Streamciphers

Question 1

In 1949, Shannon introduced the concept of perfect secrecy.

a) Explain perfect secrecy.
b) What are prerequisites for a cipher system to achieve perfect secrecy?
c) It can be shown that Vernam cipher can be perfectly secret. Explain the Vernam cipher.

Question 2

Long periods and high linear complexities of pseudorandom sequences can be achieved in several ways. One of the possibilities is to use non-linear combiners.

a) Explain non-linear combiners.
b) What are the requirements for the combining function in order to be used in such a generator?

Question 3

Golomb defined the basic criteria of pseudorandom sequence cryptographic quality in the form of three postulates. In the definition of these postulates, concepts like “a run” and “autocorrelation out of phase” are used.

a) Define a pseudorandom sequence.
b) Define a run of symbols. Define autocorrelation of a sequence.
c) Explain the three Golomb’s postulates.

Question 4

a) Define the autocorrelation function on the period of a pseudorandom sequence.
b) Explain the Golomb’s third postulate. c) Do sequences produced by non-linear feedback shift registers satisfy the Golomb’s third postulate in general? Why?

Question 5

a) Explain Golomb’s pseudorandomness postulates?
b) Why do we need non-singular automata for generating pseudorandom sequences?

Question 6

a) Enumerate and explain Golomb’s pseudorandomness postulates.
b) Explain the characteristics of linear feedback shift registers with irreducible feedback polynomials. Are they adequate for use in cryptography? Why?

Question 7

a) Explain Golomb’s pseudorandomness postulates?
b) What kind of feedback polynomial of an LFSR is needed for use in cryptography?

Why?

Question 8

a) Explain non-linear feedback shift registers.
b) Explain the binary rate multiplier.

Question 9

An LFSR is given below:

a) What is the feedback polynomial of this LFSR? What is the length ofthis LFSR?
b) Suppose the initial state of the LFSR above is 1101 (from left to right). Can the LFSR generate the output sequence 101110? Why? (Suppose the output bit is taken from the rightmost position of the LFSR)
c) Find the linear complexity, the initial state and the feedback polynomial of the minimal LFSR that generates the sequence S—IOI 110 in GF(2), by means ofthe Berlekamp-Massey algorithm. Draw the LFSR after processing each bit of S. The Berlekamp-Massey algorithm is given below:

Answer 9

IMT4552+Cryptology2+inkl+l_prcent_F8sningsforslag+14mars2016.pdf

Question 10

A Linear Feedback Shift-Register (LFSR) consists of a circulator of length 2 followed by a delay line of length 3.

a) Draw this LFSR. What is the feedback polynomial of the LFSR? What is the length of this LFSR?
b) Suppose the initial state of the LFSR above is 11101 (from left to right).

Can the LFSR genereate the output sequence 101111? Why? (Suppose the output is taken from the rightmost position of the LFSR)

c) Find the linear complexity, the initial state and the feedback polynomial of the minimal LFSR that generates the sequence S=IOI 11 in GF(2), by means of the Berlekamp-Massey algorithm. Draw the LFSR after processing each bit of S. The Berlekamp-Massey algorithm is given below:

Answer 10

IMT4552+Cryptology2+16+mars+2015.pdf