Question

1. Alice has the RSA public key (n, e) = (11413, 251) and private key d = 1651. And Bob also has his own RSA public key (n’, e’) = (20413, 2221) and private key d’ = 6661. Alice wants to send the message 1314 to Bob with both authentication and non-repudiation. Use Maple, calculate what is the ciphertext sent by Alice. And Verify that Bob is able to recover the original plaintext 1314.

Answer 1

Alice

n = 11413,e=251,d = 1651

Bob

n = 20413,e = 2221,d = 6661

Alice wants to send the message 1314 to Bob.

Bob gives his public key(n & e)  to Alice and keeps his private key secret. Alice wants to send message M to Bob.

First,she turns the message to a ciphertext,

c = m^e mod n

c = 1314²²²¹ mod 20413

c = 11297

She sends the ciphertext to Bob. Bob uses his private key to decrypt this ciphertext.

m = c^d mod n (d is the Bob's private key)

m = 11297⁶⁶⁶¹ mod 20413

m = 1314.