Using a spreadsheet (such as Excel) or a calculator, perform the operations described below. Document results of all intermediate modular multiplications. Determine a number of modular multiplications per each major transformation (such as encryption, decryption, primality testing, etc.).

a. Test all odd numbers in the range from 233 to 241 for primality using the MillerRabin test with base 2 .

b. Encrypt the message block \(M=2\) using RSA with the following parameters: \(e=23\) and \(n=233 \times 241\).

c. Compute a private key \((d, p, q)\) corresponding to the given above public key \((e, n)\).

d. Perform the decryption of the obtained ciphertext

1. without using the Chinese Remainder Theorem, and

2. using the Chinese Remainder Theorem.