Related papers: Cryptographic multilinear maps using pro-p groups
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…
In this paper we use the nonrepresentable ring E_p(m)to introduce public key cryptosystems in noncommutative settings and based on the Semigrouop Action Problem and the Decomposition Problem respectively.
A new proposal for group key exchange is introduced which proves to be both efficient and secure and compares favorably with state of the art protocols.
In this expository article we present an overview of the current state-of-the-art in post-quantum group-based cryptography. We describe several families of groups that have been proposed as platforms, with special emphasis in polycyclic…
Post-quantum cryptography is essential for securing digital communications against threats posed by quantum computers. Re-searchers have focused on developing algorithms that can withstand attacks from both classical and quantum computers,…
We discuss the use of elliptic curves in cryptography on high-dimensional surfaces. In particular, instead of a Diffie-Hellman key exchange protocol written in the form of a bi-dimensional row, where the elements are made up with 256 bits,…
The Diffie-Hellman key exchange plays a crucial role in conventional cryptography, as it allows two legitimate users to establish a common, usually ephemeral, secret key. Its security relies on the discrete-logarithm problem, which is…
Akiyama et al. (Int. J. Math. Indust., 2019) proposed a post-quantum key exchange protocol that is based on the hardness of solving a system of multivariate non-linear polynomial equations but has a design strategy different from ordinary…
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…
We study the connectivity of proper power graphs of some family of finite groups including nilpotent groups, groups with a non-trivial partition, and symmetric and alternating groups.
We study a method for key predistribution in a network of $n$ users where pairwise keys are computed by hashing users' IDs along with secret information that has been (pre)distributed to the network users by a trusted entity. A…
Word maps provide a wealth of information about finite groups. We examine the connection between the probability distribution induced by a word map and the underlying structure of a finite group. We show that a finite group is nilpotent if…
A Post-Quantum Key Exchange is needed since the availability of quantum computers that allegedly allow breaking classical algorithms like Diffie-Hellman, El Gamal, RSA and others within a practical amount of time is broadly assumed in…
General cryptographic schemes are presented where keys can be one-time or ephemeral. Processes for key exchange are derived. Public key cryptographic schemes based on the new systems are easily established. Authentication and signature…
After some excitement generated by recently suggested public key exchange protocols due to Anshel-Anshel-Goldfeld and Ko-Lee et al., it is a prevalent opinion now that the conjugacy search problem is unlikely to provide sufficient level of…
The advent of large-scale quantum computers implies that our existing public-key cryptography infrastructure has become insecure. That means that the privacy of many mobile applications involving dynamic peer groups, such as multicast…
Recently, a quantum key exchange protocol has been described, which served as basis for securing an actual bank transaction by means of quantum cryptography [quant-ph/0404115]. Here we show, that the authentication scheme applied is…
In this paper, we investigate the structure of finite group G by assuming that the intersections between p-sylowizers of some p-subgroups of G and $O^p(G)$ are S-permutable in G. We obtain some criterions for p-nilpotency of a finite group.
Existing results on cooperative control of multi-agent systems with unknown control directions require that the underlying topology is either fixed with a strongly connected graph or switching between different strongly connected graphs.…
Ulam asked whether every connected Lie group can be represented on a countable structure. This is known in the linear case. We establish it for the first family of non-linear groups, namely in the nilpotent case. Further context is…