CI7100-Cryptography & Applications Report Writing - Computer Science Assignment Help

Assignment Task

 

Task

 

Module Learning Outcomes:

• Appraise fundamental mathematical and cryptographic concepts – Security Disciplines C and E,Skills .
• Explain common cryptographic methods for securing data and information – Security Disciplines C and E.
• Evaluate mainstream industrial-strength cryptographic algorithms and standards – Security Disciplines C and E.
• Design and categorise cryptographic protocols for implementing a wide range of security requirements .
• Assess applications of cryptography in a range of domains including the latest and future trends .

 

Learning Objectives:

• Understand the definition of integers and their representation using a number system.
• Be familiar with the structure of univariate polynomials over the integers .
• Appreciate the motivation behind introducing boolean numbers.

 

Mini-Exercise 1:

• Convert 10101102 into decimal notation.
• Write the integer 12 as a decimal, binary and ternary number.
• Convert 0.011/2 into decimal notation.
• Write 5/8 as a binary (optional: ternary) number.

 

Learning Objectives:

Understand modular arithmetic:

• Know how to work with polynomials.
• Be familiar with the principles of Boolean Algebra.

 

 

Mini-Exercise 2:

Sketch tables for addition and multiplication mod 2.How could you express this using Boolean operations instead of modular arithmetic?

 

Summary:

Understand modular arithmetic 

• I Know how to work with polynomials.
• I Be familiar with the principles of Boolean Algebra.

 

 

Learning Objectives:

Understand the concept of the Greatest Common Divisor.

I Be familiar with the Euclidean Algorithm.

I Know the definition of the Modular Inverse.

I Be able to use the Extended Euclidean Algorithm in order to compute the Modular Inverse.

 

Mini-Exercise 3:

1. Compute the gcd of 75 and 28, using

    1.1 Prime factor decomposition,
    1.2 The Euclidean algorithm.
2. Find the greatest common divisor g of 799 and 987.
3. Optional: Find integers x and y such that 799x + 987y = g.

 

Mini-Exercise 4:

1. Compute the modular inverse of 28 mod 75.

2. Solve the following linear equations:

2.1 8x ? 1(mod 13)

2.2 6x ? 11(mod 29)

2.3 8x ? 7(mod 11)

 

Summary:

• Understand the concept of the Greatest Common Divisor.
• I Be familiar with the Euclidean Algorithm.
• I Know the definition of the Modular Inverse.
• I Be able to use the Extended Euclidean Algorithm in order to compute the Modular Inverse.

 

Learning Objectives:

• Understand the importance of (computational) number theory for cryptography, and the RSA algorithm in particular.
• Know the definition of a prime number and differentiate between the computational tasks of prime factorisation/primality testing.
• Comprehend the definition of Euler’s Function.
• Be familiar with Fermat’s Little Theorem and Euler’s Theorem, and their use for cryptography.

 

Understand the importance of (computational) number theory for cryptography, and the RSA algorithm in particular.

• Know the definition of a prime number and differentiate between the computational tasks of prime factorisation/primality testing.
• Comprehend the definition of Euler’s Function.
• Be familiar with Fermat’s Little Theorem and Euler’s Theorem, and their use for cryptography.

 

1. Threats, Vulnerabilities, Attacks and Risks

• Threat: set of circumstances with potential to exploit vulnerability and create a risk of harm
• Vulnerability: potentially exploitable weakness of an asset
• Attack: realisation of a threat (”threat event”)
• Risk: occurs if matching threat and vulnerability exist 

 

2.  Controls

A control can be either

• Action.
• Procedure.
• Device.
• Technique.
• Used for protection.
• Either eliminate threat and/or close vulnerability.
• Controls need to be effective.

 

Basic Security Methodology:

The basic methodology in computer security is:

• We detect uncovered vulnerabilities in our system.
• We think about potential threats to our system.
• Finally, we consider available controls (countermeasures).
• Impossible to guarantee security, can only minimise risk.
• Need for periodic review.

 

Learning Objectives – Cryptography Concepts:

Have an overview of the main cryptographic techniques.

• Be able to recognise a particular cryptographic technique from an example (historical) scenario.
• Understand the main terminology used in cryptography,for each of the techniques.

 

 

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