Abstract: A new and highly efficient architecture for elliptic curve scalar point multiplication which is optimized for a binary field recommended by NIST and is well-suited for elliptic curve cryptographic (ECC) applications is presented. To achieve the maximum architectural and timing improvements we have reorganized and reordered the critical path of the Lopez-Dahab scalar point multiplication architecture such that logic structures are implemented in parallel and operations in the critical path are diverted to noncritical paths. With G=41, the proposed design is capable of performing a field multiplication over the extension field with degree 163 in 11.92 s with the maximum achievable frequency of 251 MHz on Xilinx Virtex-4 (XC4VLX200) while 22% of the chip area is occupied, where G is the digit size of the underlying digit-serial finite field multiplier.
Abstract: In this work we study elliptic divisibility sequences over
finite fields. MorganWard in [11, 12] gave arithmetic theory of elliptic
divisibility sequences. We study elliptic divisibility sequences, equivalence
of these sequences and singular elliptic divisibility sequences
over finite fields Fp, p > 3 is a prime.
Abstract: Let p be a prime number, Fp be a finite field, and let k ∈ F*p. In this paper, we consider the number of rational points onconics Cp,k: x2 − ky2 = 1 over Fp. We proved that the order of Cp,k over Fp is p-1 if k is a quadratic residue mod p and is p + 1 if k is not a quadratic residue mod p. Later we derive some resultsconcerning the sums ΣC[x]p,k(Fp) and ΣC[y]p,k(Fp), the sum of x- and y-coordinates of all points (x, y) on Cp,k, respectively.
Abstract: Short Message Service (SMS) has grown in
popularity over the years and it has become a common way of
communication, it is a service provided through General System
for Mobile Communications (GSM) that allows users to send text
messages to others.
SMS is usually used to transport unclassified information, but
with the rise of mobile commerce it has become a popular tool for
transmitting sensitive information between the business and its
clients. By default SMS does not guarantee confidentiality and
integrity to the message content.
In the mobile communication systems, security (encryption)
offered by the network operator only applies on the wireless link.
Data delivered through the mobile core network may not be
protected. Existing end-to-end security mechanisms are provided
at application level and typically based on public key
cryptosystem.
The main concern in a public-key setting is the authenticity of
the public key; this issue can be resolved by identity-based (IDbased)
cryptography where the public key of a user can be derived
from public information that uniquely identifies the user.
This paper presents an encryption mechanism based on the IDbased
scheme using Elliptic curves to provide end-to-end security
for SMS. This mechanism has been implemented over the standard
SMS network architecture and the encryption overhead has been
estimated and compared with RSA scheme. This study indicates
that the ID-based mechanism has advantages over the RSA
mechanism in key distribution and scalability of increasing
security level for mobile service.
Abstract: Recently, many existing partially blind signature scheme based on a single hard problem such as factoring, discrete logarithm, residuosity or elliptic curve discrete logarithm problems. However sooner or later these systems will become broken and vulnerable, if the factoring or discrete logarithms problems are cracked. This paper proposes a secured partially blind signature scheme based on factoring (FAC) problem and elliptic curve discrete logarithms (ECDL) problem. As the proposed scheme is focused on factoring and ECDLP hard problems, it has a solid structure and will totally leave the intruder bemused because it is very unlikely to solve the two hard problems simultaneously. In order to assess the security level of the proposed scheme a performance analysis has been conducted. Results have proved that the proposed scheme effectively deals with the partial blindness, randomization, unlinkability and unforgeability properties. Apart from this we have also investigated the computation cost of the proposed scheme. The new proposed scheme is robust and it is difficult for the malevolent attacks to break our scheme.
Abstract: In this work, we improve a previously developed
segmentation scheme aimed at extracting edge information from
speckled images using a maximum likelihood edge detector. The
scheme was based on finding a threshold for the probability density
function of a new kernel defined as the arithmetic mean-to-geometric
mean ratio field over a circular neighborhood set and, in a general
context, is founded on a likelihood random field model (LRFM). The
segmentation algorithm was applied to discriminated speckle areas
obtained using simple elliptic discriminant functions based on
measures of the signal-to-noise ratio with fractional order moments.
A rigorous stochastic analysis was used to derive an exact expression
for the cumulative density function of the probability density
function of the random field. Based on this, an accurate probability
of error was derived and the performance of the scheme was
analysed. The improved segmentation scheme performed well for
both simulated and real images and showed superior results to those
previously obtained using the original LRFM scheme and standard
edge detection methods. In particular, the false alarm probability was
markedly lower than that of the original LRFM method with
oversegmentation artifacts virtually eliminated. The importance of
this work lies in the development of a stochastic-based segmentation,
allowing an accurate quantification of the probability of false
detection. Non visual quantification and misclassification in medical
ultrasound speckled images is relatively new and is of interest to
clinicians.
Abstract: Groups where the discrete logarithm problem (DLP) is believed to be intractable have proved to be inestimable building blocks for cryptographic applications. They are at the heart of numerous protocols such as key agreements, public-key cryptosystems, digital signatures, identification schemes, publicly verifiable secret sharings, hash functions and bit commitments. The search for new groups with intractable DLP is therefore of great importance.The goal of this article is to study elliptic curves over the ring Fq[], with Fq a finite field of order q and with the relation n = 0, n ≥ 3. The motivation for this work came from the observation that several practical discrete logarithm-based cryptosystems, such as ElGamal, the Elliptic Curve Cryptosystems . In a first time, we describe these curves defined over a ring. Then, we study the algorithmic properties by proposing effective implementations for representing the elements and the group law. In anther article we study their cryptographic properties, an attack of the elliptic discrete logarithm problem, a new cryptosystem over these curves.
Abstract: Let p ≥ 5 be a prime number and let Fp be a finite
field. In this work, we determine the number of rational points on
singular curves Ea : y2 = x(x - a)2 over Fp for some specific
values of a.