Question

Why is it that the *e* published in the RSA can not be 1
and can not be 2?

Answer #1

Consider the RSA algorithm with n=33 and E=7.
1. Encode the message 8.
2. Find the value of D.
3. Decode the message 9.
Consider the RSA algorithm with n=65 and E=5.
4. Encode the message 8.
5. Find the value of D.
6. Decode the message 2.

Let p=3 and q=17 and let an RSA public-key cryptosystem be
given.
1. Why is the number 8 not a valid encryption-key?
2. We encrypt the number M=8 with the help of the encryption-key
e=3.
Why is the encrypted message C=2?
3. Why is the decryption key d for the encryption-key, (e=3),
equal to 11?
https://en.wikipedia.org/wiki/RSA_(cryptosystem)#Encryption

Discrete Mathematics
(a) In the RSA cipher using pq = 77 and e = 7,
what should be the value of d? Choose a value for
d and explain the reason.
(b) Decrypt C = 21 using the RSA setup chosen in
(a).

In an RSA system, the public key of a given user is e = 31, n
= 3599. What is the private
key of this user?

Bob has an RSA public key of
(n, e) = (1363, 87)
(a) What is Bob’s private key?
(b) Bob receives the ciphertext which has been encrypted with
his public key
893, 1265, 406, 171, 980, 1040, 12, 1152, 573
Decrypt the message.
(You can use an appropriate package such as Matlab or Wolfram Alpha
to do the calculations)

suppose your RSA modulus is n=65 and your encyption
exponent is e=11. find the decryption exponent d.

Perform encryption using the RSA algorithm for the
following:
p=5, q=9, e=2, M=5
p=4, q=12, e=4, M=3
C=Me mod n
C is the cipher text and M is the plain text, n=p×q

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...

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...

Suppose your RSA Public-key factors are p =6323 and q = 2833,
and the public exponent e is 31. Suppose you were sent the
Ciphertext 6627708. Write a program that takes the above parameters
as input and implements the RSA decryption function to recover the
plaintext.
IN PYTHON

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