scholarly journals Perfectly Secure Shannon Cipher Construction Based on the Matrix Power Function

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 860
Author(s):  
Eligijus Sakalauskas ◽  
Lina Dindienė ◽  
Aušrys Kilčiauskas ◽  
Kȩstutis Lukšys
Keyword(s):  
Power Function ◽  
Block Cipher ◽  
Data Block ◽  
Theoretical Level ◽  
Complete Problem ◽  
The Matrix ◽  
Matrix Power ◽  
Shannon Cipher ◽  
One Way Function ◽  
Selection Of

A Shannon cipher can be used as a building block for the block cipher construction if it is considered as one data block cipher. It has been proved that a Shannon cipher based on a matrix power function (MPF) is perfectly secure. This property was obtained by the special selection of algebraic structures to define the MPF. In an earlier paper we demonstrated, that certain MPF can be treated as a conjectured one-way function. This property is important since finding the inverse of a one-way function is related to an N P -complete problem. The obtained results of perfect security on a theoretical level coincide with the N P -completeness notion due to the well known Yao theorem. The proposed cipher does not need multiple rounds for the encryption of one data block and hence can be effectively parallelized since operations with matrices allow this effective parallelization.

scholarly journals MPF Problem over Modified Medial Semigroup Is NP-Complete

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 571 ◽  
Author(s):  
Eligijus Sakalauskas ◽  
Aleksejus Mihalkovich
Keyword(s):  
Power Function ◽  
Polynomial Time ◽  
Cryptographic Protocols ◽  
Binary Field ◽  
Dual Interpretation ◽  
Np Complete ◽  
Matrix Power ◽  
Necessary Constraints ◽  
One Way Function ◽  
Polynomial Time Reduction

This paper is a continuation of our previous publication of enhanced matrix power function (MPF) as a conjectured one-way function. We are considering a problem introduced in our previous paper and prove that tis problem is NP-Complete. The proof is based on the dual interpretation of well known multivariate quadratic (MQ) problem defined over the binary field as a system of MQ equations, and as a general satisfiability (GSAT) problem. Due to this interpretation the necessary constraints to MPF function for cryptographic protocols construction can be added to initial GSAT problem. Then it is proved that obtained GSAT problem is NP-Complete using Schaefer dichotomy theorem. Referencing to this result, GSAT problem by polynomial-time reduction is reduced to the sub-problem of enhanced MPF, hence the latter is NP-Complete as well.

scholarly journals Security analysis of key agreement protocol based on matrix power function

2012 ◽  
Vol 53 ◽  
Author(s):  
Paulius Vitkus ◽  
Eligijus Sakalauskas
Keyword(s):  
Power Function ◽  
Key Agreement ◽  
Security Analysis ◽  
Braid Groups ◽  
Quadratic Problem ◽  
Key Agreement Protocol ◽  
Np Complete ◽  
Matrix Power ◽  
The One ◽  
One Way Function

Key agreement protocol (KAP) using Burau braid groups representation and matrix power function (MPF) is analyzed. MPF arguments are Burau representation matrices defined over finite field or ring. It is shown that KAP security relies on the solution of matrix multivariate quadratic system of equations over the ring with additional commutation constraints for matrices to be found. We are making a conjecture that proposed KAP is a candidate one-way function since its inversion is related with the solution of known multivariate quadratic problem which is NP-complete over any field. The one of advantages of proposed KAP is its possible effective realization even in restricted computational environments by avoiding arithmetic operations with big integers.

scholarly journals On the associativity property of MPF over M16

2018 ◽  
Vol 59 ◽  
pp. 7-12
Author(s):  
Aleksejus Mihalkovich
Keyword(s):  
Power Function ◽  
Algebraic Structure ◽  
Interesting Problem ◽  
Algebraic Structures ◽  
Basic Properties ◽  
Matrix Power ◽  
One Way Function ◽  
Future Work

