相关论文: On non-abelian homomorphic public-key cryptosystem…

Cryptography protects users by providing functionality for the encryption of data and authentication of other users. This technology lets the receiver of an electronic message verify the sender, ensures that a message can be read only by…

Quantum algorithms for factoring and discrete logarithm have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the possibility of extending this general viewpoint to finding hidden…

With the rapid surge in the prevalence of Large Language Models (LLMs), individuals are increasingly turning to conversational AI for initial insights across various domains, including health-related inquiries such as disease diagnosis.…

To ensure the secure transmission of data, cryptography is treated as the most effective solution. Cryptographic key is an important entity in this procedure. In general, randomly generated cryptographic key (of 256 bits) is difficult to…

The process of replacing an arbitrary Boolean function by a bijective one, a fundamental tool in reversible computing and in cryptography, is interpreted algebraically as a particular instance of a certain group homomorphism from the X-fold…

Large language models (LLMs) offer personalized responses based on user interactions, but this use case raises serious privacy concerns. Homomorphic encryption (HE) is a cryptographic protocol supporting arithmetic computations in encrypted…

The gold-standard for security in quantum cryptographic protocols is information-theoretic security. Information-theoretic security is surely future-proof, because it makes no assumptions on the hardness of any computational problems and…

We investigate the computational complexity of the problem of deciding if an algebra homomorphism can be factored through an intermediate algebra. Specifically, we fix an algebraic language, L, and take as input an algebra homomorphism f…

Affinely closed homogeneous spaces G/H, i.e., affine homogeneous spaces that admit only the trivial affine embedding, are characterized for any affine algebraic group G. As a corollary, a description of affine G-algebras with finitely…

Catalano and Fiore propose a scheme to transform a linearly-homomorphic encryption into a homomorphic encryption scheme capable of evaluating quadratic computations on ciphertexts. Their scheme is based on the linearly-homomorphic…

It is well known that the discrete analogue of a lattice is a linear code which is a vector subspace of Hamming space $\mathbb{F}^n$. The set $\mathbb{F}$ is a finite field and $n \in \mathbb{Z}_{>0}$. Our attempt is to construct a class of…

Homomorphic encryption (HE) is widely adopted in untrusted environments such as federated learning. A notable limitation of conventional single-key HE schemes is the stringent security assumption regarding collusion between the parameter…

Computational privacy is a property of cryptographic system that ensures the privacy of data being processed at an untrusted server. Fully Homomorphic Encryption Schemes (FHE) promise to provide such property. Contemporary FHE schemes are…

This is a study of the MOR cryptosystem using the special linear group over finite fields. The automorphism group of the special linear group is analyzed for this purpose. At our current state of knowledge, I show that the MOR cryptosystem…

A cryptographic algorithm is proposed based on fully quantum mechanical keys and ciphers. Encryption and decryption are carried out via an appropriate measurement process on entangled states as governed by a quantum mechanical, asymmetrical…

In this paper we discuss generic properties of "random subgroups" of a given group G. It turns out that in many groups G (even in most exotic of them) the random subgroups have a simple algebraic structure and they "sit" inside G in a very…

We propose a multi-bit leveled fully homomorphic encryption scheme using multivariate polynomial evaluations. The security of the scheme depends on the hardness of the Learning with Errors (LWE) problem. For homomorphic multiplication, the…

In this technical report, we explore the use of homomorphic encryption (HE) in the context of training and predicting with deep learning (DL) models to deliver strict \textit{Privacy by Design} services, and to enforce a zero-trust model of…

A method for non-abelian Cramer-Shoup cryptosystem is presented. The role of decision and search is explored, and the platform of solvable/polycyclic group is suggested. In the process we review recent progress in non-abelian cryptography…

We propose an unbounded fully homomorphic encryption scheme, i.e. a scheme that allows one to compute on encrypted data for any desired functions without needing to decrypt the data or knowing the decryption keys. This is a rational…