DISCRETE MATHEMATICS Use the RSA cipher with p = 11, q = 13, and the encryption
ID: 3141412 • Letter: D
Question
DISCRETE MATHEMATICS
Use the RSA cipher with p = 11, q = 13, and the encryption exponent e = 17 to encode the first letter of your first name and the first letter of your last name. (If one of the two letters is an A, encrypt instead the next letter of your name that is not an A). Show your work. (b) Use the Extended Euclidean Algorithm to help calculate the decryption exponent for part (a), i.e., find a positive integer d such that de = 1 mod 120. Show your work. (c) Use the decryption exponent you found in part (b) to decrypt one or the other of the two letters you encrypted in part (a). Show your work.Explanation / Answer
(a) The name is Bond......James Bond!
The first letter of the first name is J and the first letter of the last name is B.
ASCII value of J is 74.
ASCII value of B is 66.
p = 11, q = 13 e = 17
n = 11*13 = 143 (n) = (11-1)(13-1) = 120
For m = 74
c = me mod n
=> c = 7417 mod 143
=> c = 68
This is the character D.
For m = 66
c = 6617 mod 143
=> c = 66
This is the character B.
Thus the encrypted message is DB.
(b) Using Euclid's extended algorithm,
120 = 17*7 + 1
=> 1 = 120 -17*7
=> d = -7 or d = 120-7 = 113
(c) For the letter D,
c = 68,
m = cd mod n
=> m = 68113 mod 143
=> m = 74
This is the character J.
For the letter B,
c = 66
=> m = 66113 mod 143
=> m = 66
This is the character B.
Thus the decrypted message is JB.
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