Key Agreement Protocol Using Elliptic Curve Matrix Power Function

* Work is partially supported by the Lithuanian State Science and Studies Foundation.

Complex Hyperbolic Surfaces of Abelian Type

2000 Mathematics Subject Classification: 11G15, 11G18, 14H52, 14J25, 32L07.

Improved Cryptoanalysis of the Self-shrinking P-adic Cryptographic Generator

The Self-shrinking p-adic cryptographic generator (SSPCG) is a fast software stream cipher. Improved cryptoanalysis of the SSPCG is introduced. This cryptoanalysis makes more precise the length of the period of the generator. The linear complexity and the cryptography resistance against most recently used attacks are invesigated. Then we discuss how such attacks can be avoided. The results show that the sequence generated by a SSPCG has a large period, large linear complexity and is stable against the cryptographic attacks. This gives the reason to consider the SSPSG as suitable for critical cryptographic applications in stream cipher encryption algorithms.

Cryptographic Primitives with Quasigroup Transformations

AMS Subj. Classification: Primary 20N05, Secondary 94A60

On Graph-Based Cryptography and Symbolic Computations

We have been investigating the cryptographical properties of in nite families of simple graphs of large girth with the special colouring of vertices during the last 10 years. Such families can be used for the development of cryptographical algorithms (on symmetric or public key modes) and turbocodes in error correction theory. Only few families of simple graphs of large unbounded girth and arbitrarily large degree are known. The paper is devoted to the more general theory of directed graphs of large girth and their cryptographical applications. It contains new explicit algebraic constructions of in finite families of such graphs. We show that they can be used for the implementation of secure and very fast symmetric encryption algorithms. The symbolic computations technique allow us to create a public key mode for the encryption scheme based on algebraic graphs.

On a Class of Generalized Elliptic-type Integrals

The aim of this paper is to study a generalized form of elliptic-type integrals which unify and extend various families of elliptic-type integrals studied recently by several authors. In a recent communication [1] we have obtained recurrence relations and asymptotic formula for this generalized elliptic-type integral. Here we shall obtain some more results which are single and multiple integral formulae, differentiation formula, fractional integral and approximations for this class of generalized elliptic-type integrals.

Integer Points Close to a Smooth Curve

∗ This research is partially supported by the Bulgarian National Science Fund under contract MM-403/9

DNA Simulation of Genetic Algorithms: Fitness Computation

* This work has been partially supported by Spanish Project TIC2003-9319-c03-03 “Neural Networks and Networks of Evolutionary Processors”.

Structural Analysis of Contours as the Sequences of the Digital Straight Segments and of the Digital Curve Arcs

Recognition of the object contours in the image as sequences of digital straight segments and/or digital curve arcs is considered in this article. The definitions of digital straight segments and of digital curve arcs are proposed. The methods and programs to recognize the object contours are represented. The algorithm to recognize the digital straight segments is formulated in terms of the growing pyramidal networks taking into account the conceptual model of memory and identification (Rabinovich [4]).

Generalization by Computation Through Memory

Usually, generalization is considered as a function of learning from a set of examples. In present work on the basis of recent neural network assembly memory model (NNAMM), a biologically plausible 'grandmother' model for vision, where each separate memory unit itself can generalize, has been proposed. For such a generalization by computation through memory, analytical formulae and numerical procedure are found to calculate exactly the perfectly learned memory unit's generalization ability. The model's memory has complex hierarchical structure, can be learned from one example by a one-step process, and may be considered as a semi-representational one. A simple binary neural network for bell-shaped tuning is described.

On the Error-Free Computation of Fast Cosine Transform

We extend our previous work into error-free representations of transform basis functions by presenting a novel error-free encoding scheme for the fast implementation of a Linzer-Feig Fast Cosine Transform (FCT) and its inverse. We discuss an 8x8 L-F scaled Discrete Cosine Transform where the architecture uses a new algebraic integer quantization of the 1-D radix-8 DCT that allows the separable computation of a 2-D DCT without any intermediate number representation conversions. The resulting architecture is very regular and reduces latency by 50% compared to a previous error-free design, with virtually the same hardware cost.

Practical, Computation Efficient High-Order Neural Network for Rotation and Shift Invariant Pattern Recognition

In this paper, a modification for the high-order neural network (HONN) is presented. Third order networks are considered for achieving translation, rotation and scale invariant pattern recognition. They require however much storage and computation power for the task. The proposed modified HONN takes into account a priori knowledge of the binary patterns that have to be learned, achieving significant gain in computation time and memory requirements. This modification enables the efficient computation of HONNs for image fields of greater that 100 × 100 pixels without any loss of pattern information.

Experimental Support of Argument-based Syntactic Computation

Linguistic theory, cognitive, information, and mathematical modeling are all useful while we attempt to achieve a better understanding of the Language Faculty (LF). This cross-disciplinary approach will eventually lead to the identification of the key principles applicable in the systems of Natural Language Processing. The present work concentrates on the syntax-semantics interface. We start from recursive definitions and application of optimization principles, and gradually develop a formal model of syntactic operations. The result – a Fibonacci- like syntactic tree – is in fact an argument-based variant of the natural language syntax. This representation (argument-centered model, ACM) is derived by a recursive calculus that generates a mode which connects arguments and expresses relations between them. The reiterative operation assigns primary role to entities as the key components of syntactic structure. We provide experimental evidence in support of the argument-based model. We also show that mental computation of syntax is influenced by the inter-conceptual relations between the images of entities in a semantic space.

Computation of some Differential Operators in Toric Coordinates

Toric coordinates and toric vector field have been introduced in [2]. Let A be an arbitrary vector field. We obtain formulae for the divA, rotA and the Laplace operator in toric coordinates.

On a Class of Elliptic Equations for the N-Laplacian in R^n with One-Sided Exponential Growth

2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30