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.

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.

In this paper we present a theoretical implementation analysis of new matrix power cipher in embedded systems. This cipher is based on the matrix power function. This allows achieving required security and efficiency while minimizing the number of rounds. In this paper we briefly overview the matrix power and the whole cipher, discuss the security assumptions and specify the limits of security parameters. The speed of the cipher was estimated by counting operations considering the usage of look-up tables and realization in 8bits AVR microcontrollers. Theoretical speed of the matrix power cipher was compared with the fastest known AES-128 implementations. Our cipher performs faster than AES-128 when encryption and decryption are considered together. Bibl. 11, tabl. 1 (in English; abstracts in English and Lithuanian). K. Lukšys, E. Sakalauskas, A. Venčkauskas. Matricinio laipsnio šifro realizacijos įterptinėse sistemose analizė // Elektronika ir elektrotechnika. -Kaunas: Technologija, 2012. -Nr. 2(118). -P. 95-98.Šiame straipsnyje pateikiama naujo matricinio laipsnio šifro realizavimo įterptinėse sistemose teorinė analizė. Šio šifro pagrindą sudaro matricinio laipsnio funkcija. Tai leidžia minimizuojant šifro iteracijų skaičių pasiekti norimą saugumą ir efektyvumą. Straipsnyje trumpai apžvelgiama matricinio laipsnio funkcija ir visas šifras, aptariamos saugumo prielaidos ir pateikiamos saugumo parametrų ribos. Šifro greitis įvertinamas nustatant operacijų skaičius, atsižvelgiant į peržvalgos lentelių naudojimą ir realizaciją 8 bitų AVR tipo mikroprocesoriuose. Teorinis matricinio laipsnio šifro greitis palyginamas su greičiausiomis žinomomis AES-128 šifro realizacijomis. Kartu vertinant užšifravimą ir iššifravimą, mūsų siūlomu šifru šifruojama greičiau negu AES-128 šifru. Bibl. 11, lent. 1 (anglų kalba; santraukos anglų ir lietuvių k.).

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The pension landscape is changing due to the market situation, and technological change has enabled financial innovations. Pension savers usually seek financial advice to make a personalised decision in selecting the right pension fund for them. As such, decision rules based on the assumed risk profile of the decision maker could be generated by making use of stochastic dominance (SD). In the paper, the second-pillar pension funds operating in Lithuania and Slovakia are analysed according to SD rules. The importance of the distributional assumption is explored while comparing the results of empirical, student-t, Hyperbolic and Normal Inverse Gaussian distributions to generate SD-based rules that could be integrated into an advisory solution. Moreover, due to the differences in SD results under different distributional assumptions, a new SD ratio is proposed that condenses the dominance-based relations for all considered dominance orders and probability distributions. The empirical results indicate that this new SD ratio efficiently characterises not only the preference of each fund individually but also of a group of funds with the same attributes, thus enabling multi-risk and multi-country comparisons.