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It is well known that quantum computers can efficiently find a hidden subgroup $H$ of a finite Abelian group $G$. This implies that after only a polynomial (in $\log |G|$) number of calls to the oracle function, the states corresponding to…

Cryptography is the science of using mathematics to encrypt and decrypt data. Cryptography enables you to store sensitive information or transmit it across insecure networks so that it cannot be read by anyone except the intended recipient.…

Secret sharing is a fundamental primitive in cryptography, and it can be achieved even with perfect security. However, the distribution of shares requires computational assumptions, which can compromise the overall security of the protocol.…

Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum…

Homomorphic encryption is a method used in cryptopgraphy to create programs that can interact with encrypted data without ever leaving the data in the clear. This has many potential applications in cybersecurity. This paper uses…

A mathematical topology with matrix is a natural representation of a coding relational structure that is found in many fields of the world. Matrices are very important in computation of real applications, s ce matrices are easy saved in…

Diffusion models are state-of-the-art deep learning empowered generative models that are trained based on the principle of learning forward and reverse diffusion processes via progressive noise-addition and denoising. To gain a better…

In this survey paper we discuss some recent results and related open questions in additive combinatorics, in particular, questions about sumsets in finite abelian groups.

Encrypted computing is an emerging technology based on a processor that `works encrypted', taking encrypted inputs to encrypted outputs while data remains in encrypted form throughout. It aims to secure user data against possible insider…

Malware authors often use cryptographic tools such as XOR encryption and block ciphers like AES to obfuscate part of the malware to evade detection. Use of cryptography may give the impression that these obfuscation techniques have some…

In this short note we study the cohomology algebra of saturated fusion systems using finite groups which realize saturated fusion systems and Hochschild cohomology of group algebras. A similar result to a theorem of Alperin is proved for…

Tur\'an problems in extremal combinatorics ask to find asymptotic bounds on the edge densities of graphs and hypergraphs that avoid specified subgraphs. The theory of flag algebras proposed by Razborov provides powerful methods based on…

We introduce new objects, called $(G,c)$-bands, associated with a simple simply-connected algebraic group $G$, and a Coxeter element $c$ in its Weyl group. We show that bands of a given type are the $K$-points of an infinite dimensional…

Despite the potential of federated learning, it is known to be vulnerable to backdoor attacks. Many robust federated aggregation methods are proposed to reduce the potential backdoor risk. However, they are mainly validated in the CV field.…

Signed social networks are widely used to model the trust relationships among online users in security-sensitive systems such as cryptocurrency trading platforms, where trust prediction plays a critical role. In this paper, we investigate…

Quantum affine bundles are quantum principal bundles with affine quantum structure groups. A general theory of quantum affine bundles is presented. In particular, a detailed analysis of differential calculi over these bundles is performed,…

Backdoor attack intends to embed hidden backdoor into deep neural networks (DNNs), so that the attacked models perform well on benign samples, whereas their predictions will be maliciously changed if the hidden backdoor is activated by…

In this paper, we propose new classes of trapdoor functions to solve the closest vector problem in lattices. Specifically, we construct lattices based on properties of polynomials for which the closest vector problem is hard to solve unless…

We use real algebraic geometry to construct an affine $\Lambda$-building $B$ associated to the $\mathbb{F}$-points of a semisimple algebraic group, where $\mathbb{F}$ is a valued real closed field. We characterize the spherical building at…

Federated graph learning (FedGL) is an emerging federated learning (FL) framework that extends FL to learn graph data from diverse sources. FL for non-graph data has shown to be vulnerable to backdoor attacks, which inject a shared backdoor…