**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**4

# elliptic curve Related Publications

##### 4 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:**
Encryption,
decryption,
elliptic curve,
greater common divisor

##### 3 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,
elliptic curve,
wireless mobile networks,
password guessing attacks

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

**Authors:**
Ahmet Tekcan

**Abstract:**

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

##### 1 The Number of Rational Points on Conics Cp,k : x2 − ky2 = 1 over Finite Fields Fp

**Authors:**
Ahmet Tekcan

**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.

**Keywords:**
elliptic curve,
rational points,
conic