School of Computing and Information Systems
COMP30023: Computer Systems
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Tutorial Week 5
Cryptography
1. What is the difference between a symmetric-key system and a public-key
2. Suppose N people want to communicate with each of N − 1 other people
using symmetric key encryption. All communication between any two
people, i and j, is visible to all other people in this group of N , and no
other person in this group should be able to decode their communication.
How many keys are required in the system as a whole? Now suppose that
public key encryption is used. How many keys are required in this case?
3. Is AES an asymmetric or symmetric cryptography algorithm? Why should
you never use ECB mode in AES?
4. Why is asymmetric key cryptography not often used to encrypt actual
messages? Describe how asymmetric key cryptography is commonly used
in combination with symmetric key cryptography to encrypt messages.
5. In the lectures we saw that authenticated encryption can be achieved by
using secure semantic encryption and message authentication code via
Encrypt-then-authenticate paradigm: given m the output is set to (c, t)
where c := Enc(s1,m), t := MAC(s2, c) and s1 and s2 are the secret
keys of the corresponding schemes. Consider a different candidate for
authenticated encryption where (c, t′) are set as follows: c as above and
t′ = MAC(s2,m). Does this scheme provide secure authenticated encryp-
tion? If it does, show that if you can break it, then you can break either
the underlying encryption or the underlying MAC scheme. If it does not,
provide a counter example.
Continued on the next page
Weekly tutorial participation activity
To obtain a weekly tutorial mark (1% of your overall mark for the subject,
totalling to 10% over the semester), please answer the following questions in
Canvas Quiz (called Week 5 Tutorial Activity). You can have multiple
attempts but need to submit the quiz by 11:59 pm AEDT on the day of
your tutorial. Only answering all questions correctly will give you the week’s
During the tutorial, your tutor will provide you with the access code that will
unlock the quiz for the corresponding week. The access code is valid only for
students in this tutorial. As a result, we expect you to attend your tutorial
class as otherwise the access code you obtain in another tutorial will not work
If you have a valid reason for not being able to attend your tutorial, please fill in
the form accessible via Canvas by Friday 8pm AEDT of the corresponding week.
You will be given an access code during the next business day. The code will not
be provided otherwise, hence, please do not email the subject coordinator or other
staff members including your tutor asking for the code. We will monitor such
requests and may limit the number of times an access code is given to the same
student throughout the semester to encourage participation and attendance of
the tutorials.
1. One time pad is an example of an asymmetric encryption scheme. (True/False)
2. A digital signature s := Sign(SK, h), where h is a hash digest of a doc-
ument, can be verified by anyone who has access to: (Multiple answer
(a) A collision resistant hash function used to hash the document
(b) Hash h and the private/signing key SK
(c) Hash h and the public key of the corresponding digital signature
(d) The document
3. Birthday paradox: in a room with 24 people the probability of 2 of them
having a birthday on the same day is at least 1/2. More generally, the
probability that all m have a birthday on different days is approximately
2/2n where n = 365 days.
In lectures we saw that a cryptographic hash function H is secure if it
is hard to find a collision. That is, find messages m 6= m′ such that
H(m) = H(m′). Assume that H takes arbitrary size input and returns
an output of 160 bits.
After approximately how many inputs the probability of a collision is at
least 1/2 using a brute-force method to find a collision?
4. Suppose public parameters for Diffie-Hellman (DH) key exchange are g = 2
and p = 11, while secret values of two parties are x = 4 and y = 2. What
is the value of the shared secret value that each party has after DH key
exchange protocol?
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