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 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 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 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 Improved Asymmetric Cipher Based on Matrix Power Function with Provable Security

Symmetry ◽  
2017 ◽  
Vol 9 (1) ◽  
pp. 9 ◽  
Author(s):  
Eligijus Sakalauskas ◽  
Aleksejus Mihalkovich ◽  
Algimantas Venčkauskas
Keyword(s):  
Power Function ◽  
Provable Security ◽  
Matrix Power

scholarly journals Asymmetric cipher based on MPF and its security parameters evaluation

2012 ◽  
Vol 53 ◽  
Author(s):  
Aleksėjus Mihalkovič ◽  
Eligijus Sakalauskas
Keyword(s):  
Power Function ◽  
Conjugacy Problem ◽  
Matrix Power

The new asymmetric cipher algorithm based on matrix power function and matrix conjugation is presented. This algorithm is some alternative between known algorithms based on conjugacy problem, see e.g. Ko–Lee et al. and Anshel–Anshel–Goldfeld algorithm based on commutator concept. The security parameters are defined and their values are determined.

Improved Asymmetric Cipher Based on Matrix Power Function Resistant to Linear Algebra Attack

Informatica ◽  
2017 ◽  
Vol 28 (3) ◽  
pp. 517-524 ◽  
Author(s):  
Eligijus Sakalauskas ◽  
Aleksejus Mihalkovich
Keyword(s):  
Linear Algebra ◽  
Power Function ◽  
Matrix Power
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