The objective of this paper is to find suitable non-commuting algebraic structure to be used as a platform structure in the so-called matrix power function (MPF). We think it is non-trivial and interesting problem could be useful for candidate one-way function (OWF) construction with application in cryptography. Since the cornerstone of OWF construction using non-commuting algebraic structures is the satisfiability of certain associativity conditions, we consider one of the possible choices, i.e. the group M16, explore its basic properties and construct templates to use in our future work. 

scholarly journals Sigma Identification Protocol Construction Based on MPF

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1683
Author(s):  
Eligijus Sakalauskas ◽  
Inga Timofejeva ◽  
Ausrys Kilciauskas
Keyword(s):  
Power Function ◽  
Security Proof ◽  
Np Complete ◽  
Matrix Power ◽  
One Way Function ◽  
Near Semiring

A new sigma identification protocol (SIP) based on matrix power function (MPF) defined over the modified medial platform semigroup and power near-semiring is proposed. It is proved that MPF SIP is resistant against direct and eavesdropping attacks. Our security proof relies on the assumption that MPF defined in the paper is a candidate for one-way function (OWF). Therefore, the corresponding MPF problem is reckoned to be a difficult one. This conjecture is based on the results demonstrated in our previous studies, where a certain kind of MPF problem was proven to be NP-complete.

scholarly journals A Multiple and Multi-Level Substructure Method for the Dynamics of Complex Structures

2021 ◽  
Vol 11 (12) ◽  
pp. 5570
Author(s):  
Binbin Wang ◽  
Jingze Liu ◽  
Zhifu Cao ◽  
Dahai Zhang ◽  
Dong Jiang
Keyword(s):  
Structural Characteristics ◽  
Complex Structure ◽  
Complex Structures ◽  
System Matrix ◽  
Substructure Method ◽  
Residual Structure ◽  
The Matrix ◽  
Multi Level ◽  
Fixed Interface ◽  
Selection Of

Based on the fixed interface component mode synthesis, a multiple and multi-level substructure method for the modeling of complex structures is proposed in this paper. Firstly, the residual structure is selected according to the structural characteristics of the assembled complex structure. Secondly, according to the assembly relationship, the parts assembled with the residual structure are divided into a group of substructures, which are named the first-level substructure, the parts assembled with the first-level substructure are divided into a second-level substructure, and consequently the multi-level substructure model is established. Next, the substructures are dynamically condensed and assembled on the boundary of the residual structure. Finally, the substructure system matrix, which is replicated from the matrix of repeated physical geometry, is obtained by preserving the main modes and the constrained modes and the system matrix of the last level of the substructure is assembled to the upper level of the substructure, one level up, until it is assembled in the residual structure. In this paper, an assembly structure with three panels and a gear box is adopted to verify the method by simulation and a rotor is used to experimentally verify the method. The results show that the proposed multiple and multi-level substructure modeling method is not unique to the selection of residual structures, and different classification methods do not affect the calculation accuracy. The selection of 50% external nodes can further improve the analysis efficiency while ensuring the calculation accuracy.

Plasma Spraying of Self-Lubricating Cr2O3-CaF2 Coatings

1997 ◽  
Author(s):  
F. Vos ◽  
L. Delaey ◽  
M. De Bonte ◽  
L. Froyen
Keyword(s):  
Plasma Spraying ◽  
Matrix Material ◽  
Production Method ◽  
Atmospheric Plasma ◽  
Spray Parameters ◽  
The Matrix ◽  
Preparation Step ◽  
Plasma Sprayed ◽  
The Relationship ◽  
Selection Of

Abstract Results are presented of a project analysing the relationship between the production parameters of plasma sprayed self-lubricating Cr2O3-CaF2 coatings and their structural, wear and lubricating properties. The production method consists of a preparation step where a powder blend of the matrix material (Cr203) and solid lubricant (CaF2) is agglomerated, followed by atmospheric plasma spraying (APS) of the agglomerates. Selection of the most appropriate agglomeration and plasma spray parameters as well as the microstructure of the coatings will be discussed.

scholarly journals Improvement of the Impact Properties of Composite Laminates by Means of Nano-Modification of the Matrix—A Review

