**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**415

# Search results for: elliptic curve

##### 415 Proposed Developments of Elliptic Curve Digital Signature Algorithm

**Authors:**
Sattar B. Sadkhan,
Najlae Falah Hameed

**Abstract:**

**Keywords:**
Elliptic Curve Digital Signature Algorithm,
DSA.

##### 414 The Number of Rational Points on Elliptic Curves and Circles over Finite Fields

**Authors:**
Betül Gezer,
Ahmet Tekcan,
Osman Bizim

**Abstract:**

**Keywords:**
Elliptic curves over finite fields,
rational points on
elliptic curves and circles.

##### 413 An Attack on the Lucas Based El-Gamal Cryptosystem in the Elliptic Curve Group Over Finite Field Using Greater Common Divisor

**Authors:**
Lee Feng Koo,
Tze Jin Wong,
Pang Hung Yiu,
Nik Mohd Asri Nik Long

**Abstract:**

Greater common divisor (GCD) attack is an attack that relies on the polynomial structure of the cryptosystem. This attack required two plaintexts differ from a fixed number and encrypted under same modulus. This paper reports a security reaction of Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field under GCD attack. Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field was exposed mathematically to the GCD attack using GCD and Dickson polynomial. The result shows that the cryptanalyst is able to get the plaintext without decryption by using GCD attack. Thus, the study concluded that it is highly perilous when two plaintexts have a slight difference from a fixed number in the same Elliptic curve group over finite field.

**Keywords:**
Decryption,
encryption,
elliptic curve,
greater common divisor.

##### 412 Implementation and Analysis of Elliptic Curve Cryptosystems over Polynomial basis and ONB

**Authors:**
Yong-Je Choi,
Moo-Seop Kim,
Hang-Rok Lee,
Ho-Won Kim

**Abstract:**

**Keywords:**
Elliptic Curve Cryptosystem,
Crypto Algorithm,
Polynomial Basis,
Optimal Normal Basis,
Security.

##### 411 Efficient Hardware Implementation of an Elliptic Curve Cryptographic Processor Over GF (2 163)

**Authors:**
Massoud Masoumi,
Hosseyn Mahdizadeh

**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.

**Keywords:**
Elliptic curve cryptography,
FPGA implementation,
scalar point multiplication.

##### 410 Novel Method for Elliptic Curve Multi-Scalar Multiplication

**Authors:**
Raveen R. Goundar,
Ken-ichi Shiota,
Masahiko Toyonaga

**Abstract:**

**Keywords:**
elliptic curve cryptosystems,
multi-scalar multiplication,
addition chains,
Fibonacci sequence.

##### 409 Improved of Elliptic Curves Cryptography over a Ring

**Authors:**
A. Chillali,
A. Tadmori,
M. Ziane

**Abstract:**

In this article we will study the elliptic curve defined over the ring An and we define the mathematical operations of ECC, which provides a high security and advantage for wireless applications compared to other asymmetric key cryptosystem.

**Keywords:**
Elliptic Curves,
Finite Ring,
Cryptography.

##### 408 Cryptography Over Elliptic Curve Of The Ring Fq[e], e4 = 0

**Authors:**
Chillali Abdelhakim

**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.

**Keywords:**
Elliptic Curve Over Ring,
Discrete Logarithm Problem.

##### 407 A Study of General Attacks on Elliptic Curve Discrete Logarithm Problem over Prime Field and Binary Field

**Authors:**
Tun Myat Aung,
Ni Ni Hla

**Abstract:**

**Keywords:**
Discrete logarithm problem,
general attacks,
elliptic curves,
strong curves,
prime field,
binary field,
attack experiments.

##### 406 Alternative Key Exchange Algorithm Based on Elliptic Curve Digital Signature Algorithm Certificate and Usage in Applications

**Authors:**
A. Andreasyan,
C. Connors

**Abstract:**

The Elliptic Curve Digital Signature algorithm-based X509v3 certificates are becoming more popular due to their short public and private key sizes. Moreover, these certificates can be stored in Internet of Things (IoT) devices, with limited resources, using less memory and transmitted in network security protocols, such as Internet Key Exchange (IKE), Transport Layer Security (TLS) and Secure Shell (SSH) with less bandwidth. The proposed method gives another advantage, in that it increases the performance of the above-mentioned protocols in terms of key exchange by saving one scalar multiplication operation.

