LSFR and GCD Calculation

Surname 1
Student’s Name
Professor’s Name
Subject
Date
Question 1
a)
(1, 7) (0, 2)
x1 =1 y1 =0
x2 =7 y2 =2
Calculating the linear equation
(y- y1) = y2− x1
x2 −x1
(x- x1)
y-0 = 2−0
7−1 (x-1)
y= 2
6 (x-1)
y= 1
3(x-1)
b)
(1, 6) (0, 1)
x1 =1 y1 =0
x2 =6 y2 =1
Calculating the linear equation
(y- y1) = y2− x1
x2 −x1
(x- x1)

Surname 2
y-0 = 1−0
6−1 (x-1)
y= 1
5(x-1)
y= 1
5(x-1)
Question 1
a)
LSFR is defined as the element of pseudo random generator which generates a set of encryption
keys (Kim 3). The general formula LSFR are easily generalized in any finite model; GF (p).
LSFR is easily implemented in software and hardware thus they are widely applied in stream
cipher (Gómez 4; Denning 42).
The LFSR equation: xn+5 = xn + xn+3
When x=0, then X0+5 = x0 + x0+3 = 0+0 = 0
When x=1, then X1+5 = x1 + x1+3 = 1+0 = 1
When x=2, then X2+5 = x2 + x2+3 = 0+0 = 0
When x=3, then X3+5 = x3 + x2+3 = 0 = 1
When x=4, then X4+5 = x4 + x4+3 = 0+0 = 0
Thus the LSFR sequence becomes: 0, 1, 0, 1,0......
Therefore, the first 20 bits are: 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1
b)
The first 20 bit follows a PN-sequence by investigation. The PN-sequences a period generalized
using the formula 2n−1. Therefore, the period of LSFR is 2n−1.
Question 2
Definition