2018 ◽  
Vol 8 (12) ◽  
pp. 2406 ◽  
Author(s):  
Hamed Saghafi ◽  
Mohamad Fotouhi ◽  
Giangiacomo Minak
Keyword(s):  
Composite Laminates ◽  
Cost Effective ◽  
Careful Consideration ◽  
Impact Performance ◽  
Compression After Impact ◽  
The Matrix ◽  
The Right ◽  
2D And 3D ◽  
The Impact ◽  
Selection Of

This paper reviews recent works on the application of nanofibers and nanoparticle reinforcements to enhance the interlaminar fracture toughness, to reduce the impact induced damage and to improve the compression after impact performance of fiber reinforced composites with brittle thermosetting resins. The nanofibers have been mainly used as mats embedded between plies of laminated composites, whereas the nanoparticles have been used in 0D, 1D, 2D, and 3D dimensional patterns to reinforce the matrix and consequently the composite. The reinforcement mechanisms are presented, and a comparison is done between the different papers in the literature. This review shows that in order to have an efficient reinforcement effect, careful consideration is required in the manufacturing, materials selection and reinforcement content and percentage. The selection of the right parameters can provide a tough and impact resistant composite with cost effective reinforcements.

Nucleation & Growth of Precipitates in Transformations Driven by Diffusion

1997 ◽  
Vol 481 ◽  
Author(s):  
N. Clavaguera ◽  
M.T. Clavaguera-Mora
Keyword(s):  
Free Energy ◽  
Calculated Data ◽  
Energy Difference ◽  
Calphad Approach ◽  
Free Energies ◽  
Free Energy Difference ◽  
Diffusion Controlled ◽  
The Matrix ◽  
Rapidly Solidified ◽  
Selection Of

ABSTRACTA theoretical analysis of the transformation kinetics which accounts for nuclei, either prequenched or created homogeneously, and whose growth are controlled by diffusion is presented. The change in growth habit intervening during the transformation is analysed in terms of the evolution of the free energy difference between the precipitate and the matrix at the interface, ΔG1. In the Avrami formalism, this quantity accounts for the competition between interface and diffusion controlled growth whereas the nucleation events are driven by the free energy difference between the precipitate and the bulk matrix. Competition and selection of precipitate phases in highly undercooled melts using the CALPHAD approach for the evaluation of the free energies and the changes in diffusivity with concentration are analysed. Experimental vs. calculated data are discussed in some rapidly solidified metallic systems.

scholarly journals Identification, Extraction, and Preparation of Reliable Lime Samples for 14C Dating of Plasters and Mortars with the “Pure Lime Lumps” Technique

Radiocarbon ◽  
2012 ◽  
Vol 54 (3-4) ◽  
pp. 933-942 ◽  
Author(s):  
Giovanni L A Pesce ◽  
Richard J Ball ◽  
Gianluca Quarta ◽  
Lucio Calcagnile
Keyword(s):  
Case Studies ◽  
Radiocarbon Dating ◽  
Historic Sites ◽  
14C Dating ◽  
Relative Simplicity ◽  
Lime Mortars ◽  
The Matrix ◽  
The 1960S ◽  
Selection Of ◽  
Contamination Problem

Radiocarbon dating was first applied to historic lime mortars during the 1960s. However, despite the relative simplicity of the technique in principle, a number of subsequent studies have highlighted important aspects that should be considered. One of the most significant of these challenges arises from sample contamination by carbonaceous substances such as incompletely burnt limestone and aggregates of fossil origin containing “dead” 14C. More recent studies have shown that in the majority of old lime-based mixtures the contamination problem can be avoided through selection of pure lime lumps. These particular types of lumps are believed to originate from areas where the lime is incompletely mixed with the aggregate. It has been demonstrated that even a single lime lump can provide sufficient material for a 14C date of the mortar from which the lump was taken (Pesce et al. 2009). This paper describes the practical challenges associated with location, extraction, and preparation of 4 lime lumps extracted from 2 new sites for 14C dating. These include distinguishing the lime lumps from other lumps present in the matrix and the removal of material surrounding the lime lump. The coherence of 14C dating with other archaeological information on the chronology of historic sites is highlighted through case studies.

Sign in / Sign up

Export Citation Format

Share Document