Eligijus Sakalauskas

THE MULTIVARIATE QUADRATIC POWER PROBLEM OVER ZN IS NP- COMPLETE

New NP-complete problem, named as multivariate quadratic power (MQP) problem, is presented. It is based on solution of multivariate quadratic power system of equations over the semigroup Z n , denoted by MQP( Z n ), where n is positive integer. Two sequential polynomial-time reductions from known NP-complete multivariate quadratic (MQ) problem over the field Z 2 , i.e. MQ( Z 2 ) to MQP( Z n ) are constructed. It is proved that certain restricted MQP( Z n ) problem over some subgroup of Z n is equivalent to MQ( Z 2 ) problem. This allow us to prove that MQP( Z n ) is NP-complete also. MQP problem is linked to some author’s previously declared matrix power function (MPF) used for several cryptographic protocols construction. Obtained NP-complete problem will be used to create new candidate one-way function (OWF) based on MPF for new cryptographic primitives’ construction. DOI: http://dx.doi.org/10.5755/j01.itc.41.1.821

Improved Asymmetric Cipher Based on Matrix Power Function with Provable Security

The improved version of the author’s previously declared asymmetric cipher protocol based on matrix power function (MPF) is presented. Proposed modification avoids discrete logarithm attack (DLA) which could be applied to the previously declared protocol. This attack allows us to transform the initial system of MPF equations to so-called matrix multivariate quadratic (MMQ) system of equations, which is a system representing a subclass of multivariate quadratic (MQ) systems of equations. We are making a conjecture that avoidance of DLA in protocol, presented here, should increase its security, since an attempt to solve the initial system of MPF equations would appear to be no less complex than solving the system of MMQ equations. No algorithms are known to solve such a system of equations. Security parameters and their secure values are defined. Security analysis against chosen plaintext attack (CPA) and chosen ciphertext attack (CCA) is presented. Measures taken to prevent DLA attack increase the security of this protocol with respect to the previously declated protocol.

A Simple Off-line E-Cash System with Observers

A simple and transparent mobile e-cash system with observers is presented. Observers are cryptographic bank chips inserted in customer’s payment device, e.g. smart phone. System satisfies e-cash divisibility, anonymity, off-line payments, transferability and double-spending prevention requirements. Proposed e-cash system is based on two well-known cryptographic primitives, namely ElGamal encryption and Schnorr identification protocols, therefore it can be named as simple and transparent in the sense of security considerations. In Schnorr identification scheme Brand’s double spending prevention protocol is implemented during payment protocol. The use of observers allows to avoid e-cash data growing in size as it takes place in all divisible, anonymous, off-line and transferable e-cash systems. To increase observer’s security and avoid their clonability the use of physical unclonable function in the chip of observer is proposed. DOI: http://dx.doi.org/10.5755/j01.itc.47.1.18021

Enhanced Matrix Power Function for Cryptographic Primitive Construction

A new enhanced matrix power function (MPF) is presented for the construction of cryptographic primitives. According to the definition in previously published papers, an MPF is an action of two matrices powering some base matrix on the left and right. The MPF inversion equations, corresponding to the MPF problem, are derived and have some structural similarity with classical multivariate quadratic (MQ) problem equations. Unlike the MQ problem, the MPF problem seems to be more complicated, since its equations are not defined over the field, but are represented as left–right action of two matrices defined over the infinite near-semiring on the matrix defined over the certain infinite, additive, noncommuting semigroup. The main results are the following: (1) the proposition of infinite, nonsymmetric, and noncommuting algebraic structures for the construction of the enhanced MPF, satisfying associativity conditions, which are necessary for cryptographic applications; (2) the proof that MPF inversion is polynomially equivalent to the solution of a certain kind of generalized multivariate quadratic (MQ) problem which can be reckoned as hard; (3) the estimation of the effectiveness of direct MPF value computation; and (4) the presentation of preliminary security analysis, the determination of the security parameter, and specification of its secure value. These results allow us to make a conjecture that enhanced MPF can be a candidate one-way function (OWF), since the effective (polynomial-time) inversion algorithm for it is not yet known. An example of the application of the proposed MPF for the Key Agreement Protocol (KAP) is presented. Since the direct MPF value is computed effectively, the proposed MPF is suitable for the realization of cryptographic protocols in devices with restricted computation resources.

Computational resources for mobile E-wallet system with observers

The next generation of individual payment systems that will replace traditional smart cards will be mobile devices supplied with e-wallet functions. The spread of such e- wallet systems will depend on their security, functionality, ease of use and the effectiveness of realization. This paper proposes an effective realization of e-wallet system, providing e-cash divisibility, off-line payment and deposit options as well as purchasers anonymity against the vendor and satisfying general electronic payment security requirements of double spending prevention, unforgeability as well as unclonability of purchasers identity. The latter is achieved through the implementation of banks tamper resistant hardware agent, known as observer, provided with physically unclonable function (PUF), capable of yielding a unique unclonable code (UUC), in users mobile device. The estimation of the necessary computational resources in the usage of the proposed mobile e- wallet system is presented in order to determine whether the proposal is worth the computation cost.

On Methodology of E-wallet Construction for Partially Off-line Payment System

We propose a methodology for the construction of e-wallet with off-line divisible e-cash, with such properties as anonymity against vendor and full traceability from bank. Since this system is fully controlled by bank from the issuance of e-money to e-cash deposit, the prevention of an overpayment and the detection of a dishonest user are provided.

New integral quality of TV service criterion construction based on quality of experience statistical estimation

With the rapid development of DTV methods and tools, preconditions are being made for the creation and implementation of new services. New services can be spread using various technologies, such as Web and DVB. However, the qualitative parameters of services for individual technologies are different. As it is known, the qualitative parameters for digital TV are regulated by the ITU and ETSI recommendations. However, rapid development of different technologies integration leads to creation of common criterions for quality of service and metrics for their evaluation. It is known that the qualitative parameters for audio/video content consist of two components - objective and subjective. DTV operators are faced with a difficult task - how to match the requirements of broadcast parameters to ensure the required quality of experience (QoE) to the end user optimizing transmission parameters related to quality of service (QoS). The aim of this work is to create an integral and statistically confident subjective criterion representing QoE, which depends on any set of objective parameters related with different technologies and representing QoS.

Matrix Power Cipher

A new symmetric matrix power cipher is presented. The main component of this cipher is the key dependent S-box based on the matrix power function (MPF). We give the details of the cipher and explain how MPF can be used in multiple rounds. The matrix power cipher due to its special algebraic structure can be highly parallelized and each round can be separated up to m 2 distinct threads, where m is an order of square matrices used in the cipher. A security analysis and main security parameters are also provided. DOI: http://dx.doi.org/10.5755/j01.itc.41.4.820