(Due at the beginning of
class on
This problem set will be graded out of 50 points. It
will count for 10% of your final grade.
1) Modular arithmetic
a) Which of the numbers 1,2,…,20 are coprime to 21?
What is j(21)? [3]
b) What is 3^2008 mod 11?
[3]
c) Name the two mathematical
problems at the heart of most public key systems? [2]
d) What is repeated squaring
and what is it used to compute? [2]
2) RSA & Diffie-Hellman
a) Describe in detail how RSA
works for encryption. What are the public and private keys, how is the message
encrypted and how is the ciphertext decrypted? [3]
b) Describe how RSA is used for
signatures. [2]
c) Describe in detail how Diffie-Hellman can be used for encryption. What are the
public and private keys, how is the message encrypted and how is the ciphertext decrypted? [3]
d) Consider the ElGamal signature scheme with public key <g, p, gS
mod p> where message M is
signed using gRm, Rm + M * S mod
(p –1). Why is it necessary to have a different Rm for each message M? [2]
3) Crypto systems and network
protocols
a) Which is more secure:
112-bit 3DES or 112 bit RSA and why? [2]
b) Describe the basic SSL
handshake. [5]
c) When you use your browser to
connect to your bank’s server using https how come the client (your browser)
does not need its own (public and private) keys? [3]
4) Kerberos vs. PKC, IPSec vs SSL
a) Why is it a myth that
Kerberos requires its (KDC) servers to be online 24x7 whereas there is no such
requirement of PKC-based systems? [2].
b) Why is it a myth that
Kerberos is more secure since the password lives in one’s head whereas in
PKC-based systems the private key lives on disk? [2]
c) Downloadable applications
are often digitally signed to ensure they have not been tampered with. What is
wrong with having an executable, e.g. browser, signed by a CA where the
executable contains the corresponding public key? [2]
d) Describe a DOS attack that
will disable SSL over TCP/IP but will fail to disable IPSec
and explain why. [4]
5) Miscellaneous
a) What is a critical property
of real world polling booths that is absent from all electronic voting schemes?
[2]
b) Alice and Bob have fallen in
love (via the Internet) and Bob wishes to mail
c) Why does
Windows use only the Ctrl-alt-delete sequence to initiate log-in? [3]