1,721,049 research outputs found
Recursive towers of function fields over finite fields
No full textThe theory of recursive towers of function fields over finite fields was developed by A. Garcia and the author since 1995. We give a survey about the main ideas and results, and we propose some problems for future work
High-Performance Modular Multiplication on the Cell Processor
Full text linkThis paper presents software implementation speed records for modular multiplication arithmetic on the synergistic processing elements of the Cell broadband engine (Cell) architecture. The focus is on moduli which are of special interest in elliptic curve cryptography, that is, moduli of bit-lengths ranging from 192- to 521-bit. Finite field arithmetic using primes which allow particularly fast reduction is compared to Montgomery multiplication. The special primes considered are the five recommended NIST primes, as specified in the FIPS 186-3 standard, and the prime used in the elliptic curve curve25519. While presented and benchmarked on the Cell architecture, the proposed techniques to efficiently implement the modular multiplication algorithms are suited to run on any architecture which is able to compute multiple computations concurrently; e.g. graphics processing units.LACA
Diversity-Multiplexing Gain Trade-off of a MIMO System with Relays
Full text linkWe find the diversity-multiplexing gain trade-off of a multiple-antenna (MIMO) system with M transmit antennas, N receive antennas, R relay nodes, and with independent Rayleigh fading, in which the relays apply a distributed space-time code. In this two-stage scheme the trade-off is shown to coincide with that of a MIMO system with R transmit and min{M, N} receive antennas
The weight distribution of the coset leaders for some classes of codes with related parity-check matrices
No full textAbstractWe construct an infinite sequence of codes with related parity-check matrices. We show how to reduce the calculations of the weight distribution of the coset leaders for all these codes, to the calculation of finitely many numbers Flj. This method is applied in determining the weight distribution of the coset leaders for several classes of codes
A new algorithm for finding low-weight polynomial multiples and its application to TCHo
No full textIn this paper we present an algorithm for finding low-weight multiples of polynomials over the binary field using coding theoretic methods. The code defined by the public polynomial is cyclic, allowing an attacker to search for any shift of the sought codeword. Therefore, a code with higher length and dimension is used, having a larger number of low-weight codewords. Additionally, since the degree of the sought polynomial is known, the sought codewords of weight w are transformed by a linear mapping into codewords of weight w-2. Applying an algorithm for finding low-weight codewords on the constructed code yields complexity for a key-recovery attack against TCHo that is lower than previously expected
The weight enumerator polynomials of some classes of codes with composite parity-check polynomials
No full textAbstractWe find the Hamming weight distribution of some classes of linear codes. The cyclic codes in these classes have composite parity-check polynomials
A characterization of codes meeting the Griesmer bound
No full textFor any binary linear code of length n, dimension k, and minimum distance d, the Griesmer bound says that uif128-1}. In this paper we completely characterize all codes which meet the Griesmer bound with equality and for which d ⩽ 2usuk−1}. In particular we prove Belov's conjecture
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