Hi, I am still having difficulties with the concept of RSA Public Key Encryption

ID: 3938241 • Letter: H

Question

Hi,

I am still having difficulties with the concept of RSA Public Key Encryption.

Please any of your help is very appreciated.

Assume that for the RSA Public Key Encryption method you have chosen the two numbers p= 23 and q=41. and that you have chosen e= 7.

1. Establish that this e value is a valid choice. Hint(what is unique about 7 that makes it easier to check this?)

2. For these choices, what is the public key that you would distribute?

3. Compute 13 mod 5 (This question has nothing to do with the set up for #1&#2)

1. n = p*q

therefore, n = 23*41 = 943

We need to choose e such that e<(p-1)(q-1) and e and (p-1)(q-1) are coprime

(p-1)(q-1) = 22*40 = 880

Also, gcd(880, 7) = 1

Hence, they are coprime.

Since, 7 is a small prime number, it makes it easier to check if it is coprime with (p-1)(q-1) by simply taking mod of that number by 7.

2. The public key is (n, e) which in this case is (943, 7).

3. 13mod5 = 3

since 13 = 5*2 + 3

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