76 research outputs found
Candidate One-Way Functions and One-Way Permutations Based on Quasigroup String Transformations
In this paper we propose a definition and construction of a new family of
one-way candidate functions , where
is an alphabet with elements. Special instances of these functions can have
the additional property to be permutations (i.e. one-way permutations). These
one-way functions have the property that for achieving the security level of
computations in order to invert them, only bits of input are needed.
The construction is based on quasigroup string transformations. Since
quasigroups in general do not have algebraic properties such as associativity,
commutativity, neutral elements, inverting these functions seems to require
exponentially many readings from the lookup table that defines them (a Latin
Square) in order to check the satisfiability for the initial conditions, thus
making them natural candidates for one-way functions.Comment: Submitetd to conferenc
Stream cipher based on quasigroup string transformations in
In this paper we design a stream cipher that uses the algebraic structure of
the multiplicative group \bbbz_p^* (where p is a big prime number used in
ElGamal algorithm), by defining a quasigroup of order and by doing
quasigroup string transformations. The cryptographical strength of the proposed
stream cipher is based on the fact that breaking it would be at least as hard
as solving systems of multivariate polynomial equations modulo big prime number
which is NP-hard problem and there are no known fast randomized or
deterministic algorithms for solving it. Unlikely the speed of known ciphers
that work in \bbbz_p^* for big prime numbers , the speed of this stream
cipher both in encryption and decryption phase is comparable with the fastest
symmetric-key stream ciphers.Comment: Small revisions and added reference
An Explicit Construction of Systematic MDS Codes with Small Sub-packetization for All-Node Repair
An explicit construction of systematic MDS codes, called HashTag+ codes, with
arbitrary sub-packetization level for all-node repair is proposed. It is shown
that even for small sub-packetization levels, HashTag+ codes achieve the
optimal MSR point for repair of any parity node, while the repair bandwidth for
a single systematic node depends on the sub-packetization level. Compared to
other codes in the literature, HashTag+ codes provide from 20% to 40% savings
in the average amount of data accessed and transferred during repair
Expanded Combinatorial Designs as Tool to Model Network Slicing in 5G
The network slice management function (NSMF) in 5G has a task to configure
the network slice instances and to combine network slice subnet instances from
the new-generation radio access network and the core network into an end-to-end
network slice instance. In this paper, we propose a mathematical model for
network slicing based on combinatorial designs such as Latin squares and
rectangles and their conjugate forms. We extend those designs with attributes
that offer different levels of abstraction. For one set of attributes we prove
a stability Lemma for the necessary conditions to reach a stationary ergodic
stage. We also introduce a definition of utilization ratio function and offer
an algorithm for its maximization. Moreover, we provide algorithms that
simulate the work of NSMF with randomized or optimized strategies, and we
report the results of our implementation, experiments and simulations for one
set of attributes.Comment: Accepted for publication in IEEE Acces
Rebuttal to claims in Section 2.1 of the ePrint report 2021/583 Entropoid-based cryptography is group exponentiation in disguise
In the recent ePrint report 2021/583 titled Entropoid-based cryptography is group exponentiation in disguise Lorenz Panny gave a cryptanalysis of the entropoid based instances proposed in our eprint report 2021/469. We acknowledge the correctness of his claims for the concrete instances described in our original report 2021/469.
However, we find that claims for the general applicability of his attack on the general Entropoid framework are misleading. Namely, based on the Theorem 1 in his report, which claims that for every entropic quasigroup , there exists an Abelian group , commuting automorphisms , of , and an element , such that the author infers that \emph{ all instantiations of the entropoid framework should be breakable in polynomial time on a quantum computer. }
There are two misleading parts in these claim: \textbf{1.} It is implicitly assumed that all instantiations of the entropoid framework would define entropic quasigroups - thus fall within the range of algebraic objects addressed by Theorem 1. \emph{We will show a construction of entropic groupoids that are not quasigroups}; \textbf{2.} It is implicitly assumed that finding the group , the commuting automorphisms and and the constant \emph{would be easy for every given entropic operation} and its underlying groupoid . However, the provable existence of a mathematical object \emph{does not guarantee an easy finding} of that object.
Treating the original entropic operation as a one-dimensional entropic operation, we construct multidimensional entropic operations , for and we show that newly constructed operations do not have the properties of that led to the recovery of the automorphism , the commutative operation and the linear isomorphism and its inverse .
We give proof-of-concept implementations in SageMath 9.2 for the new multidimensional entropic operations defined over several basic operations and we show how the non-associative and non-commutative exponentiation works for the key exchange and digital signature schemes originally proposed in report 2021/469
- β¦