Cryptography and Mathematics: LSFR, GCD and Fermat Theorem

Running head: CRYPTOGRAPHY 1
Cryptography
Student Name
Institution

CRYPTOGRAPHY 2
Question 1
a)
(1, 7) (0, 2)
x1 =1 y1 =0
x2 =7 y2 =2
Equation of line
(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
Equation of line
(y- y1) = y2− x1
x2 −x1
(x- x1)
y-0 = 1−0
6−1 (x-1)
y= 1
5(x-1)
y= 1
5(x-1)

CRYPTOGRAPHY 3
Question 1
a)
LSFR I the main element of pseudo random generator used to generate a set of encryption keys
(González Vasco & Steinwandt, 2008). 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 (Bhandari, 2016; Pardo & Luis, 2013).
The LFSR equation is given as: xn+5 = xn + xn+3
When x=0
X0+5 = x0 + x0+3 = 0+0 = 0
When x=1
X1+5 = x1 + x1+3 = 1+0 = 1
When x=2
X2+5 = x2 + x2+3 = 0+0 = 0
Thus the sequence becomes: 0, 1, 0......
Therefore, the first 20 bits : 0,1,0, 0,1,0, 0,1,0, 0,1,0, 0,1,0, 0,1,0, 0,1
b)
By investigation; the first 20 bit follows a PN-sequence. A PN-sequence and the pseudo noise
sequences have a period of the general formula 2n−1. Therefore, the period is 2n−1.
Question 2
Definition