Question

Calculate using Excel or calculator:

Test all odd numbers in the range from 233 to 241 for primality using the Miller-Rabin test with base 2.

Encrypt the message block M = 2 using RSA with the following parameters: e = 23 and n = 233 * 241.

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

Perform the decryption of the obtained ciphertext

1. without using the Chinese Remainder Theorem, and

2. using the Chinese Remainder Theorem.

Sow clear and full list of steps and all results with comments. You may use Excel – it is easier to calculate and present.

Answer 1

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

N=233*241=56153

P = 233, Q= 241, M=2, e =23

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

d. Perform the decryption of the obtained ciphertext1.

1) without using the Chinese Remainder Theorem, and
M = 21811^19367 mod 56153 = 2

2) using the Chinese Remainder Theorem.