In an RSA encryption system, given that p=11 and q=13 . The pair of keys (public

Question

In an RSA encryption system, given that p=11 and q=13. The pair of keys (public [d], private [e]) needs to be generated from p and q. The choice of one of the two keys is with some freedom, and the choice of the other key is fixed after the first key is chosen. The pair of keys can be used to encrypt and decrypt messages.

1. With the pair of keys (d,e), if you are asked to show your true identity, then which key should be used to sign a message? If the plaintext is 8, then what is the value of the signed message?

Explanation / Answer

n = 11 *13 = 143

phi n = (11-1)*(13-1) =120

d = (1+120k)/e

for k =1

d = (1+120)/e

for e =11

we must choose

d=11

for plaintext m =8

the cipher text is

m^e mod n=

8^11mod 141 =131

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