International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Qingju Wang

Affiliation: KU Leuven

Publications

Year
Venue
Title
2018
CRYPTO
Improved Division Property Based Cube Attacks Exploiting Algebraic Properties of Superpoly 📺
The cube attack is an important technique for the cryptanalysis of symmetric key primitives, especially for stream ciphers. Aiming at recovering some secret key bits, the adversary reconstructs a superpoly with the secret key bits involved, by summing over a set of the plaintexts/IV which is called a cube. Traditional cube attack only exploits linear/quadratic superpolies. Moreover, for a long time after its proposal, the size of the cubes has been largely confined to an experimental range, e.g., typically 40. These limits were first overcome by the division property based cube attacks proposed by Todo et al. at CRYPTO 2017. Based on MILP modelled division property, for a cube (index set) I, they identify the small (index) subset J of the secret key bits involved in the resultant superpoly. During the precomputation phase which dominates the complexity of the cube attacks, $$2^{|I|+|J|}$$2|I|+|J| encryptions are required to recover the superpoly. Therefore, their attacks can only be available when the restriction $$|I|+|J|<n$$|I|+|J|<n is met.In this paper, we introduced several techniques to improve the division property based cube attacks by exploiting various algebraic properties of the superpoly. 1.We propose the “flag” technique to enhance the preciseness of MILP models so that the proper non-cube IV assignments can be identified to obtain a non-constant superpoly.2.A degree evaluation algorithm is presented to upper bound the degree of the superpoly. With the knowledge of its degree, the superpoly can be recovered without constructing its whole truth table. This enables us to explore larger cubes I’s even if $$|I|+|J|\ge n$$|I|+|J|≥n.3.We provide a term enumeration algorithm for finding the monomials of the superpoly, so that the complexity of many attacks can be further reduced. As an illustration, we apply our techniques to attack the initialization of several ciphers. To be specific, our key recovery attacks have mounted to 839-round Trivium, 891-round Kreyvium, 184-round Grain-128a and 750-round Acornrespectively.
2017
TOSC
Design of Lightweight Linear Diffusion Layers from Near-MDS Matrices
Chaoyun Li Qingju Wang
Near-MDS matrices provide better trade-offs between security and efficiency compared to constructions based on MDS matrices, which are favored for hardwareoriented designs. We present new designs of lightweight linear diffusion layers by constructing lightweight near-MDS matrices. Firstly generic n×n near-MDS circulant matrices are found for 5 ≤ n ≤9. Secondly, the implementation cost of instantiations of the generic near-MDS matrices is examined. Surprisingly, for n = 7, 8, it turns out that some proposed near-MDS circulant matrices of order n have the lowest XOR count among all near-MDS matrices of the same order. Further, for n = 5, 6, we present near-MDS matrices of order n having the lowest XOR count as well. The proposed matrices, together with previous construction of order less than five, lead to solutions of n×n near-MDS matrices with the lowest XOR count over finite fields F2m for 2 ≤ n ≤ 8 and 4 ≤ m ≤ 2048. Moreover, we present some involutory near-MDS matrices of order 8 constructed from Hadamard matrices. Lastly, the security of the proposed linear layers is studied by calculating lower bounds on the number of active S-boxes. It is shown that our linear layers with a well-chosen nonlinear layer can provide sufficient security against differential and linear cryptanalysis.
2015
EPRINT
2015
EPRINT
2015
EPRINT
2015
CRYPTO
2015
ASIACRYPT
2013
CHES