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25 July, 22:18

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?

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Answers (1)
  1. 26 July, 01:42
    0
    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)
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