**Keywords:**
Cryptography,
elliptic curve digital signature algorithm,
key exchange,
network security protocols.

##### 405 SIP Authentication Scheme using ECDH

**Authors:**
Aytunc Durlanik,
Ibrahim Sogukpinar

**Abstract:**

**Keywords:**
SIP,
Elliptic Curve Cryptography,
voice over IP.

##### 404 Implementing Authentication Protocol for Exchanging Encrypted Messages via an Authentication Server Based on Elliptic Curve Cryptography with the ElGamal-s Algorithm

**Authors:**
Konstantinos Chalkias,
George Filiadis,
George Stephanides

**Abstract:**

In this paper the authors propose a protocol, which uses Elliptic Curve Cryptography (ECC) based on the ElGamal-s algorithm, for sending small amounts of data via an authentication server. The innovation of this approach is that there is no need for a symmetric algorithm or a safe communication channel such as SSL. The reason that ECC has been chosen instead of RSA is that it provides a methodology for obtaining high-speed implementations of authentication protocols and encrypted mail techniques while using fewer bits for the keys. This means that ECC systems require smaller chip size and less power consumption. The proposed protocol has been implemented in Java to analyse its features and vulnerabilities in the real world.

**Keywords:**
Elliptic Curve Cryptography,
ElGamal,
authentication protocol.

##### 403 Rational Points on Elliptic Curves 2 3 3y = x + a inF , where p 5(mod 6) is Prime

**Authors:**
Gokhan Soydan,
Musa Demirci,
Nazli Yildiz Ikikardes,
Ismail Naci Cangul

**Abstract:**

In this work, we consider the rational points on elliptic curves over finite fields Fp where p ≡ 5 (mod 6). We obtain results on the number of points on an elliptic curve y2 ≡ x3 + a3(mod p), where p ≡ 5 (mod 6) is prime. We give some results concerning the sum of the abscissae of these points. A similar case where p ≡ 1 (mod 6) is considered in [5]. The main difference between two cases is that when p ≡ 5 (mod 6), all elements of Fp are cubic residues.

**Keywords:**
Elliptic curves over finite fields,
rational points.

##### 402 Positive Definite Quadratic Forms, Elliptic Curves and Cubic Congruences

**Authors:**
Ahmet Tekcan

**Abstract:**

**Keywords:**
Binary quadratic form,
elliptic curves,
cubic congruence.

##### 401 Elliptic Divisibility Sequences over Finite Fields

**Authors:**
Betül Gezer,
Ahmet Tekcan,
Osman Bizim

**Abstract:**

**Keywords:**
Elliptic divisibility sequences,
singular elliptic divisibilitysequences,
elliptic curves,
singular curves.

##### 400 Fingerprint Image Encryption Using a 2D Chaotic Map and Elliptic Curve Cryptography

**Authors:**
D. M. S. Bandara,
Yunqi Lei,
Ye Luo

**Abstract:**

**Keywords:**
Arnold cat map,
biometric encryption,
block cipher,
elliptic curve cryptography,
fingerprint encryption,
Koblitz’s Encoding.

##### 399 The Number of Rational Points on Elliptic Curves y2 = x3 + a3 on Finite Fields

**Authors:**
Musa Demirci,
Nazlı Yıldız İkikardeş,
Gökhan Soydan,
İsmail Naci Cangül

**Abstract:**

**Keywords:**
Elliptic curves over finite fields,
rational points,
quadratic residue.

##### 398 A New Design Partially Blind Signature Scheme Based on Two Hard Mathematical Problems

**Authors:**
Nedal Tahat

**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.

**Keywords:**
Cryptography,
Partially Blind Signature,
Factoring,
Elliptic Curve Discrete Logarithms.

##### 397 Cryptanalysis of Chang-Chang-s EC-PAKA Protocol for Wireless Mobile Networks

**Authors:**
Hae-Soon Ahn,
Eun-Jun Yoon

**Abstract:**

With the rapid development of wireless mobile communication, applications for mobile devices must focus on network security. In 2008, Chang-Chang proposed security improvements on the Lu et al.-s elliptic curve authentication key agreement protocol for wireless mobile networks. However, this paper shows that Chang- Chang-s improved protocol is still vulnerable to off-line password guessing attacks unlike their claims.

