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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Structured Matrices Approach for Legendre Pairs
勒让德对 结构化 矩阵方法
2023/4/17
Legendre Pairs are combinatorial objects with a rich 20+ years history. Their main application is that they furnish a structured form of the Hadamard conjecture and they have been studied by several a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Branching random walks driven by products of random matrices
随机矩阵 乘积驱动 分支随机 游走
2023/4/18
A branching random walk is a system of particles, where each particle gives birth to new particles of the next generation, which move on $\mathbb R^d$ according to some probability law. In this talk, ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Products of random matrices
随机矩阵 乘积 极限定理收敛率
2023/4/19
Let $(g_n)_{n\geq 1}$ be a sequence of independent and identically distributed random matrices of type $d \times d $ with real coefficients. Consider the products $G_n : = g_n \ldots g_1$ and the rand...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Estimating Factor-Based Spot Volatility Matrices with Noisy and Asynchronous High-Frequency Data
噪声 异步高频 数据估算 因子 现货波动率 矩阵
2023/5/4
With noisy and asynchronous high-frequency data collected for an ultra-large number of assets, we estimate high-dimensional spot volatility matrices satisfying a low-rank plus sparse structure. A loca...
Constructing Low-latency Involutory MDS Matrices with Lightweight Circuit
Lightweight cryptography MDS matrix Involutory matrix
2019/2/27
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 ma...
Construction of Lightweight MDS Matrices from Generalized Feistel Structures
Lightweight cryptography MDS matrix Generalized Feistel Structures
2018/11/12
This paper investigates the construction of lightweight MDS matrices with generalized Feistel structures (GFS). The approach developed by this paper consists in deriving MDS matrices from the product ...
Integer Matrices Homomorphic Encryption and Its application
integer matrices encryption implementation application
2018/11/2
We construct an integer matrices encryption scheme based on binary matrices encryption scheme proposed in [9], and support homomorphic addition and multiplication operations, we prove the correctness ...
Block Cipher Invariants as Eigenvectors of Correlation Matrices
invariant subspace attack nonlinear invariant attack linear cryptanalysis
2018/8/21
A new approach to invariant subspaces and nonlinear invariants is developed. This results in both theoretical insights and practical attacks on block ciphers. It is shown that, with minor modification...
Hadamard Matrices, d-Linearly Independent Sets and Correlation-Immune Boolean Functions with Minimum Hamming Weights
Boolean functions Correlation-immune Minimum-weight
2018/3/26
It is known that correlation-immune (CI) Boolean functions used in the framework of side channel attacks need to have low Hamming weights. In 2013, Bhasin et al. studied the minimum Hamming weight of ...
2018随机矩阵与自由概率论研讨会（Workshop on Random Matrices and Free Probability Theory）
2018 随机矩阵与自由概率论 研讨会
2017/12/20
The workshop will explore large-N asymptotics of random matrices, in connection with the operator-algebra models of their limiting behavior that appear in free probability theory. The behavior or rand...
Recently a lot of attention is paid to the search for efficiently implementable MDS matrices for lightweight symmetric primitives. Previous work concentrated on locally optimizing the multiplication w...
Lightweight MDS Serial-type Matrices with Minimal Fixed XOR Count
MDS matrix Serial matrix lightweight cryptography
2017/11/13
Many block ciphers and hash functions require the diffusion property of Maximum Distance Separable (MDS) matrices. Serial matrices with the MDS property obtain a trade-off between area requirement and...
Construction and Filtration of Lightweight Formalized MDS Matrices
block cipher linear diffusion layer MDS matrix
2017/5/23
The 4x4 MDS matrix over F2 is widely used in the design of block cipher's linear diffusion layers. However, considering the cost of a lightweight cipher's implementation, the sum of XOR operations of ...
This work considers the problem of constructing efficient MDS matrices over the field \F2m\F2m. Efficiency is measured by the metric XOR count which was introduced by Khoo et al. in CHES 2014. Recentl...
On the Efficient Construction of Lightweight Orthogonal MDS Matrices
MDS matrix XOR count polynomial residue ring
2017/5/2
In present paper, we mainly investigate the problem of efficiently constructing lightweight orthogonal MDS matrices over the matrix polynomial residue ring. Surprisingly, this problem did not receive ...