract

A dedicated pseudorandom function (PRF) called AES-PRF was proposed by Mennink and Neves at FSE 2018 (ToSC 2017, Issue 3). AES-PRF is obtained from AES by using the output of the 5-th round as the feed-forward to the output state. This paper presents extensive security analysis of AES-PRF and its variants. Specifically, we consider unbalanced variants where the output of the s-th round is used as the feed-forward. We also analyze the security of “dual” constructions of the unbalanced variants, where the input state is used as the feed-forward to the output of the s-th round. We apply an impossible differential attack, zero-correlation linear attack, traditional differential attack, zero correlation linear distinguishing attack and a meet-in-the-middle attack on these PRFs and reduced round versions. We show that AES-PRF is broken whenever s ≤ 2 or s ≥ 6, or reduced to 7 rounds, and Dual-AES-PRF is broken whenever s ≤ 4 or s ≥ 8. Our results on AES-PRF improve the initial security evaluation by the designers in various ways, and our results on Dual-AES-PRF give the first insight to its security.

2017

TOSC

Analysis of AES, SKINNY, and Others with Constraint Programming
Abstract

Search for different types of distinguishers are common tasks in symmetrickey cryptanalysis. In this work, we employ the constraint programming (CP) technique to tackle such problems. First, we show that a simple application of the CP approach proposed by Gerault et al. leads to the solution of the open problem of determining the exact lower bound of the number of active S-boxes for 6-round AES-128 in the related-key model. Subsequently, we show that the same approach can be applied in searching for integral distinguishers, impossible differentials, zero-correlation linear approximations, in both the single-key and related-(twea)key model. We implement the method using the open source constraint solver Choco and apply it to the block ciphers PRESENT, SKINNY, and HIGHT (ARX construction). As a result, we find 16 related-tweakey impossible differentials for 12-round SKINNY-64-128 based on which we construct an 18-round attack on SKINNY-64-128 (one target version for the crypto competition https://sites.google.com/site/skinnycipher announced at ASK 2016). Moreover, we show that in some cases, when equipped with proper strategies (ordering heuristic, restart and dynamic branching strategy), the CP approach can be very efficient. Therefore, we suggest that the constraint programming technique should become a convenient tool at hand of the symmetric-key cryptanalysts.

#### Program Committees

- FSE 2020

#### Coauthors

- Patrick Derbez (2)
- Xiaoyang Dong (1)
- Kai Fu (2)
- Fei Gao (1)
- David Gerault (1)
- Yinghua Guo (1)
- Hao Guo (1)
- Lei Hu (13)
- Kai Hu (1)
- Tetsu Iwata (1)
- Pascal Lafourcade (1)
- Chaoyun Li (3)
- Shun Li (2)
- Ximeng Liu (1)
- Xiaoshuang Ma (2)
- Kexin Qiao (4)
- Dhiman Saha (1)
- Yu Sasaki (2)
- Danping Shi (8)
- Ferdinand Sibleyras (1)
- Ling Song (4)
- Bing Sun (1)
- Ling Sun (2)
- Yao Sun (1)
- Yosuke Todo (3)
- Qingju Wang (1)
- Xiaoyun Wang (1)
- Haoyang Wang (1)
- Peng Wang (2)
- Meiqin Wang (5)
- Zihao Wei (2)
- Wenling Wu (1)
- Qianqian Yang (2)
- Yingjie Zhang (1)
- Jian Zou (1)