Related papers: A Double Cryptography Using The Keedwell Cross Inv…
The present study further strengthens the use of the Keedwell CIPQ against attack on a system by the use of the Smarandache Keedwell CIPQ for cryptography in a similar spirit in which the cross inverse property has been used by Keedwell.…
By studying the holomorphic structure of automorphic inverse property quasigroups and loops[AIPQ and (AIPL)] and cross inverse property quasigroups and loops[CIPQ and (CIPL)], it is established that the holomorph of a loop is a Smarandache;…
In this paper, we propose a novel construction for a symmetric encryption scheme, referred as SEBQ which is based on the structure of quasigroup. We utilize concepts of chaining like mode of operation and present a block cipher with…
A new condition called ${\cal T}$ condition is introduced for the first time and used to study a pair of isotopic loops. Under this condition, a loop in the pair is a WIPL if and only if the other loop is a WIPL. Furthermore, such WIPLs are…
We prove a general theorem for constructing integral quantum cluster algebras over ${\mathbb{Z}}[q^{\pm 1/2}]$, namely that under mild conditions the integral forms of quantum nilpotent algebras always possess integral quantum cluster…
This study digs out some new algebraic properties of an Osborn loop that will help in the future to unveil the mystery behind the middle inner mappings $T_{(x)}$ of an Osborn loop. These new algebraic properties, will open our eyes more to…
Group homomorphic encryption represents one of the most important building blocks in modern cryptography. It forms the basis of widely-used, more sophisticated primitives, such as CCA2-secure encryption or secure multiparty computation.…
Let Cl1(1,3) and Cl2(1,3) be the subsets of elements of the Clifford algebra Cl(1,3) of ranks 1 and 2 respectively. Recently it was proved that the subset Cl2(p,q)+iCl1(p,q) of the complex Clifford algebra can be considered as a Lie…
We study the computational complexity of quantum state isomorphism problems under group actions: given two quantum circuits that prepare pure or mixed states, decide whether the two states are related by a group action. This can be seen as…
In this article we provide evidence for a well-known conjecture which states that quasi-isometric simply-connected nilpotent Lie groups are isomorphic. We do so by constructing new examples which are rigid in the sense that whenever they…
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…
In this paper, we investigate the computational complexity of isomorphism testing for finite groups and quasigroups, given by their multiplication tables. We crucially take advantage of their various decompositions to show the following: -…
In response to the evolving landscape of quantum computing and the escalating vulnerabilities in classical cryptographic systems, our paper introduces a unified cryptographic framework. Rooted in the innovative work of Kuang et al., we…
This paper presents a quasigroup encryptor that has very good scrambling properties. We show that the output of the encryptor maximizes the output entropy and the encrypted output for constant and random inputs is very similar. The system…
A fully homomorphic encryption system hides data from unauthorized parties, while still allowing them to perform computations on the encrypted data. Aside from the straightforward benefit of allowing users to delegate computations to a more…
We introduce the notion of isolated genus two curves. As there is no known efficient algorithm to explicitly construct isogenies between two genus two curves with large conductor gap, the discrete log problem (DLP) cannot be efficiently…
An algebraic quantum group is a multiplier Hopf algebra with integrals. In this paper we will develop a theory of algebraic quantum hypergroups. It is very similar to the theory of algebraic quantum groups, except that the comultiplication…
We introduce a quantum double quasitriangular quasi-Hopf algebra $D(H)$ associated to any quasi-Hopf algebra $H$. The algebra structure is a cocycle double cross product. We use categorical reconstruction methods. As an example, we recover…
C-loops are loops satisfying the identity $x(y\cdot yz) = (xy\cdot y)z$. We develop the theory of extensions of C-loops, and characterize all nuclear extensions provided the nucleus is an abelian group. C-loops with central squares have…
In this work we present a principle which says that quasimorphisms can be obtained via "local data" of the group action on certain appropriate spaces. In a rough manner the principle says that instead of starting with a given group and try…