Question

Discrete Math

In this problem, we will implement the RSA algorithm to encrypt and decrypt the message ”148”.For this exercise, you may want to use some kind of calculator that can compute the mod function.

1. Set the primes p and q as follows:p=31 and q=47. What are the values for N and φ?

2.The value for e is chosen to be 11. Use Euclid’s algorithm to verify that e and φ are relatively prime and to find d, the multiplicative inverse of e modφ.

3. Encrypt the message m by computing m^e mod N

4.The result of the previous question is the ciphertext c that is transmitted. To decrypt the message, compute c^d mod N.

Answer #1

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For solving the problems, you are required to use the following
formalization of the RSA public-key cryptosystem.
In the RSA public-key cryptosystem,
each participants creates his public key and secret key according
to the following steps:
· Select two very large
prime number p and q. The number of bits needed to represent p and
q might be 1024.
· Compute
n = pq
(n) = (p – 1) (q – 1).
The formula for (n) is owing to...

Below is an example of key generation, encryption, and
decryption using RSA. For the examples below, fill in the
blanks to indicate what each part is or answer the
question.
Public key is (23, 11) What is 23 called?
_______________, What is 11 called?_______________
Private key is (23, 13) What is 23
called?_______________, What is 13
called?_______________
23 can be part of the public key because it is very hard
to _______________ large prime numbers.
ENCRYPT (m) = m^e mod...

Consider the following two prime numbers and demonstrate RSA
algorithm.
139 and 151
Now consider a message M= 5, encrypt M using the encryption key
and find the encrypted message E
Now decrypt E, using the decryption key.

1. Dexter wants to set up his own public keys. He chooses p = 23
and q = 37 with e = 5. Answer the following using RSA cryptographic
method: a) Encrypt the message ‘100’ and find the CIPHER number (C)
to be sent. ‘100’ should be taken together as M while computing
encryption [5 Marks] C = Me mod pq (Use This Formula) b) Find the
decryption key ‘d’, using extended Euclidean GCD algorithm. [10
Marks] c) Now decrypt...

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