Related papers: Invariant-Based Cryptography: Toward a General Fra…
This paper presents a new encryption scheme called Compact Coding that encodes information in time, phase, and intensity domains, simultaneously. While these approaches have previously been used one at a time, the proposed scheme brings to…
This paper presents a noncommutative theory of symmetric functions, based on the notion of quasi-determinant. We begin with a formal theory, corresponding to the case of symmetric functions in an infinite number of independent variables.…
We introduce the notion of porous invariants for multipath (or branching/nondeterministic) affine loops over the integers; these invariants are not necessarily convex, and can in fact contain infinitely many 'holes'. Nevertheless, we show…
Aperture synthesis observations with full polarisation have long been used to study the magnetic fields of synchrotron emitting sources. Recently proposed closure invariants give us a powerful method for extracting information from measured…
Several cryptographic protocols constructed based on less-known algorithmic problems, such as those in non-commutative groups, group rings, semigroups, etc., which claim quantum security, have been broken through classical reduction methods…
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…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
We develop invariant theory for the quantum group ${\rm U}_q$ of $G_2$ at generic $q$ in the setting of braided symmetric algebras. Let ${\mathcal A}_m$ be the braided symmetric algebra over $m$-copies of the $7$-dimensional simple ${\rm…
We investigate the relation between local unitary symmetries and entanglement invariants of multi-qubit systems. The Hilbert space of such systems can be stratified in terms of states with different types of symmetry. We review the…
We define a new topological invariant of line arrangements in the complex projective plane. This invariant is a root of unity defined under some combinatorial restrictions for arrangements endowed with some special torsion character on the…
This paper studies separating invariants: mappings on $D$ dimensional domains which are invariant to an appropriate group action, and which separate orbits. The motivation for this study comes from the usefulness of separating invariants in…
We give an algorithm allowing to construct bases of local unitary invariants of pure k-qubit states from the knowledge of polynomial covariants of the group of invertible local filtering operations. The simplest invariants obtained in this…
Consider complex semisimple Lie algebras of a given dimension specified by their structure constants. We describe a finite collection of rational functions in the structure constants that form a complete set of invariants: two sets of…
In this paper, we address the problem of secure distributed computation in scenarios where user data is not uniformly distributed, extending existing frameworks that assume uniformity, an assumption that is challenging to enforce in data…
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…
The trend towards delegating data processing to a remote party raises major concerns related to privacy violations for both end-users and service providers. These concerns have attracted the attention of the research community, and several…
In this paper, we evaluate the different fully homomorphic encryption schemes, propose an implementation, and numerically analyze the applicability of gradient descent algorithms to solve quadratic programming in a homomorphic encryption…
An algebraic algorithm is developed for computation of invariants ('generalized Casimir operators') of general Lie algebras over the real or complex number field. Its main tools are the Cartan's method of moving frames and the knowledge of…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
As quantum computing technology continues to advance, post-quantum cryptographic methods capable of resisting quantum attacks have emerged as a critical area of focus. Given the potential vulnerability of existing homomorphic encryption…