LAST NAME: 

FIRST NAME: 


1. For 1000 bit numbers, give an estimate of the following.

1a) The maximum value of such a number.



1b) The running time of finding gcd's and modular inverses.



1c) The running time of modular expontiation and the Fermat prime test.



1d) The running time of factoring such a number using trial division.



2. Given the number n = 21, list the numbers which have multiplicative
   inverses mod n.








3. For the RSA algorithm, what are each of the following used for?

3a) n



3b) e



3c) d



3d) Give a formula indicating how a message is encrypted (using n, e, and/or d).



3e) Give a formula indicating how a ciphertext is decrypted (using n, e, and/or d).