**Keywords:**
Authentication,
key agreement,
wireless mobile networks,
elliptic curve,
password guessing attacks.

##### 396 On The Elliptic Divisibility Sequences over Finite Fields

**Authors:**
Osman Bizim

**Abstract:**

**Keywords:**
Elliptic divisibility sequences,
equivalent sequences,
singular sequences.

##### 395 Solving 94-bit ECDLP with 70 Computers in Parallel

**Authors:**
Shunsuke Miyoshi,
Yasuyuki Nogami,
Takuya Kusaka,
Nariyoshi Yamai

**Abstract:**

**Keywords:**
Pollard’s rho method,
BN curve,
Montgomery
multiplication.

##### 394 Experimental and Numerical Study of The Shock-Accelerated Elliptic Heavy Gas Cylinders

**Authors:**
Jing S. Bai,
Li Y. Zou,
Tao Wang,
Kun Liu,
Wen B. Huang,
Jin H. Liu,
Ping Li,
Duo W. Tan,
CangL. Liu

**Abstract:**

**Keywords:**
About four key words or phrases in alphabeticalorder,
separated by commas.

##### 393 The Elliptic Curves y2 = x3 - t2x over Fp

**Authors:**
Ahmet Tekcan

**Abstract:**

Let p be a prime number, Fp be a finite field and t ∈ F*p= Fp- {0}. In this paper we obtain some properties of ellipticcurves Ep,t: y2= y2= x3- t2x over Fp. In the first sectionwe give some notations and preliminaries from elliptic curves. In the second section we consider the rational points (x, y) on Ep,t. Wegive a formula for the number of rational points on Ep,t over Fnp for an integer n ≥ 1. We also give some formulas for the sum of x?andy?coordinates of the points (x, y) on Ep,t. In the third section weconsider the rank of Et: y2= x3- t2x and its 2-isogenous curve Et over Q. We proved that the rank of Etand Etis 2 over Q. In the last section we obtain some formulas for the sums Σt∈F?panp,t for an integer n ≥ 1, where ap,t denote the trace of Frobenius.

**Keywords:**
Elliptic curves over finite fields,
rational points onelliptic curves,
rank,
trace of Frobenius.

##### 392 The Number of Rational Points on Singular Curvesy 2 = x(x - a)2 over Finite Fields Fp

**Authors:**
Ahmet Tekcan

**Abstract:**

**Keywords:**
Singular curve,
elliptic curve,
rational points.

##### 391 Finding More Non-Supersingular Elliptic Curves for Pairing-Based Cryptosystems

**Authors:**
Pu Duan,
Shi Cui,
Choong Wah Chan

**Abstract:**

**Keywords:**
Family of group order,
kth root of unity,
non-supersingular elliptic curves polynomial field.

##### 390 New DES based on Elliptic Curves

**Authors:**
Ghada Abdelmouez M.,
Fathy S. Helail,
Abdellatif A. Elkouny

**Abstract:**

**Keywords:**
DES,
Elliptic Curves,
hybrid system,
symmetricencryption.

##### 389 Performance Analysis of Certificateless Signature for IKE Authentication

**Authors:**
Nazrul M. Ahmad,
Asrul H. Yaacob,
Ridza Fauzi,
Alireza Khorram

**Abstract:**

**Keywords:**
Certificateless signature,
IPSec,
RSA signature,
IKE authentication.

##### 388 The Control Vector Scheme for Design of Planar Primitive PH curves

**Authors:**
Ching-Shoei Chiang,
Sheng-Hsin Tsai,
James Chen

**Abstract:**

**Keywords:**
PH curve,
hodograph,
Bézier curve.

##### 387 The Number of Rational Points on Elliptic Curves y2 = x3 + b2 Over Finite Fields

**Authors:**
Betül Gezer,
Hacer Özden,
Ahmet Tekcan,
Osman Bizim

**Abstract:**

Let p be a prime number, Fpbe a finite field and let Qpdenote the set of quadratic residues in Fp. In the first section we givesome notations and preliminaries from elliptic curves. In the secondsection, we consider some properties of rational points on ellipticcurves Ep,b: y2= x3+ b2 over Fp, where b ∈ F*p. Recall that theorder of Ep,bover Fpis p + 1 if p ≡ 5(mod 6). We generalize thisresult to any field Fnp for an integer n≥ 2. Further we obtain someresults concerning the sum Σ[x]Ep,b(Fp) and Σ[y]Ep,b(Fp), thesum of x- and y- coordinates of all points (x, y) on Ep,b, and alsothe the sum Σ(x,0)Ep,b(Fp), the sum of points (x, 0) on Ep,b.

**Keywords:**
Elliptic curves over finite fields,
rational points on elliptic curves.

##### 386 Comparison of the Distillation Curve Obtained Experimentally with the Curve Extrapolated by a Commercial Simulator

**Authors:**
Lívia B. Meirelles,
Erika C. A. N. Chrisman,
Flávia B. de Andrade,
Lilian C. M. de Oliveira

**Abstract:**

**Keywords:**
Distillation curve,
petroleum distillation,
simulation,
true boiling point curve.