. RSA public key encryption system. Suppose p = 5 and q = 11 are our “large” pri
ID: 3715325 • Letter: #
Question
. RSA public key encryption system. Suppose p = 5 and q = 11 are our “large” primes.
a. compute the n needed in the RSA algorithm.
b. Explain or show why e = 7 is an acceptable encoding value.
c. Compute the ciphertext for the plaintext character string ENCRYPTION where E = 5, N = 14, , C = 3, R = 18, etc..
Symbol
Numeric(m)
P^7
Cipher- (P^7)mod(55)
E
5
N
14
C
3
R
18
Y
5
P
16
T
20
I
10
O
15
N
14
d. Find a decryption key (there is one less than 30) and show/explain how you found it. Decrypt the values obtained in c. above. See slides.
Symbol
Numeric(m)
P^7
Cipher- (P^7)mod(55)
E
5
N
14
C
3
R
18
Y
5
P
16
T
20
I
10
O
15
N
14
Explanation / Answer
By RSA algorithm
1. n=p*q=5*11=55
2. e value is a)Must be an integer.
b) Not be a factor of n.
c ) 1 < e < ?(n)
?(n) = (P-1)(Q-1) =4*10=40
from above conditions, e=7 is an acceptable value
3.
Symbol Numeric(m) P^7 Cipher- (P^7)mod(55)
E 5 78125 25
N 14 105413504 9
C 3 2187 42
R 18 612220032 17
Y 5 78125 25
P 16 268435456 36
T 20 1280000000 15
I 10 10000000 10
O 15 170859375 5
N 14 105413504 9
4 .Now calculate decryption Key, d :
d = (k*?(n) + 1) / e for some integer k
d=(2*40+1)/7=23
For k = 4, value of d is 23.
Decrypted Data = encrypted data pow d mod n.
= ENCRYPTION
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