COMP3223解密算法

Toni Lassila Due 07/03/2022
School of Computing
University of Leeds
Cryptography (COMP3223)
Coursework 1 Submit electronically through Minerva by Monday 7th March 09:00am
Exercise 1: Eve intercepts the following cryptotext and the information that the plaintext is in English, encoded with the
26-character alphabet (a = 0, b = 1, etc.), and encrypted with the Vigenere cipher:
a) Write a short program (e.g. in Python) that reads the cryptotext y and computes the Index of Coincidence:
IC(y) = 1
n(n − 1)
X
a∈B
H(a)(H(a) − 1),
where H(a) is the absolute frequency of the letter a ∈ B in the string y and n is the length of the string. Include
the source code of your program in your answer. [3 marks]
b) Divide the cryptotext into d columns yd,i by taking every dth letter starting from the ith letter. Compute IC(yd,i)
for key lengths d = 1, 2, 3, 4, 5 and columns i = 1, . . . , d. [2 marks]
c) Apply the index of coincidence -test to the values of IC(yd,i) and deduce what is the most likely key length d used
in the Vigenere cipher. [2 marks]
Exercise 2: Let G be any group with finitely many elements. Prove that there exists a positive integer m such that for all
elements a ∈ G we have
a
m = a ◦ a ◦ . . . ◦ a | {z }
m times
= e,
where e is the neutral element of G. [6 marks]
Exercise 3: Alice and Bob use a block cipher such as DES for secure communication.
a) The 3DES cipher involves three rounds of DES applied successively with a total key length of 168 bits. Explain why
4DES using four rounds of DES does not increase the security compared to 3DES when the attacker has access to
a known plaintext-ciphertext pair and explain the method of attack. [4 marks]
b) Alice and Bob use DES in the cipher block chaining (CBC) mode. Suppose that during transmission, one bit in the
i’th ciphertext block Ci
is flipped. How many plaintext blocks will be affected during decryption and how? Justify
your answer by appealing to the definition of the CBC operation mode. [3 marks]
[TOTAL: 20 marks]
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