Related papers: QRKE: Extensions
In this survey, we describe a general key exchange protocol based on semidirect product of (semi)groups (more specifically, on extensions of (semi)groups by automorphisms), and then focus on practical instances of this general idea. This…
The kernel polynomial method based on Jacobi polynomials $P_n^{\alpha,\beta}(x)$ is proposed. The optimal-resolution positivity-preserving kernels and the corresponding damping factors are obtained. The results provide a generalization of…
Quantum Key Exchange (QKE, also known as Quantum Key Distribution or QKD) allows communicating parties to securely establish cryptographic keys. It is a well-established fact that all QKE protocols require that the parties have access to an…
We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev…
After 38 years of birthday Diffie-Hellman Key Exchange (DHKE), there are many proposed improvements in the DHKE protocol to encounter modern security issues. This protocol seems quite simple to be implemented, but it can be vulnerable to…
The paper is devoted to the problem of multivariate polynomial interpolation and its application to quantum secret sharing. We show that using quantum Fourier transform one can produce the protocol for quantum secret sharing distribution.
Should quantum computers become available, they will reduce the effective key length of basic secret-key primitives, such as blockciphers. To address this we will either need to use blockciphers which inherently have longer keys or use…
In this paper we consider cryptographic applications of the arithmetic on the hyperoctahedral group. On an appropriate subgroup of the latter, we particularly propose to construct public key cryptosystems based on the discrete logarithm.…
In this paper we show that certain special cases of the hidden subgroup problem can be solved in polynomial time by a quantum algorithm. These special cases involve finding hidden normal subgroups of solvable groups and permutation groups,…
We use matrices over bit strings as platforms for Diffie-Hellman-like public key exchange protocols. When multiplying matrices like that, we use Boolean OR operation on bit strings in place of addition and Boolean AND operation in place of…
We consider a key exchange procedure whose security is based on the difficulty of computing discrete logarithms in a group, and where exponentiation is hidden by a conjugation. We give a platform-dependent cryptanalysis of this protocol.…
Advances in quantum computing make Shor's algorithm for factorising numbers ever more tractable. This threatens the security of any cryptographic system which often relies on the difficulty of factorisation. It also threatens methods based…
All instances of the semidirect key exchange protocol, a generalisation of the famous Diffie-Hellman key exchange protocol, satisfy the so-called "telescoping equality"; in some cases, this equality has been used to construct an attack. In…
We employ the generalized Remez algorithm, initially suggested by P. T. P. Tang, to perform an experimental study of Chebyshev polynomials in the complex plane. Our focus lies particularly on the examination of their norms and zeros. What…
Currently there is an active Post-Quantum Cryptography (PQC) solutions search, which attempts to find cryptographic protocols resistant to attacks by means of for instance Shor polynomial time algorithm for numerical field problems like…
In all existing protocols of private communication with encryption and decryption, the pre-shared key can be used for only one time. We give a deterministic quantum key expansion protocol where the pre-shared key can be recycled. Our…
This paper presents a novel post-quantum cryptosystem based on high-memory masked convolutional codes. Unlike conventional code-based schemes that rely on block codes with fixed dimensions and limited error-correction capability, our…
Quantum key distribution (QKD) enables two parties to establish a secret key over a potentially hostile channel by exchanging photonic quantum states, relying on the fact that it is impossible for an eavesdropper to tap the quantum channel…
In this paper we generalize the Ritt-Kolchin method of characteristic sets and the classical Gr\"obner basis technique to prove the existence and obtain methods of computation of multivariate difference-differential dimension polynomials…
In this work we demonstrate that the q-numbers and their two-parameter generalization, the q,p-numbers, can be used to obtain some polynomial invariants for torus knots and links. First, we show that the q-numbers, which are closely…