Sigma Identification Protocol Construction Based on MPF Defined over Non-Commuting Platform Group

Mihalkovich, Aleksejus; Lukšys, Kęstutis; Sakalauskas, Eligijus

doi:10.3390/math10152649

Cited by 2 publications

(2 citation statements)

References 16 publications

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“…Previously in [9] we proposed a key exchange protocol where we used 𝕄 as a platform group for the MPF with similar templates for matrices. Also, using the ideas presented in that paper we proposed a sigma identification protocol in [10]. Here we focus on these ideas presented in a more general way, i.e.…”

Section: Mathematical Backgroundmentioning

confidence: 99%

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On the decisional problem based on matrix power function defined over non-commutative group

Mihalkovich,

Zitkevicius

2024

Math. models, eng.

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In this paper, we perform statistical analysis for the decisional problem which is fundamental for the security of the key exchange protocol based on matrix power function. We have proven previously that the considered decisional problem is NP-complete and hence our proposal could potentially be quantum-safe. However, we did not explore the dependence of the complexity of the considered problem on the security parameters. Here we show that for small matrices certain information could be gained from the distribution of the entries of the public key matrices. On the other hand, we show that as the size of the matrices grows, the public key matrices are indistinguishable from truly random matrices.

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Section: Mathematical Backgroundmentioning

confidence: 99%

“…In this paper, we consider one of such problems which is fundamental for the security of the cryptographic protocols presented in [9] and [10]. The objective of this problem is to recover the secret key of the legitimate user based on his public key [9].…”

Section: Introductionmentioning

confidence: 99%

On the decisional problem based on matrix power function defined over non-commutative group

Mihalkovich,

Zitkevicius

2024

Math. models, eng.

Self Cite

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The security analysis of the key exchange protocol based on the matrix power function defined over a family of non-commuting groups

Mihalkovich,

Zitkevicius,

Sakalauskas

2024

MATH

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<p>In this paper, we revisited the previously proposed key exchange protocol based on the matrix power function. We prove that the entries of the public key matrices of both parties of the protocol are uniform. Using this result we defined a security game for our protocol and show that the malicious attacker cannot gain any significant advantage in winning this game by applying faithful representation or the linearization approaches. Moreover, we showed that the shared key is computationally indistinguishable from the imitation key if the security parameters are properly chosen.</p>

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Sigma Identification Protocol Construction Based on MPF Defined over Non-Commuting Platform Group

Cited by 2 publications

References 16 publications

On the decisional problem based on matrix power function defined over non-commutative group

On the decisional problem based on matrix power function defined over non-commutative group

The security analysis of the key exchange protocol based on the matrix power function defined over a family of non-commuting groups

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