Related papers: On non-abelian homomorphic public-key cryptosystem…
We propose a new homomorphic public-key cryptosystem over arbitrary nonidentity finite group based on the difficulty of the membership problem for groups of integer matrices. Besides, a homomorphic cryptosystem is designed for the first…
In this paper homomorphic cryptosystems are designed for the first time over any finite group. Applying Barrington's construction we produce for any boolean circuit of the logarithmic depth its encrypted simulation of a polynomial size over…
In [15], Leonardi and Ruiz-Lopez propose an additively homomorphic public key encryption scheme whose security is expected to depend on the hardness of the learning homomorphism with noise problem (LHN). Choosing parameters for their…
Homomorphic encryption is a sophisticated encryption technique that allows computations on encrypted data to be done without the requirement for decryption. This trait makes homomorphic encryption appropriate for safe computation in…
The purpose of the paper is to give new key agreement protocols (a multi-party extension of the protocol due to Anshel-Anshel-Goldfeld and a generalization of the Diffie-Hellman protocol from abelian to solvable groups) and a new…
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…
We propose a public key encryption cryptosystem based on solutions of linear equation systems with predefinition of input parameters through shared secret computation for factorizable substitutions. The existence of multiple equivalent…
Group homomorphic encryption represents one of the most important building blocks in modern cryptography. It forms the basis of widely-used, more sophisticated primitives, such as CCA2-secure encryption or secure multiparty computation.…
The theory of finite simple groups is a (rather unexplored) area likely to provide interesting computational problems and modelling tools useful in a cryptographic context. In this note, we review some applications of finite non-abelian…
Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum…
Homomorphic encryption is a powerful cryptographic tool that enables secure computations on the private data. It evaluates any function for any operation securely on the encrypted data without knowing its corresponding plaintext. For…
The point of this paper is to use affine automorphisms from algebraic geometry to build cryptographic multivariate mappings. We will construct groups G,H, both isomorphic to the cyclic group with a prime number of elements and multilinear…
Performing smart computations in a context of cloud computing and big data is highly appreciated today. Fully homomorphic encryption (FHE) is a smart category of encryption schemes that allows working with the data in its encrypted form. It…
Fully homomorphic encryption is an encryption method with the property that any computation on the plaintext can be performed by a party having access to the ciphertext only. Here, we formally define and give schemes for quantum homomorphic…
A fully homomorphic encryption system hides data from unauthorized parties, while still allowing them to perform computations on the encrypted data. Aside from the straightforward benefit of allowing users to delegate computations to a more…
Fully homomorphic encryption (FHE) enables an entity to perform arbitrary computation on encrypted data without decrypting the ciphertexts. An ongoing group-theoretical approach to construct an FHE scheme uses a certain "compression"…
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…
Cloud computing is the broad and diverse phenomenon. Users are allowed to store huge amount of data on cloud storage for future use. Most of the cloud service providers store data in plain text format or in secured manner but client will…
The recent discovery of fully-homomorphic classical encryption schemes has had a dramatic effect on the direction of modern cryptography. Such schemes, however, implicitly rely on the assumptions that solving certain computation problems…
A characterization of predicate encryption (PE) with support for homomorphic operations is presented and we describe the homomorphic properties of some existing PE constructions. Even for the special case of IBE, there are few known…