Ask Computer Engineering Expert

Task 1

a. Consider the table in Figure given below showing the relative frequencies of letters in English. Arrange the frequencies from largest to smallest, and make a cumulative plot, using Excel for ex. Which smallest group of letters accounts for at least 50% of all letters used in English?

Requirements:

Include all steps to reach the solution as a clear, well-labelled graph and correct answer to letter set

1722_Frequencies of letters.jpg

b. An affine cipher scheme can be mathematically expressed in the following form

 C(x) = (αx +β) mod 26.

Here α and β  are numbers selected in the range 1 ≤ α , β < 26, and x represents a letter converted to a number using the rule a = 0,  b = 1,…,   y = 24 and z = 25.

i. What are the α and β  values for the Caesar cipher? Show the steps and solution

ii. Encrypt the plaintext “MOUNTPANORAMA” using  α = 11 and  β = 7.
Show the solution plus the transformed alphabet

iii. Why is  α = 2 and  β = 0 not a good choice of affine cipher parameters when there are 26 letters in the alphabet?
Provide a convincing argument supported by worked ex

c. An affine cipher does not alter the letter frequencies of the plaintext, but merely rearranges them. Describe a general method for recovering α and β  from the two most frequent letters observed in a large amount of ciphertext.

Presentation of the argument or proof, using equations, to recover the affine cipher parameters and the use of a supporting ex

Task 2

a. The keyspace for a cipher is the set all of possible keys that can be used for the cipher. A DES key consists of 56 (independent) bits.

i. Express the size of the DES keyspace to the nearest power of 10, and find three exs of physical quantities, or other known values, that are approximately the same size.

Correct power of 10, and 3 exs with evidence of correctness

ii. Consider the collection of passwords defined by combinations of digits and letters (both upper and lower case). What password length would be required so that the number of possible passwords is at least the size of the DES keyspace? Correct password length with working solution

b. Encryption is only useful if there is a matching reversible operation called decryption. In a Feistel cipher, the F-function or round function need not be reversible.

i. Show that F-function of DES is not reversible

Provide an ex showing that part of all of the DES round function cannot be reversible

ii. describe how a Feistel cipher whose main component is not reversible can actually support decryption.

Provide a correct written description supported by diagram

Task 3

a. Let DESk(P) denote the DES encryption of the plaintext P by the key K.

i. If we set K to be the key consisting of all zeroes, describe why encrypting twice with this key for DES has the same effect as encrypting then decrypting. Equivalently, account for the following property when using the all-zero key:

 DESk(DESk(P)) = P

Provide correct argument involving interaction of key schedule, encryption and decryption of DES

ii. Find another key that also has this property, and describe the structure of the DES key schedule that permit such keys to exist.

Provide the correct identification of the additional key and a convincing explanation of the DES key schedule property that produces equivalent keys for encryption and decryption

b. Let  denote the complement of a sequence of bits, so that for ex 0100 = 1011. Then considering the round structure of DES, show that

DESk(P) =  2443_DES.jpg

In other words, complementing the key, plaintext and ciphertext produces the same ciphertext as when none of these values is complemented.

Hint: Use the following property of the XOR function X ⊕ X  = 0. Provide a correct argument for describeing the reason for the complementation in DES, using diagrams involving the round function

Task 4

a. The basis of differential cryptanalysis is finding a pair of differences (ΔP ,ΔC  ) such that plaintext pairs whose XOR difference is ΔP lead to a corresponding ciphertext difference ΔC  after a certain number of rounds. The pair (ΔP ,ΔC ) is called a differential.

The figure below shows a 64-bit differential for DES, which can be written in hexadecimal as:

ΔP = ΔC  = 40 08 00 00 04 00 00 00

1947_Differential for DES.jpg

This differential predicts the difference of ciphertexts after 3 rounds with a probability of

1/4 x1x1/4=1/22

i. How many plaintext pairs of difference ΔP need to be considered by an attacker on average before ΔC is observed as the difference between the ciphertexts after 3 rounds? Hint: How many times on average must you flip a coin before seeing a head? Correct answer with working shown

ii. The differential in the figure above has the property that ΔP = ΔC  after three rounds, and is called iterative since it can be joined to itself to create a differential for a larger number of rounds. What is the probability of this differential if it is extended out to 15 rounds? Correct answer with working shown

iii. The data complexity of a differential attack is the number of pairs needed to recover information about the key. Show that if the attack is using a differential with probability " then the data complexity must be at least 1/p pairs. Correct answer with working shown

iv. Consider a version of DES extended out to 64 rounds, using the same Ffunction, and consider an attack using the iterative differential described in this task. At what round would the data complexity of the attack exceed the amount of available plaintext? Correct answer with working shown.

Computer Engineering, Engineering

  • Category:- Computer Engineering
  • Reference No.:- M92050

Have any Question?


Related Questions in Computer Engineering

Does bmw have a guided missile corporate culture and

Does BMW have a guided missile corporate culture, and incubator corporate culture, a family corporate culture, or an Eiffel tower corporate culture?

Rebecca borrows 10000 at 18 compounded annually she pays

Rebecca borrows $10,000 at 18% compounded annually. She pays off the loan over a 5-year period with annual payments, starting at year 1. Each successive payment is $700 greater than the previous payment. (a) How much was ...

Jeff decides to start saving some money from this upcoming

Jeff decides to start saving some money from this upcoming month onwards. He decides to save only $500 at first, but each month he will increase the amount invested by $100. He will do it for 60 months (including the fir ...

Suppose you make 30 annual investments in a fund that pays

Suppose you make 30 annual investments in a fund that pays 6% compounded annually. If your first deposit is $7,500 and each successive deposit is 6% greater than the preceding deposit, how much will be in the fund immedi ...

Question -under what circumstances is it ethical if ever to

Question :- Under what circumstances is it ethical, if ever, to use consumer information in marketing research? Explain why you consider it ethical or unethical.

What are the differences between four types of economics

What are the differences between four types of economics evaluations and their differences with other two (budget impact analysis (BIA) and cost of illness (COI) studies)?

What type of economic system does norway have explain some

What type of economic system does Norway have? Explain some of the benefits of this system to the country and some of the drawbacks,

Among the who imf and wto which of these governmental

Among the WHO, IMF, and WTO, which of these governmental institutions do you feel has most profoundly shaped healthcare outcomes in low-income countries and why? Please support your reasons with examples and research/doc ...

A real estate developer will build two different types of

A real estate developer will build two different types of apartments in a residential area: one- bedroom apartments and two-bedroom apartments. In addition, the developer will build either a swimming pool or a tennis cou ...

Question what some of the reasons that evolutionary models

Question : What some of the reasons that evolutionary models are considered by many to be the best approach to software development. The response must be typed, single spaced, must be in times new roman font (size 12) an ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

Why might a bank avoid the use of interest rate swaps even

Why might a bank avoid the use of interest rate swaps, even when the institution is exposed to significant interest rate

Describe the difference between zero coupon bonds and

Describe the difference between zero coupon bonds and coupon bonds. Under what conditions will a coupon bond sell at a p

Compute the present value of an annuity of 880 per year

Compute the present value of an annuity of $ 880 per year for 16 years, given a discount rate of 6 percent per annum. As

Compute the present value of an 1150 payment made in ten

Compute the present value of an $1,150 payment made in ten years when the discount rate is 12 percent. (Do not round int

Compute the present value of an annuity of 699 per year

Compute the present value of an annuity of $ 699 per year for 19 years, given a discount rate of 6 percent per annum. As