Question

This question tests your knowledge of encryption and decryption using the RSA method. the numbers in soled are deliberately chosen to be mall enough to focus on gown understanding without excessive calculations. Alice and Bob decide to use an RSA cryptosystem with public key (77, 13) for communication. Alice wants to send Bob the message m = 22. Determine Alice's ciphertext c. Determine Bob's private boy Carry out Bob's decryption of Aloe's ciphertext c, and compare his result with Alice's message

Answer 1

1.Lets assume the two keys of alice and bob be p and q respectively

P=77, q=13

Now according to RSA algorithm

N=p*q = 77*13 = 1001

φ = (p-1)(q-1) = 76*12 = 912

Now we choose an integer e such that 1 < e < φ(n) and e and φ (n) are coprime. Let e =11

Compute a value for d such that (d * e) % φ(n) = 1. One solution is d = 83

[( 83* 11) % 912 = 1]

Public key is (e, n) => (11,1001)

2.Private key is (d, n) => (83, 1001)

3.Compare of results for bob and alice

The encryption of m = 29 is c = 29^11 % 1001 = 679

The decryption of c = 679 is m = 679^77 % 1001 = 29

Please note it is possible solution for RSA algorithm .However there can be multiple solution existing