Related papers: Homomorphic public-key cryptosystems and encryptin…

A symmetric key encryption scheme is described for blocks of general size N that is a product of powers of many prime numbers. This is accomplished by realising each number (representing a message unit) as a point in a product of affine…

The length-based approach is a heuristic for solving randomly generated equations in groups which possess a reasonably behaved length function. We describe several improvements of the previously suggested length-based algorithms, that make…

In this endeavor, a proof-of-concept homomorphic application is developed to determine the production readiness of encryption ecosystems. A movie recommendation app is implemented for this purpose and productionized through containerization…

Recent advancements in Large Language Models (LLMs) have transformed communication, yet their role in secure messaging remains underexplored, especially in surveillance-heavy environments. At the same time, many governments all over the…

In this paper, algorithms for multivariate public key cryptography and digital signature are described. Plain messages and encrypted messages are arrays, consisting of elements from a fixed finite ring or field. The encryption and…

We propose a new cryptosystem based on polycyclic groups. The cryptosystem is based on the fact that the word problem can be solved effectively in polycyclic groups, while the known solutions to the conjugacy problem are far less efficient.

We had recently shown that every positive integer can be represented uniquely using a recurrence sequence, when certain restrictions on the digit strings are satisfied. We present the details of how such representations can be used to build…

In 2009, Gentry proposed the first Fully Homomorphic Encryption (FHE) scheme, an extremely powerful cryptographic primitive that enables to perform computations, i.e., to evaluate circuits, on encrypted data without decrypting them first.…

In 2002, Johnson et al. posed an open problem at the Cryptographers' Track of the RSA Conference: how to construct a secure homomorphic signature on a semigroup, rather than on a group. In this paper, we introduce, for the first time, a…

Why study Lattice-based Cryptography? There are a few ways to answer this question. 1. It is useful to have cryptosystems that are based on a variety of hard computational problems so the different cryptosystems are not all vulnerable in…

We present an efficient quantum circuit for block encoding pairing Hamiltonian often studied in nuclear physics. Our block encoding scheme does not require mapping the creation and annihilation operators to the Pauli operators and…

We describe, for the first time, a completely rigorous homotopy (path--following) algorithm (in the Turing machine model) to find approximate zeros of systems of polynomial equations. If the coordinates of the input systems and the initial…

In this paper, we have proposed a public key cryptography using recursive block matrices involving generalized Fibonacci numbers over a finite field Fp. For this, we define multinacci block matrices, a type of upper triangular matrix…

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…

With the rapid development of cloud computing, the privacy security incidents occur frequently, especially data security issues. Cloud users would like to upload their sensitive information to cloud service providers in encrypted form…

Cryptography is always very important in data origin authentications, entity authentication, data integrity and confidentiality. In recent years, a variety of chaotic cryptographic schemes have been proposed. These schemes have typical…

Secure E-voting is a challenging protocol. Several approaches based on homomorphic crypto systems, mix-nets blind signatures are proposed in the literature .But most of them need complicated homomorphic encryption which involves complicated…

The discrete logarithm problem is one of the backbones in public key cryptography. In this paper we study the discrete logarithm problem in the group of circulant matrices over a finite field. This gives rise to secure and fast public key…

We propose a bit-oriented quantum public-key scheme which uses Boolean function as private-key and randomly changed pairs of quantum state and classical string as public-keys. Contrast to the typical classical public-key scheme, one…

Fully Homomorphic Encryption (FHE) represents a paradigm shift in cryptography, enabling computation directly on encrypted data and unlocking privacy-critical computation. Despite being increasingly deployed in real platforms, the…