Related papers: A New Cryptosystem Based on Positive Braids
We present a new algorithm to solve the conjugacy problem in Artin braid groups, which is faster than the one presented by Birman, Ko and Lee. This algorithm can be applied not only to braid groups, but to all Garside groups (which include…
SIDH is a post-quantum key exchange algorithm based on the presumed difficulty of finding isogenies between supersingular elliptic curves. However, SIDH and related cryptosystems also reveal additional information: the restriction of a…
Based on quantum encryption, we present a new idea for quantum public-key cryptography (QPKC) and construct a whole theoretical framework of a QPKC system. We show that the quantum-mechanical nature renders it feasible and reasonable to use…
Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in $SU(2)_k$ quantum group theories, a rich source of examples of non-Abelian anyons such as the…
A During last two decades, there has been a prolific growth in the chaos based image encryption algorithms. Up to an extent these algorithms have been able to provide an alternative to exchange large media files (images and videos) over the…
The development of large quantum computers will have dire consequences for cryptography. Most of the symmetric and asymmetric cryptographic algorithms are vulnerable to quantum algorithms. Grover's search algorithm gives a square root time…
Digital signatures are fundamental cryptographic primitives that ensure the authenticity and integrity of digital documents. In the post-quantum era, classical public key-based signature schemes become vulnerable to brute-force and…
Quantum algorithms have demonstrated promising speed-ups over classical algorithms in the context of computational learning theory - despite the presence of noise. In this work, we give an overview of recent quantum speed-ups, revisit the…
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…
The article explores the creation of a cryptosystem using a halidon group ring of a dihedral group. Due to the non-abelian nature of the group, constructing the cryptosystem is more challenging compared to an abelian group. The logic used…
Today's information society relies on cryptography to achieve security goals such as confidentiality, integrity, authentication, and non-repudiation for digital communications. Here, public-key cryptosystems play a pivotal role to share…
Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum…
We consider actions of a group or a semigroup on a set, which generalize the setup of discrete logarithm based cryptosystems. Such cryptographic group actions have gained increasing attention recently in the context of isogeny-based…
Cryptographic group actions are a leading contender for post-quantum cryptography, and have also been used in the development of quantum cryptographic protocols. In this work, we explore quantum state group actions, which consist of a group…
This article introduces a novel cryptographic paradigm based on nonderived polyadic algebraic structures. Traditional cryptosystems rely on binary operations within groups, rings, or fields, whose well-understood properties can be exploited…
A new approach to quantum cryptography to be called KCQ, keyed communication in quantum noise, is developed on the basis of quantum detection and communication theory for classical information transmission. By the use of a shared secret key…
We propose an authentication scheme where forgery (a.k.a. impersonation) seems infeasible without finding the prover's long-term private key. The latter would follow from solving the conjugacy search problem in the platform (noncommutative)…
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…
Homomorphic encryption is a very useful gradient protection technique used in privacy preserving federated learning. However, existing encrypted federated learning systems need a trusted third party to generate and distribute key pairs to…
A new type of algebras that represent a generalization of both quantum groups and braided groups is defined. These algebras are given by a pair of solutions of the Yang--Baxter equation that satisfy some additional conditions. Several…