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

Sakalauskas, Eligijus; Mihalkovich, Aleksejus

doi:10.15388/informatica.2017.142

Cited by 9 publications

(6 citation statements)

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“…The authors of the latter paper showed that the system of matrix equations used to find the private key of Alice (or Bob) can be transformed to a system of linear equations and hence mentioned protocols can be broken in polynomial time. Eventually, we were able to evade this attack in our paper [21]. We also performed an investigation of public parameter generation issues in [22].…”

Section: Our Previous Contributions and Novelty Of This Papermentioning

confidence: 97%

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Key Exchange Protocol Defined over a Non-Commuting Group Based on an NP-Complete Decisional Problem

2020

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In this paper we present a cryptographic primitive based on non-commutative cryptography. This primitive is used for key exchange protocol (KEP) construction. We prove that the security of this primitive relies on a nondeterministic polynomial complete (NP-Complete) decisional problem. Recently there are no known quantum cryptanalysis algorithms effectively solving NP-Complete problems. So far, KEPs are widely used in secure communication channel creation, e.g., in hypertext transfer protocol secure (https://) and are based on traditional cryptographic primitives representing commutative cryptography. However, the security of these protocols does not rely on NP-Complete problems and hence, according to P. W. Shorr, they are vulnerable to quantum cryptanalysis. We use one of seven non-commuting groups of order 16 which is not isomorphic to any other group to define a platform group for a key exchange protocol based on previously considered matrix power function (MPF). By investigating basic properties on the group M16 and their implementation for our goals we fix the order of actions in MPF from left to right. Furthermore, we define a special form of the base matrix and separate templates for left and right power matrices. Using properties of the specified templates and Schaeffer criteria we prove that the security of the proposed key exchange relies on an NP-Complete decisional problem.

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Section: Our Previous Contributions and Novelty Of This Papermentioning

confidence: 97%

“…where L ∈ Mat(Z τ ) is some fixed publicly known matrix. Example with more complicated linear span of matrices was presented in [21]. We also analyzed this linear span in greater detail in [22].…”

Section: Description Of Mpf and Its Basic Propertiesmentioning

confidence: 99%

Key Exchange Protocol Defined over a Non-Commuting Group Based on an NP-Complete Decisional Problem

2020

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“…The authors of [16] also suggested some improvements of our protocols to resist the proposed attack. In [7] we fixed this flaw for the asymmetric encryption protocol, presented in [1]. The intriguing idea was to extend MPF construction to non-commutative algebraic structures, namely S and R, hence expecting higher complexity of MPF problem and achieving a higher potential security for the construction of cryptographic primitives.…”

Section: Remarkmentioning

confidence: 99%

“…Some cryptographic primitives were built on the basis that MPF is a conjectured OWF in [1][2][3][4][5]. Furthermore, some results were published considering the security of presented primitives in [6][7][8]. The security of these primitives is based on the complexity of MPF inversion named as MPF problem.…”

Section: Introductionmentioning

confidence: 99%

MPF Problem over Modified Medial Semigroup Is NP-Complete

Sakalauskas

Mihalkovich

2018

Symmetry

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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.

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“…Some novel solutions are even improvements of concepts well known to the automobile industry (i.e. car keys) (Grosse and Upadhyay, 2013); others are based asymmetric cyphers (Sakalauskas and Mihalkovich, 2017), on certificateless key encapsulations (Gao et al, 2017;Wu et al, 2018), ID-based cryptography (Meshram et al, 2017), or image-based encryption (Khan et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

System-Assigned Passwords: The Disadvantages of the Strict Password Management Policies

Brumen¹

2020

Informatica

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After Morris and Thompson wrote the first paper on password security in 1979, strict password policies have been enforced to make sure users follow the rules on passwords. Many such policies require users to select and use a system-generated password. The objective of this paper is to analyse the effectiveness of strict password management policies with respect to how users remember system-generated passwords of different textual types-plaintext strings, passphrases, and hybrid graphical-textual PsychoPass passwords. In an experiment, participants were assigned a random string, passphrase, and PsychoPass passwords and had to memorize them. Surprisingly, no one has remembered either the random string or the passphrase, whereas only 10% of the participants remembered their PsychoPass password. The policies where administrators let systems assign passwords to users are not appropriate. Although PsychoPass passwords are easier to remember, the recall rate of any system-assigned password is below the acceptable level. The findings of this study explain that system-assigned strong passwords are inappropriate and put unacceptable memory burden on users.

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

Cited by 9 publications

References 5 publications

Key Exchange Protocol Defined over a Non-Commuting Group Based on an NP-Complete Decisional Problem

Key Exchange Protocol Defined over a Non-Commuting Group Based on an NP-Complete Decisional Problem

MPF Problem over Modified Medial Semigroup Is NP-Complete

System-Assigned Passwords: The Disadvantages of the Strict Password Management Policies

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