Related papers: On homomorphic encryption using abelian groups: Cl…
Quantum computing has undergone rapid development in recent years. Owing to limitations on scalability, personal quantum computers still seem slightly unrealistic in the near future. The first practical quantum computer for ordinary users…
In this paper, we study groups of automorphisms of algebraic systems over a set of $p$-adic integers with different sets of arithmetic and coordinate-wise logical operations and congruence relations modulo $p^k,$ $k\ge 1.$ The main result…
Deep learning (DL) approaches are achieving extraordinary results in a wide range of domains, but often require a massive collection of private data. Hence, methods for training neural networks on the joint data of different data owners,…
The goal of this chapter is to present a survey of homomorphic encryption techniques and their applications. After a detailed discussion on the introduction and motivation of the chapter, we present some basic concepts of cryptography. The…
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…
The rise of quantum computing/technology potentially introduces significant security challenges to cloud computing, necessitating quantum-resistant encryption strategies as well as protection schemes and methods for cloud infrastructures…
In this paper we consider the problem of testing whether two finite groups are isomorphic. Whereas the case where both groups are abelian is well understood and can be solved efficiently, very little is known about the complexity of…
Federated Learning (FL) enables collaborative model training without sharing raw data, making it a promising approach for privacy-sensitive domains. Despite its potential, FL faces significant challenges, particularly in terms of…
We know the classical public cryptographic algorithms are based on certain NP-hard problems such as the integer factoring in RSA and the discrete logarithm in Diffie-Hellman. They are going to be vulnerable with fault-tolerant quantum…
The trend towards delegating data processing to a remote party raises major concerns related to privacy violations for both end-users and service providers. These concerns have attracted the attention of the research community, and several…
This paper proposes a new homomorphic functional encryption using modular multiplications over a hidden ring. Unlike traditional homomorphic encryption where users can only passively perform ciphertext addition or multiplication, the…
Recently, several public key exchange protocols based on symbolic computation in non-commutative (semi)groups were proposed as a more efficient alternative to well established protocols based on numeric computation. Notably, the protocols…
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…
Construct the first provably secure linear homomorphic ring signature scheme. Ring signatures allow a signer to anonymously sign a message on behalf of a user group (ring) and are widely applied in areas such as identity protection,…
Cryptographic group actions are a leading contender for post-quantum cryptography, and have also been used in the development of quantum cryptographic protocols. In this work, we explore quantum state group actions, which consist of a group…
Motivated by a connection, described here for the first time, between the hidden normal subgroup problem (HNSP) and abelian hypergroups (algebraic objects that model collisions of physical particles), we develop a stabilizer formalism using…
In this paper we consider the description of homomorphic and fully homomorphic ciphers in the $p$-adic model of encryption. This model describes a wide class of ciphers, but certainly not all. Homomorphic and fully homomorphic ciphers are…
The use of Machine Learning (ML) for data-driven decision-making often relies on access to sensitive datasets, which introduces privacy challenges. Traditional encryption methods protect data at rest or in transit but fail to secure it…
Fully Homomorphic Encryption (FHE) is a relatively recent advancement in the field of privacy-preserving technologies. FHE allows for the arbitrary depth computation of both addition and multiplication, and thus the application of…
Large-scale quantum computing is a significant threat to classical public-key cryptography. In strong "quantum access" security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model…