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?

Question

Computers & Technology

Guest

24 May, 19:31

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?

+4

Answers (1)

Know the Answer?

Kyle Weaver · Answer 1

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)