On the associativity property of MPF over M16

Mihalkovich, Aleksejus

doi:10.15388/lmr.a.2018.02

Cited by 5 publications

(9 citation statements)

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“…In this paper we recall one of the possible non-commuting groups to be used as a platform for MPF. Previous investigation of the properties of the MPF defined over the group M 16 presented in [25] has shown that we can construct cryptographic primitives using this group as a platform. Due to the properties of M 16 presented in that paper, we have to define templates for private session parameters.…”

Section: Our Previous Contributions and Novelty Of This Papermentioning

confidence: 99%

“…Nevertheless, we can use some facts from our previous research to establish a working key exchange protocol between Alice and Bob. To achieve this goal, we have previously considered the basic properties of the MPF defined over M 16 in [25]. Relying on the obtained conclusions and a specified form of the base matrix W we defined several possible templates for power matrices mainly focusing on the left side of (8).…”

Section: Description Of Mpf and Its Basic Propertiesmentioning

confidence: 99%

“…The idea we shall use for constructing a key exchange protocol is based on the properties of the M 16 previously discussed in [25]. Our goal is to remove the non-commuting entries of the matrix W by calculating the public session parameter of the form (6), where X, Y are two power matrices defined over Z 8 .…”

Section: Definition Of Publicly Known Datamentioning

confidence: 99%

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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: 99%

Section: Description Of Mpf and Its Basic Propertiesmentioning

confidence: 99%

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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 consider a general form of one of the previously explored noncommuting groups, namely the group M 16 (Mihalkovich, 2018;Mihalkovich et al, 2020). We define this general form in the next section and present some important facts useful for our goals.…”

Section: Our Contributionsmentioning

confidence: 99%

“…The proof of this fact in the special case of M 16 was presented in Mihalkovich (2018). Since the idea of the proof remains the same, we omit it to shorten the paper.…”

Section: Mathematical Backgroundmentioning

confidence: 99%

CBC Mode of MPF Based Shannon Cipher Defined Over a Non-Commuting Platform Group

Mihalkovich¹,

Levinskas²,

Dindienė³

et al. 2022

Informatica

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Commonly modern symmetric encryption schemes (e.g. AES) use rather simple actions repeated many times by defining several rounds to calculate the ciphertext. An idea we previously offered was to trade these multiple repeats for one non-linear operation. Recently we proposed a perfectly secure symmetric encryption scheme based on the matrix power function (MPF). However, the platform group we used was commuting. In this paper, we use a non-commuting group whose cardinality is a power of 2 as a platform for MPF. Due to the convenient cardinality value, our scheme is more suitable for practical implementation. Moreover, due to the non-commuting nature of the platform group, some “natural” constraints on the power matrices arise. We think that this fact complicates the cryptanalysis of our proposal. We demonstrate that the newly defined symmetric cipher possesses are perfectly secure as they were previously done for the commuting platform group. Furthermore, we show that the same secret key can be used multiple times to encrypt several plaintexts without loss of security. Relying on the proven properties we construct the cipher block chaining mode of the initial cipher and show that it can withstand an adaptive chosen plaintext attack.

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Investigation of the Statistical Properties of the CTR Mode of the Block Cipher Based on MPF

Levinskas,

Mihalkovich,

Dindiene

et al. 2024

Communications in Computer and Information Science

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On the associativity property of MPF over M16

Cited by 5 publications

References 0 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

CBC Mode of MPF Based Shannon Cipher Defined Over a Non-Commuting Platform Group

Investigation of the Statistical Properties of the CTR Mode of the Block Cipher Based on MPF

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