Problems in public key encryption

1.) Letting Space=00, A=01, B=02, …, Z=26, encode the following message using the public key (42173,23).

I DO NOT LIKE OVALTINE BUT I DO LIKE CAPTAIN MIDNIGHT

To do the encoding, block the letters in groups of two. So, for example, DO = 0415. To test your solution, send your message to our “encryptor.”

2.) As in (1), the following message was encoded using the same scheme and public key. See if you can properly decode it using the decryption exponent D= 5447.

24018 24784 23890 27866 4286 21586 24719 14460

3.) Digital Signatures:

The other aspect of the RSA algorithms, that was not discussed above, is its ability to verify the sender of the message. This is done using a digital signature. To be of any use this signature must be easy to generate and easy for the receiver to verify, but difficult to decode otherwise. There are various methods for generating such digital signatures, but one of the easiest exploits the inverse relation of the public enciphering and secret deciphering keys by reversing their roles.

To generate a digital signature, the sender “encodes” each plaintext block