Biblio

The main information and communication systems (ICS) effectiveness parameters are: reliability, resiliency, network bandwidth, service quality, profitability and cost, malware protection, information security, etc. Most modern ICS refers to multiuser systems, which implement the most promising method of distributing subscribers (users), namely, the code distribution, at which, subscribers are provided with appropriate forms of discrete sequences (signatures). Since in multiuser systems, channels code division is based on signal difference, then the ICS construction and systems performance indicators are determined by the chosen signals properties. Distributed spectrum technology is the promising direction of information security for telecommunication systems. Currently used data generation and processing methods, as well as the broadband signal classes used as a physical data carrier, are not enough for the necessary level of information security (information secrecy, imitation resistance) as well as noise immunity (impedance reception, structural secrecy) of the necessary (for some ICS applications). In this case, discrete sequences (DS) that are based on nonlinear construction rules and have improved correlation, ensemble and structural properties should be used as DS that extend the spectrum (manipulate carrier frequency). In particular, with the use of such signals as the physical carrier of information or synchronization signals, the time expenditures on the disclosure of the signal structure used are increasing and the setting of "optima", in terms of the counteracting station, obstacles becomes problematic. Complex signals obtained on such sequences basis have structural properties, similar to random (pseudorandom) sequences, as well as necessary correlation and ensemble properties. For designing signals for applications applied for measuring delay time, signal detecting, synchronizing stations and etc, side-lobe levels of autocorrelation function (ACF) minimization is essential. In this paper, the problem of optimizing the synthesis of nonlinear discrete sequences, which have improved ensemble, structural and autocorrelation properties, is formulated and solved. The use of nonlinear discrete signals, which are formed on the basis of such sequences, will provide necessary values for impedance protection, structural and information secrecy of ICS operation. Increased requirements for ICS information security, formation and performance data in terms of internal and external threats (influences), determine objectively existing technical and scientific controversy to be solved is goal of this work.The paper presents the results of solving the actual problem of performance indicators improvements for information and communication systems, in particular secrecy, information security and noise immunity with interfering influences, based on the nonlinear discrete cryptographic signals (CS) new classes synthesis with the necessary properties.

Symmetry ergodic matrices exponentiation (SEME) problem is to find x, given CxMDx, where C and D are the companion matrices of primitive polynomials and M is an invertible matrix over finite field. This paper proposes a new zero-knowledge identification scheme based on SEME problem. It is perfect zero-knowledge for honest verifiers. The scheme could provide a candidate cryptographic primitive in post quantum cryptography. Due to its simplicity and naturalness, low-memory, low-computation costs, the proposed scheme is suitable for using in computationally limited devices for identification such as smart cards.

Multivariate public key cryptosystem acts as a signature system rather than encryption system due to the minus mode used in system. A multivariate encryption system with determinate equations in central map and chaotic shell protection for central map and affine map is proposed in this paper. The outputs of two-dimension chaotic system are discretized on a finite field to disturb the central map and affine map in multivariate cryptosystem. The determined equations meet the shortage of indeterminate equations in minus mode and make the general attack methods are out of tenable condition. The analysis shows the proposed multivariate symmetric encryption system based on chaotic shell is able to resist general attacks.

This paper proposes a novel scheme for RFID anti-counterfeiting by applying bisectional multivariate quadratic equations (BMQE) system into an RF tag data encryption. In the key generation process, arbitrarily choose two matrix sets (denoted as A and B) and a base Rab such that [AB] = λRABT, and generate 2n BMQ polynomials (denoted as p) over finite field Fq. Therefore, (Fq, p) is taken as a public key and (A, B, λ) as a private key. In the encryption process, the EPC code is hashed into a message digest dm. Then dm is padded to d'm which is a non-zero 2n×2n matrix over Fq. With (A, B, λ) and d'm, Sm is formed as an n-vector over F2. Unlike the existing anti-counterfeit scheme, the one we proposed is based on quantum cryptography, thus it is robust enough to resist the existing attacks and has high security.

Elliptic Curve Cryptography (ECC) is a promising public key cryptography, probably takes the place of RSA. Not only ECC uses less memory, key pair generation and signing are considerably faster, but also ECC's key size is less than that of RSA while it achieves the same level of security. However, the magic behind RSA and its friends can be easily explained, is also widely understood, the foundations of ECC are still a mystery to most of us. This paper's aims are to provide detailed mathematical foundations of ECC, especially, the subgroup and its generator (also called base point) formed by one elliptic curve are researched as highlights, because they are very important for practical ECC implementation. The related algorithms and their implementation details are demonstrated, which is useful for the computing devices with restricted resource, such as embedded systems, mobile devices and IoT devices.

Elliptic Curve Cryptosystems are very much delicate to attacks or physical attacks. This paper aims to correctly implementing the fault injection attack against Elliptic Curve Digital Signature Algorithm. More specifically, the proposed algorithm concerns to fault attack which is implemented to sufficiently alter signature against vigilant periodic sequence algorithm that supports the efficient speed up and security perspectives with most prominent and well known scalar multiplication algorithm for ECDSA. The purpose is to properly injecting attack whether any probable countermeasure threatening the pseudo code is determined by the attack model according to the predefined methodologies. We show the results of our experiment with bits acquire from the targeted implementation to determine the reliability of our attack.

We propose a general approach to construct cryptographic significant Boolean functions of (r + 1)m variables based on the additive decomposition F2rm × F2m of the finite field F2(r+1)m, where r ≥ 1 is odd and m ≥ 3. A class of unbalanced functions is constructed first via this approach, which coincides with a variant of the unbalanced class of generalized Tu-Deng functions in the case r = 1. Functions belonging to this class have high algebraic degree, but their algebraic immunity does not exceed m, which is impossible to be optimal when r > 1. By modifying these unbalanced functions, we obtain a class of balanced functions which have optimal algebraic degree and high nonlinearity (shown by a lower bound we prove). These functions have optimal algebraic immunity provided a combinatorial conjecture on binary strings which generalizes the Tu-Deng conjecture is true. Computer investigations show that, at least for small values of number of variables, functions from this class also behave well against fast algebraic attacks.

We propose a general approach to construct cryptographic significant Boolean functions of (r + 1)m variables based on the additive decomposition F2rm × F2m of the finite field F2(r+1)m, where r ≥ 1 is odd and m ≥ 3. A class of unbalanced functions is constructed first via this approach, which coincides with a variant of the unbalanced class of generalized Tu-Deng functions in the case r = 1. Functions belonging to this class have high algebraic degree, but their algebraic immunity does not exceed m, which is impossible to be optimal when r > 1. By modifying these unbalanced functions, we obtain a class of balanced functions which have optimal algebraic degree and high nonlinearity (shown by a lower bound we prove). These functions have optimal algebraic immunity provided a combinatorial conjecture on binary strings which generalizes the Tu-Deng conjecture is true. Computer investigations show that, at least for small values of number of variables, functions from this class also behave well against fast algebraic attacks.