Abstract: The arithmetic operations over GF(2m) have been
extensively used in error correcting codes and public-key
cryptography schemes. Finite field arithmetic includes addition,
multiplication, division and inversion operations. Addition is very
simple and can be implemented with an extremely simple circuit.
The other operations are much more complex. The multiplication
is the most important for cryptosystems, such as the elliptic
curve cryptosystem, since computing exponentiation, division, and
computing multiplicative inverse can be performed by computing
multiplication iteratively. In this paper, we present a parallel
computation algorithm that operates Montgomery multiplication over
finite field using redundant basis. Also, based on the multiplication
algorithm, we present an efficient semi-systolic multiplier over finite
field. The multiplier has less space and time complexities compared
to related multipliers. As compared to the corresponding existing
structures, the multiplier saves at least 5% area, 50% time, and 53%
area-time (AT) complexity. Accordingly, it is well suited for VLSI
implementation and can be easily applied as a basic component for
computing complex operations over finite field, such as inversion and
division operation.
Abstract: Linear error-block codes are a natural generalization of linear error correcting codes. The purpose of this paper is to generalize some results on the packing and the covering radii to the error-block case. We study their properties when a code undergoes some specific modifications and combinations with another code. We give a few bounds on the packing and the covering radii of these codes.
Abstract: Error correcting codes are used for detection and correction of errors in digital communication system. Error correcting coding is based on appending of redundancy to the information message according to a prescribed algorithm. Reed Solomon codes are part of channel coding and withstand the effect of noise, interference and fading. Galois field arithmetic is used for encoding and decoding reed Solomon codes. Galois field multipliers and linear feedback shift registers are used for encoding the information data block. The design of Reed Solomon encoder is complex because of use of LFSR and Galois field arithmetic. The purpose of this paper is to design and implement Reed Solomon (255, 239) encoder with optimized and lesser number of Galois Field multipliers. Symmetric generator polynomial is used to reduce the number of GF multipliers. To increase the capability toward error correction, convolution interleaving will be used with RS encoder. The Design will be implemented on Xilinx FPGA Spartan II.
Abstract: This paper proposes a method which reduces power consumption in single-error correcting, double error-detecting checker circuits that perform memory error correction code. Power is minimized with little or no impact on area and delay, using the degrees of freedom in selecting the parity check matrix of the error correcting codes. The genetic algorithm is employed to solve the non linear power optimization problem. The method is applied to two commonly used SEC-DED codes: standard Hamming and odd column weight Hsiao codes. Experiments were performed to show the performance of the proposed method.
Abstract: This paper mainly about the study on one of the
widely used error correcting codes that is Low parity check Codes
(LDPC). In this paper, the Regular LDPC code has been discussed
The LDPC codes explained in this paper is about the Regular Binary
LDPC codes or the Gallager.
Abstract: In this paper, a two factor scheme is proposed to
generate cryptographic keys directly from biometric data, which
unlike passwords, are strongly bound to the user. Hash value of the
reference iris code is used as a cryptographic key and its length
depends only on the hash function, being independent of any other
parameter. The entropy of such keys is 94 bits, which is much higher
than any other comparable system. The most important and distinct
feature of this scheme is that it regenerates the reference iris code by
providing a genuine iris sample and the correct user password. Since
iris codes obtained from two images of the same eye are not exactly
the same, error correcting codes (Hadamard code and Reed-Solomon
code) are used to deal with the variability. The scheme proposed here
can be used to provide keys for a cryptographic system and/or for
user authentication. The performance of this system is evaluated on
two publicly available databases for iris biometrics namely CBS and
ICE databases. The operating point of the system (values of False
Acceptance Rate (FAR) and False Rejection Rate (FRR)) can be set
by properly selecting the error correction capacity (ts) of the Reed-
Solomon codes, e.g., on the ICE database, at ts = 15, FAR is 0.096%
and FRR is 0.76%.
Abstract: In this paper we present a generic approach for the problem of the blind estimation of the parameters of linear and convolutional error correcting codes. In a non-cooperative context, an adversary has only access to the noised transmission he has intercepted. The intercepter has no knowledge about the parameters used by the legal users. So, before having acess to the information he has first to blindly estimate the parameters of the error correcting code of the communication. The presented approach has the main advantage that the problem of reconstruction of such codes can be expressed in a very simple way. This allows us to evaluate theorical bounds on the complexity of the reconstruction process but also bounds on the estimation rate. We show that some classical reconstruction techniques are optimal and also explain why some of them have theorical complexities greater than these experimentally observed.