Michael Walker
CS 253
Dr. Chodrow

RSA Cryptosystem discussion

The RSA cryptosystem uses number theory and modular arithmetic to 
encrypt a message taken in as a stream of characters and converted 
to ascii format. My program driver displays the ascii message, the 
encrypted message, the decrypted message, and the original message
after decoding and decrypting. Because my constants are small 
compared to the normal RSA constants, and because my message is
padded with 32 extra bits for security, the message must be very
small.

Destroying p, q, and N' is important if the message is to be 
safely encrypted. If someone had p and q, calculating the variables
needed to encrypt or decrypt the message. Similarly, N' is
(p-1) * (q-1), where p and q are prime. Because N' is the unique
product of two primes - 1, the code breaker could make a function
that could find the primes in a relatively small amount of time.
Thus, all three should be discarded, as they are unnecessary for 
decryption and encryption, and as they pose a security problem if
they get into the wrong hands.

Sending a byte of encrypted message at a time is a bad idea. Because
a character is normally 1 byte, the malicious reciever could guess
that each byte represented an encrypted character. Because a byte
is 8 bits (0 or 1), there are only 2^8, or 256, possibilities for
the byte. Thus, finding the byte representation for the character
is not difficult, and the message will be insecure.

On the other hand, a long key ensures that the encryption will 
be harder to break. A 130 digit (500 bit) prime set gives 2^500
different bit possibilities (a very large number!). Discovering
a key this large takes a long time using a large amount of
computing power.