Exercise 10.4.2: Public-key cryptography.
The following is a simple public-key cryptosystem for character strings in ASCII code:
The decryption function is P = C$^5$ mod 35. The corresponding encryption function C = P$^e$ mod 35 is kept secret.
Each hexadecimal code of an ASCII character has 2 digits. Each digit of the pair is encrypted separately using the above function.
Ex: The hexadecimal code for the ASCII character B is 42. The two digits 4 and 2 are encrypted as ($4^e$ mod 35, $2^e$ mod 35).
(a) Decrypt the ciphertext:
(9,4)(32,0)(6,15)(7,7) (6,10) (32,0)(7,4) (6,15) (7,10) (32,0)(32,9) (33,1) (32,17) (33,0)(33,0)(33,0)(32,17) (33,0)(33,0)(33,0)(32,1).
(The parentheses and the commas are not part of the ciphertext but are used only to increase readability.)
(b) The RSA code is based on 2 principles:
• n is the product of 2 prime numbers, p and q
• e * d mod (p - 1) * (q - 1) = 1
Break the above simple encryption scheme by finding the corresponding encryption function by using the two underlying
principles of the scheme.
