Discrete Math Solve and Explain decrypt the message

Discrete Math

Solve and Explain briefly

1) Alice and Bob communicate using the Rabin public-key cryptosystem. They decide to use the “complete” Rabin system.

Bob chooses an integer n= pq and an integer K Î Z_n. He sends his public key (n, k) to Alice.

Alice encrypts her digital message M and sends her encrypted message N to Bob.

You are Bob. What are Alice’s four possible messages?

P q n k

11 23 253 103

2) Alice and Bob communicate using the RSA public-key cryptosystem. They decide to use “double encryption”. Bob chooses n= (p)(q) and two values of e, and sends his public key (n, e₁, e₂) to Alice. Alice encrypts a numerical message M, and sends the encrypted message N to Bob.

You are Bob. Decrypt the message

N pq e₁ e₂

2021 (43)(47) 527 389

3) Alice and Bob communicate using the El Gamal public-key cryptosystem. Bob chooses (n, g, x) and sends his public key to Alice. Alice sends her encrypted message N to Bob. You are Bob. Decrypt the numerical message

n g x

31 17 23