Related papers: Generalized RSA/DH/ECC via Geometric Cryptosystem

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…

We develop a public key cryptosystem based on invariants of diagonalizable groups and investigate properties of such cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of…

Here we investigate the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks. We do this for a variety of…

We introduce randomized algorithms to Clifford's Geometric Algebra, generalizing randomized linear algebra to hypercomplex vector spaces. This novel approach has many implications in machine learning, including training neural networks to…

This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…

The HQC encryption framework is a general code-based encryption scheme for which decryption returns a noisy version of the plaintext. Any instantiation of the scheme will therefore use an error-correcting procedure relying on a fixed…

Though manifold-based clustering has become a popular research topic, we observe that one important factor has been omitted by these works, namely that the defined clustering loss may corrupt the local and global structure of the latent…

We present a code-based public-key cryptosystem, in which we use Reed-Solomon codes over an extension field as secret codes and disguise it by considering its shortened expanded code over the base field. Considering shortened expanded codes…

Type-two constructions abound in cryptography: adversaries for encryption and authentication schemes, if active, are modeled as algorithms having access to oracles, i.e. as second-order algorithms. But how about making cryptographic schemes…

We discuss some applications of 3-manifold topology to cryptography. In particular, we propose a public-key and a symmetric-key cryptographic scheme based on the Thurston norm on the first cohomology of hyperbolic manifolds.

The rise of quantum information science has opened up a new venue for applications of the geometric phase (GP), as well as triggered new insights into its physical, mathematical, and conceptual nature. Here, we review this development by…

One of the scalability issues of blockchains is the increase of their sizes which can prevent users from storing them and thus from contributing to the decentralization effort. Recent works developed the concept of coded blockchains, which…

Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes…

This paper presents a new probabilistic approach to embedding message text on an elliptic curve, by using the concept of the RSA Algorithm and its security, and such approach allows us discovering the message from the point, only according…

Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…

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…

Here we show the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks, for the topological universality class of the…

We present a geometric algorithm to compute the geometric kernel of a generic polyhedron. The geometric kernel (or simply kernel) is definedas the set of points from which the whole polyhedron is visible. Whilst the computation of the…

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…

Fully homomorphic encryption is a kind of encryption scheme, which enables arbitrary computation on encrypted data without accessing the data. We present the quantum version of fully homomorphic encryption scheme, which is constructed based…