Related papers: A Double Cryptography Using The Keedwell Cross Inv…
Topological phases, edge states, and flat bands in synthetic quantum systems are a key resource for topological quantum computing and noise-resilient information processing. We introduce a scheme based on step-dependent quantum walks on…
Secure communication is of paramount importance in modern society. Asymmetric cryptography methods such as the widely used RSA method allow secure exchange of information between parties who have not shared secret keys. However, the…
The emergence of quantum computing presents profound challenges to existing cryptographic infrastructures, whilst the development of central bank digital currencies (CBDCs) has raised concerns regarding privacy preservation and excessive…
Integrable couplings are associated with non-semisimple Lie algebras. In this paper, we propose a new method to generate new integrable systems through making perturbation in matrix spectral problems for integrable couplings, which is…
For the black box groups $X$ encrypting ${\rm{PGL}}_2(q)$, $q$ odd, we propose an algorithm constructing a subgroup encrypting ${\rm{Sym}}_4$ and subfield subgroups of $X$. We also present the analogous algorithms for black box groups…
We describe the hashing technique to obtain a fast approximation of a target quantum gate in the unitary group SU(2) represented by a product of the elements of a universal basis. The hashing exploits the structure of the icosahedral group…
We provide an analog of the Drinfeld quantum double construction in the context of crossed Hopf group coalgebras introduced by Turaev. We prove that, provided the base group is finite, the double of a semisimple crossed Hopf group coalgebra…
A quantum cryptography scheme based on entanglement between a single particle state and a vacuum state is proposed. The scheme utilizes linear optics devices to detect the superposition of the vacuum and single particle states. Existence of…
It is known that a multiloop Lie algebra, which constructed using multiloop realization, can be a Lie torus if the given multiloop Lie algebra satisfies several conditions, and it is also known that a family of extended affine Lie algebras…
Encoding qubits in multiple degrees of freedom (DOFs) of a quantum system allows less-decoherence quantum information processing with much less quantum resources. We present a compact and scalable quantum circuit to determinately implement…
We identify the quantum isometry groups of spectral triples built on the symmetric groups with length functions arising from the nearest-neighbor transpositions as generators. It turns out that they are isomorphic to certain "doubling" of…
We develop a theory of loops with involution. On this basis we define a Cayley-Dickson doubling on loops, and use it to investigate the lattice of varieties of loops with involution, focusing on properties that remain valid in the…
We give a general proof for the existence and realizability of Clifford gates in the Ising topological quantum computer. We show that all quantum gates that can be implemented by braiding of Ising anyons are Clifford gates. We find that the…
We present e cient algorithms for computing isogenies between hyperelliptic curves, leveraging higher genus curves to enhance cryptographic protocols in the post-quantum context. Our algorithms reduce the computational complexity of isogeny…
A topological group is called a pro-Lie group if it is isomorphic to a closed subgroup of a product of finite-dimensional real Lie groups. This class of groups is closed under the formation of arbitrary products and closed subgroups and…
One particular approach to quantum groups (matrix pseudo groups) provides the Manin quantum plane. Assuming an appropriate set of non-commuting variables spanning linearly a representation space one is able to show that the endomorphisms on…
Optical encryption inherently provides strong security advantages, with hybrid optoelectronic systems offering additional degrees of freedom by integrating optical and algorithmic domains. However, existing optical encryption schemes…
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…
It is a well known result in the covering groups that a subgroup $G$ of the fundamental group at the identity of a semi-locally simply connected topological group determines a covering morphism of topological groups with characteristic…
We introduce a computational problem of distinguishing between two specific quantum states as a new cryptographic problem to design a quantum cryptographic scheme that is "secure" against any polynomial-time quantum adversary. Our problem,…