Related papers: Group-based Cryptography in the Quantum Era
Quantum communication is an important application that derives from the burgeoning field of quantum information and quantum computation. Focusing on secure communication, quantum cryptography has two major directions of development, namely…
The National Institute of Standards and Technology (NIST) has finalized the selection of post-quantum cryptographic (PQC) algorithms for use in the era of quantum computing. Despite their integration into TLS protocol for key establishment…
In this paper we propose cryptosystems based on subgroup distortion in hyperbolic groups. We also include concrete examples of hyperbolic groups as possible platforms.
Quantum computing is currently gaining significant attention, not only from the academic community but also from industry, due to its potential applications across several fields for addressing complex problems. For any practical problem…
Commutativity gadgets provide a technique for lifting classical reductions between constraint satisfaction problems to quantum-sound reductions between the corresponding nonlocal games. We develop a general framework for commutativity…
Group field theories are a new type of field theories over group manifolds and a generalization of matrix models, that have recently attracted much interest in quantum gravity research. They represent a development of and a possible link…
We develop a general approach to finding combinatorial models for cluster algebras. The approach is to construct a labeled graph called a framework. When a framework is constructed with certain properties, the result is a model…
Quantum cryptography can, in principle, provide unconditional security guaranteed by the law of physics only. Here, we survey the theory and practice of the subject and highlight some recent developments.
We consider continuous-variable quantum key distribution with discrete-alphabet encodings. In particular, we study protocols where information is encoded in the phase of displaced coherent (or thermal) states, even though the results can be…
We present a few combinatorial identities which were encountered in our work on the spectral theory of quantum graphs. They establish a new connection between the theory of random matrix ensembles and combinatorics.
Quantum computer is no longer a hypothetical idea. It is the worlds most important technology and there is a race among countries to get supremacy in quantum technology. Its the technology that will reduce the computing time from years to…
Homomorphic encryption is a form of encryption which allows computation to be carried out on the encrypted data without the need for decryption. The success of quantum approaches to related tasks in a delegated computation setting has…
Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs…
We develop a public key cryptosystem based on invariants of diagonalizable groups and investigate properties of such cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of…
Fully homomorphic encryption enables arbitrary computation on encrypted data without decrypting the data. Here it is studied in the context of quantum information processing. Based on universal quantum circuit, we present a quantum fully…
We introduce a quantum automorphism group for hypergraphs, which turns out to generalize the quantum automorphism group of Bichon for classical graphs. Further, we show that our quantum automorphism group acts on hypergraph C*-algebras as…
A family of nonhermitian quantum graphs (exhibiting, presumably, a hidden form of hermiticity) is proposed and studied via their discretization.
The topic of this thesis is the development of a versatile and geometrically motivated differential calculus on non-commutative or quantum spaces, providing powerful but easy-to-use mathematical tools for applications in physics and related…
In a previous paper we generalized the definition of a multilinear map to arbitrary groups and introduced two multiparty key-exchange protocols using nilpotent groups. In this paper we have a closer look at the protocols and will address…
The algebraic formulation of the quantum group gauge models in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider gauge groups taking values in the quantum groups and noncommutative gauge fields…