Asymmetric cipher based on MPF and its security parameters evaluation

Abstract

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

“…However, it is shown in Liu et al (2016), that this asymmetric key exchange is vulnerable to a certain linear algebra attack. Furthermore, their idea also holds in case of asymmetric encryption proposed in Mihalkovich and Sakalauskas (2012).…”

“…The essential modification of the protocol suggested in Mihalkovich and Sakalauskas (2012) is an extra matrix Z 2 , which is published as a public parameter. In the next section we will show that this improvement of the initial protocol is enough to protect secret key from linear algebra cryptanalysis.…”

“…This means that no additional co-processors have to be used to perform actions with large elements as opposed to RSA encryption or elliptic curves cryptography. Examples of these protocols can be found in Sakalauskas and Luksys (2012), Sakalauskas et al (2008), Mihalkovich and Sakalauskas (2012), Sakalauskas and Mihalkovich (2014). The constructed protocols belong to non-commuting cryptography, which currently is of special interest to researchers.…”

“…where E is a matrix representing the function value. In this paper we mainly focus on papers (Sakalauskas et al, 2008;Mihalkovich and Sakalauskas, 2012;Sakalauskas et al, 2017) and (Liu et al, 2016). In the latter paper authors present an attack based on linear algebra, which can be applied to protocols, presented in Sakalauskas et al (2008) and Mihalkovich and Sakalauskas (2012) to break them in polynomial time.…”

“…In this paper we mainly focus on papers (Sakalauskas et al, 2008;Mihalkovich and Sakalauskas, 2012;Sakalauskas et al, 2017) and (Liu et al, 2016). In the latter paper authors present an attack based on linear algebra, which can be applied to protocols, presented in Sakalauskas et al (2008) and Mihalkovich and Sakalauskas (2012) to break them in polynomial time. Our aim is to prove that the latest version of the so-called matrix power asymmetric cipher (MPAC), presented in Sakalauskas et al (2017), is resistant to the declared attack, thus repairing the flaw found.…”