147 research outputs found
Full Orbit Sequences in Affine Spaces via Fractional Jumps and Pseudorandom Number Generation
Let be a positive integer. In this paper we provide a general theory to
produce full orbit sequences in the affine -dimensional space over a finite
field. For our construction covers the case of the Inversive Congruential
Generators (ICG). In addition, for we show that the sequences produced
using our construction are easier to compute than ICG sequences. Furthermore,
we prove that they have the same discrepancy bounds as the ones constructed
using the ICG.Comment: To appear in Mathematics of Computatio
An Algebraic System for Constructing Cryptographic Permutations over Finite Fields
In this paper we identify polynomial dynamical systems over finite fields as
the central component of almost all iterative block cipher design strategies
over finite fields. We propose a generalized triangular polynomial dynamical
system (GTDS), and give a generic algebraic definition of iterative (keyed)
permutation using GTDS. Our GTDS-based generic definition is able to describe
widely used and well-known design strategies such as substitution permutation
network (SPN), Feistel network and their variants among others. We show that
the Lai-Massey design strategy for (keyed) permutations is also described by
the GTDS. Our generic algebraic definition of iterative permutation is
particularly useful for instantiating and systematically studying block ciphers
and hash functions over aimed for multiparty computation and
zero-knowledge based cryptographic protocols. Finally, we provide the
discrepancy analysis a technique used to measure the (pseudo-)randomness of a
sequence, for analyzing the randomness of the sequence generated by the generic
permutation or block cipher described by GTDS
Fractional jumps: complete characterisation and an explicit infinite family
In this paper we provide a complete characterisation of transitive fractional
jumps by showing that they can only arise from transitive projective
automorphisms. Furthermore, we prove that such construction is feasible for
arbitrarily large dimension by exhibiting an infinite class of projectively
primitive polynomials whose companion matrix can be used to define a full orbit
sequence over an affine space
A VLSI synthesis of a Reed-Solomon processor for digital communication systems
The Reed-Solomon codes have been widely used in digital communication systems such as computer networks, satellites, VCRs, mobile communications and high- definition television (HDTV), in order to protect digital data against erasures, random and burst errors during transmission. Since the encoding and decoding algorithms for such codes are computationally intensive, special purpose hardware implementations are often required to meet the real time requirements. -- One motivation for this thesis is to investigate and introduce reconfigurable Galois field arithmetic structures which exploit the symmetric properties of available architectures. Another is to design and implement an RS encoder/decoder ASIC which can support a wide family of RS codes. -- An m-programmable Galois field multiplier which uses the standard basis representation of the elements is first introduced. It is then demonstrated that the exponentiator can be used to implement a fast inverter which outperforms the available inverters in GF(2m). Using these basic structures, an ASIC design and synthesis of a reconfigurable Reed-Solomon encoder/decoder processor which implements a large family of RS codes is proposed. The design is parameterized in terms of the block length n, Galois field symbol size m, and error correction capability t for the various RS codes. The design has been captured using the VHDL hardware description language and mapped onto CMOS standard cells available in the 0.8-µm BiCMOS design kits for Cadence and Synopsys tools. The experimental chip contains 218,206 logic gates and supports values of the Galois field symbol size m = 3,4,5,6,7,8 and error correction capability t = 1,2,3, ..., 16. Thus, the block length n is variable from 7 to 255. Error correction t and Galois field symbol size m are pin-selectable. -- Since low design complexity and high throughput are desired in the VLSI chip, the algebraic decoding technique has been investigated instead of the time or transform domain. The encoder uses a self-reciprocal generator polynomial which structures the codewords in a systematic form. At the beginning of the decoding process, received words are initially stored in the first-in-first-out (FIFO) buffer as they enter the syndrome module. The Berlekemp-Massey algorithm is used to determine both the error locator and error evaluator polynomials. The Chien Search and Forney's algorithms operate sequentially to solve for the error locations and error values respectively. The error values are exclusive or-ed with the buffered messages in order to correct the errors, as the processed data leave the chip
Applications of MATLAB in Science and Engineering
The book consists of 24 chapters illustrating a wide range of areas where MATLAB tools are applied. These areas include mathematics, physics, chemistry and chemical engineering, mechanical engineering, biological (molecular biology) and medical sciences, communication and control systems, digital signal, image and video processing, system modeling and simulation. Many interesting problems have been included throughout the book, and its contents will be beneficial for students and professionals in wide areas of interest
Digital processing of signals in the presence of inter-symbol interference and additive noise
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