相关论文: Generalized RSA/DH/ECC via Geometric Cryptosystem

We believe that there is no real data protection without our own tools. Therefore, our permanent aim is to have more of our own codes. In order to achieve that, it is necessary that a lot of young researchers become interested in…

A new effective decoding algorithm is presented for arbitrary algebraic-geometric codes on the basis of solving a generalized key equation with the majority coset scheme of Duursma. It is an improvement of Ehrhard's algorithm, since the…

We introduce a natural generalization of staircase codes in which each bit is protected by arbitrarily many component codewords rather than two. This enables powerful energy-efficient FEC based on iterative decoding of Hamming components.

Nowadays, using cryptographic systems play an effective role in security and safety technologies. One of the most applied kind of cryptography is Symmetric Cryptography and its applications. New aspects of symmetric Cryptography…

Sending money in cryptocurrencies is majorly based on public keys or their hashed forms -- "addresses." These long random-looking strings are user unfriendly for transferring by other means than via copy-and-paste or QR codes. Replacing…

Encryption schemes attempt to provide a means for entities to communicate confidentially over a public channel. Such schemes have been studied for centuries, and their use has become widespread. However, developments in the area of quantum…

Elliptic Curve Cryptography (ECC) is an encryption method that provides security comparable to traditional techniques like Rivest-Shamir-Adleman (RSA) but with lower computational complexity and smaller key sizes, making it a competitive…

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…

This paper puts forward a safe mechanism of data transmission to tackle the security problem of information which is transmitted in Internet. The encryption standards such as DES (Data Encryption Standard), AES (Advanced Encryption…

Generalized Cluster Algebras (GCA) are generalizations of Cluster Algebras (CA) with higher-order exchange relations. Previously, Chekhov-Shapiro conjectured that every GCA can be embedded into a CA. In this paper, we prove a modified…

In this paper, we provide a general framework for counting geometric structures in pseudo-random graphs. As applications, our theorems recover and improve several results on the finite field analog of questions originally raised in the…

How to understand deep learning systems remains an open problem. In this paper we propose that the answer may lie in the geometrization of deep networks. Geometrization is a bridge to connect physics, geometry, deep network and quantum…

Designing software systems for Geometric Computing applications can be a challenging task. Software engineers typically use software abstractions to hide and manage the high complexity of such systems. Without the presence of a unifying…

We consider geometric methods of ``rotating" the toric code in higher dimensions to reduce the qubit count. These geometric methods can be used to prepare higher dimensional toric code states using single shot techniques, and in turn these…

We propose variations of the class of hidden monomial cryptosystems in order to make it resistant to all known attacks. We use identities built upon a single bivariate polynomial equation with coefficients in a finite field. Indeed, it can…

New cryptographic techniques such as homomorphic encryption (HE) allow computations to be outsourced to and evaluated blindfolded in a resourceful cloud. These computations often require private data owned by multiple participants, engaging…

Like all of quantum information theory, quantum cryptography is traditionally based on two level quantum systems. In this letter, a new protocol for quantum key distribution based on higher dimensional systems is presented. An experimental…

Using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the Information Geometry based on these entropies. Our aim, at this stage, is modest, as we are first constructing…

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…

Quantum algorithms can break factoring and discrete logarithm based cryptography and weaken symmetric cryptography and hash functions. In order to estimate the real-world impact of these attacks, apart from tracking the development of…