Cryptography Reference
In-Depth Information
(b) This cryptographic analogy of the briefcase protocol does not always work;
what property does a symmetric cryptosystem need to have for it to work?
(c) Give an example of a symmetric cryptosystem that has this property.
2
. Which of the following statements are true?
(a) The RSA cryptosystem will be broken if large primes can be factored.
(b) The ElGamal cryptosystem is not used in practice because of security
concerns.
(c) RSA encryption is efficient to compute, whereas ElGamal encryption is not.
(d) RSA encryption does not involve significant message expansion.
(e) The security of the ElGamal cryptosystem is equivalent to solving the
discrete logarithm problem.
3
. RSA operates on plaintexts that are modular numbers, thus we must have
some means of converting plaintext and ciphertext into modular numbers. This
activity suggests different ways in which this conversion can be done.
(a) Use ASCII to write the plaintext CAT as a string of 21 bits.
(b) Divide this bit string into seven blocks of three bits and write each as an
integer from 0 to 7.
(c) Encrypt each of these seven blocks using RSA, where
p
=
3,
q
=
5 and
3, writing the resulting ciphertext as a sequence of seven integers in the
range 0 to 14.
(d) Using four bits per number, convert the ciphertext to a bit string.
(e) Write the ciphertext in hex.
4
. Consider setting up RSA with
p
=
7 and
q
=
11.
(a) What are the suitable values for
e
?
(b) If
e
e
=
13, what is the value of
d
?
(c) What is the largest 'block size' in bits that we could use for RSA encryption
using these parameters?
5
. An ElGamal cryptosystem can be implemented in such a way that all users
share the same system-wide parameters
p
and
g
. This raises the question as to
whether it is possible for all users of an RSA cryptosystem to share a common
modulus
n
.
(a) Suppose that Alice and Bob have each generated their own RSA public keys
with the same modulus
n
but different public exponents
e
A
and
e
B
. Explain
why Alice will be able to decrypt encrypted messages sent to Bob (and vice
versa).
(b) Suppose that a trusted third party generates Alice and Bob's RSA key pairs
for them. Find out, perhaps by consulting external resources, whether it is
now acceptable for Alice and Bob to share a common modulus
n
.
=
6
. Over the years there have been various factoring 'challenge' competitions
set up.
