Crypto example exam
Crypto Example Paper
1
Crypto and SecDev Example Paper
1. Calculate 1 / 8 mod 11 (the inverse of 8) by hand using the equation
subtracting algorithm. Use your result to calculate 5 / 8 mod 11. [ 8 marks ]
2. It is proposed that a modern mechanical rotor machine would make a useful
encryption machine since it does not rely on computer technology, which can
be compromised. How many rotors would be needed for secure encryption?
Justify your answer. [6 marks ]
3. An isolated civilisation has developed a written language based on an alphabet
with just 4 letters: α, β, γ and δ. Their written documents are very long. The
letters do not occur with equal frequency: α occurs 3/8 of the time ; β and γ 1/4
of the time each and δ 1/8 of the time. The probability of any two letter
combination occurring is however just the product of the probability of each
letter occurring independently and there are no special digrams or trigrams.
Calculate the redundancy of his language. You do not need to calculate an
exact number but can leave terms like log2(3) in your answer. [ 12 marks ]
4. How is polynomial arithmetic similar and how does it differ from using
integers mod n? In what way is it better? When must integers mod n be used
rather than polynomial arithmetic? [ 6 marks ]
What is the difference between a+b and a-b when a and b are both integers
mod 2? [3 marks ]
Convert 10102 and 1102 to polynomials, add them up, and convert the
answer back to bit strings. [3 marks ]
5. Describe the RSA public key encryption system and show how it works when
prime numbers 5 and 7 are used to construct the modulus n = 35. Choose an
encryption parameter e and calculate the corresponding decryption parameter
d. Use these values to encrypt the plaintext value 17 and decrypt the resulting
cipher text to recover the plaintext. [ 10 marks ]
6. What is the difference between a peer-to-peer network and a centralised
network? What things are harder to do with a peer-to-peer network? [3 marks]
Why do digital coins have a unique ID while pound coins do not? Is this
similar to the unique ID on bank notes? [ 3 marks ]
What is a crypto-coin ledger and why is it important? [ 3 marks ]
How can you get change when you spend your crypto-coin? [3 marks ]