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

Formal methods for verification of programs are extended to testing of programs. Their combination is intended to lead to benefits in reliable program development, testing, and evolution. Our geometric theory of testing is intended to serve…

This thesis introduces a formal general framework for scaling blockchain protocols by sharding. The framework is modular and it can be adjusted for different needs or sets of assumptions. We prove that sharded protocols obtained by…

In this work, we generalize the integer enumeration basis. We also construct bijections between the elements of special sets and the elements of some groups, and treat the special case of the hyperoctohedral groups. Then, we find a code…

Exploring the symmetries underlying a previously proposed encryption scheme which relies on single-qubit rotations, we derive an improved upper bound on the maximum information that an eavesdropper might extract from all the available…

Generalized Concatenated (GC), also known as Integrated Interleaved (II) Codes, are studied from an erasure correction point of view making them useful for Redundant Arrays of Independent Disks (RAID) types of architectures combining global…

As quantum computing matures toward the realization of Cryptographically Relevant Quantum Computers (CRQC), global cryptographic infrastructure faces an existential threat. This paper introduces a two-dimensional coordinate system to map…

The geometry of atomic arrangement underpins the structural understanding of molecules in many fields. However, no general framework of mathematical/computational theory for the geometry of atomic arrangement exists. Here we present…

Fully Homomorphic Encryption (FHE) provides a powerful paradigm for secure computation, but its practical adoption is severely hindered by the prohibitive computational cost of its bootstrapping procedure. The complexity of all current…

In this lecture, we review some of the concepts of generalized geometry, as introduced by Hitchin and developed in the speaker's thesis. We also prove a Hodge decomposition for the twisted cohomology of a compact generalized K\"ahler…

A new scheme of probabilistic subgroup-related encryption is introduced. Some applications of this scheme based on the RSA, Diffie-Hellman and ElGamal encryption algorithms are described. Security assumptions and main advantages of this…

A block scrambling-based encryption scheme is presented to enhance the security of Encryption-then-Compression (EtC) systems with JPEG compression, which allow us to securely transmit images through an untrusted channel provider, such as…

Quantum computers can break the RSA and El Gamal public-key cryptosystems, since they can factor integers and extract discrete logarithms. If we believe that quantum computers will someday become a reality, we would like to have…

This paper shows that Physics is very close to the substitution-diffusion paradigm of symmetric ciphers. Based on this analogy, we propose a new cryptographic algorithm. Statistical Physics gives design principles to devise fast, scalable…

In this paper we are proposing an algorithm which uses AES technique of 128/192/256 bit cipher key in encryption and decryption of data. AES provides high security as compared to other encryption techniques along with RSA. Cloud computing…

Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several…

Homomorphic encryption is a form of encryption which allows computation to be carried out on the encrypted data without the need for decryption. The success of quantum approaches to related tasks in a delegated computation setting has…

In the present work, we consider a scenario where an arbitrary two-qubit pure state is applied to generate a randomly distributed key via the generalized EPR protocol. Using the twirling procedure to convert the pure state into a Werner…

Quantum homomorphic encryption integrates quantum computing with homomorphic encryption, which allows calculations to be performed directly on encrypted data without decryption on the server side. In this paper, we explore distributed…

Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d,d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge…

In this paper geometry is studied with a novel approach. Every geometrical object is defined as a symbol which satisfies some properties. These symbols are then coded into a class of numbers which are named here as many dots numbers (MDN).…