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In setting up to do RSA public key encryption, let p = 3 and q = 23 be the two initial prime numbers. Also let e = 5 be a randomly chosen value less than and relatively prime to Φ(n).

Given the values above, compute the following. You must show all work to receive full credit:

What is the value of n ?
What is Φ(n) ?
Show that the value d = 9 is the modulo Φ(n) inverse of e.
What is the corresponding public key for these values?
What is the corresponding private key for these values?

Respuesta :

abdullahfarooqi

Answer:

1. 69

2. 44

3. See explanation

4. (69,5)

5. (69,9)

Explanation:

1. n=p*q=23*3=69

2. Φ(n)=(p-1)(q-1)=2(22)=44

3. e=5,

    ed mod Φ(n)=9*5 mod 44=45 mod 44=1

4. Public key=(n,e)=(69,5)

5. Private key=(n,d)=(69,9)

lhmarianateixeira

In this exercise, we have to use the encryption knowledge to calculate what is needed, so we have:

1. 69

2. 44

3. 1

4. (69,5)

5. (69,9)

What is public key encryption?

Public key encryption, or public key cryptography, is a method of encrypting data with two different keys and making one of the keys, the public key, available for anyone to use. The other key is known as the private key.

1.So to perform the calculations of N, we have:

[tex]n=p*q=23*3=69[/tex]

2.  For relatively prime calculations we have:

[tex]\phi (n)=(p-1)(q-1)=2(22)=44[/tex]

3. So for the inverse module, we have:

 [tex]ed mod Φ(n)=9*5 mod 44=45 mod 44=1[/tex]

4. For the public key, we have:

[tex]Public key=(n,e)=(69,5)[/tex]

5. For the private key, we have:

[tex]Private key=(n,d)=(69,9)[/tex]

See more about encryption at brainly.com/question/8455171