Related papers: A cryptographic application of the Thurston norm
Security of information has become a major issue during the last decades. New algorithms based on chaotic maps were suggested for protection of different types of multimedia data, especially digital images and videos in this period.…
We present novel homomorphic encryption schemes for integer arithmetic, intended for use in secure single-party computation in the cloud. These schemes are capable of securely computing only low degree polynomials homomorphically, but this…
We present a crytographic protocol based upon entangled qutrit pairs. We analyse the scheme under a symmetric incoherent attack and plot the region for which the protocol is secure and compare this with the region of violations of certain…
This paper proposes to put forward an innovative algorithm for symmetric key block cipher named as "Triple Prime Symmetric Key Block Cipher with Variable Key-Spaces (TPSKBCVK)" that employs triple prime integers as private key-spaces of…
Recent advances in cryptography promise to enable secure statistical computation on encrypted data, whereby a limited set of operations can be carried out without the need to first decrypt. We review these homomorphic encryption schemes in…
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…
We demonstrate that the framework of bounded quantum reference frames has application to building quantum-public-key cryptographic protocols and proving their security. Thus, the framework we introduce can be seen as a public-key analogue…
In this paper, we propose to use a twisted dihedral group algebra for public-key cryptography. For this, we introduce a new $2$-cocycle $\alpha_{\lambda}$ to twist the dihedral group algebra. Using the ambient space…
After more than 70 years of development, holography has become an essential tool of modern optics in many applications. In fact, for various applications of different kinds of holographic techniques, stability and antijamming ability are…
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 show that solutions of Thurston equation on triangulated 3-manifolds in a commutative ring carry topological information. We also introduce a homogeneous Thurston equation and a commutative ring associated to triangulated 3-manifolds.
Recently, Aaronson et al. (arXiv:2009.07450) showed that detecting interference between two orthogonal states is as hard as swapping these states. While their original motivation was from quantum gravity, we show its applications in quantum…
Following the analogies between knots and primes, 3-manifolds and number rings in arithmetic topology, we show a topological analogue of the Hasse norm principle for finite cyclic coverings of 3-manifolds, which was originally stated for…
Given a triangulation of a closed, oriented, irreducible, atoroidal 3-manifold every oriented, incompressible surface may be isotoped into normal position relative to the triangulation. Such a normal oriented surface is then encoded by…
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…
We bound the $L^2$-norm of an $L^2$ harmonic $1$-form in an orientable cusped hyperbolic $3$-manifold $M$ by its topological complexity, measured by the Thurston norm, up to a constant depending on $M$. It generalizes two inequalities of…
Confidentiality and Integrity are two paramount objectives in the evaluation of information and communication technology. In this paper, we propose an arithmetic approach for designing asymmetric key cryptography. Our method is based on the…
This article proposes a comprehensive approach to implementing encryption schemes based on the automorphism group of the Hermitian function field. We utilize a three-parameter group with logarithmic representations outside the group's…
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…
Classical work of Thurston and Gabai shows that finitely many taut sutured manifold hierarchies determine the Thurston norm of a compact oriented irreducible $3$-manifold with toroidal boundary. We give an explicit procedure to extract this…