JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisites

A Course on “Computer Networks, Mathematics”.

Course Objectives:

• To understand the importance of cryptanalysis in our increasingly computer-drivenworld.
• To understand the fundamentals of Cryptography
• To understand the Lattice- based cryptanalysis and elliptic curves and pairings
• To understand birthday- based algorithms for functions and attacks on stream ciphers
• To apply the techniques for secure transactions in real world applications

Course Outcomes:

• Ability to apply cryptanalysis in system design to protect it from various attacks.
• Ability to identify and investigate vulnerabilities and security threats and the mechanisms to counter them.
• Ability to analyze security of cryptographic algorithm against brute force attacks, birthday attacks.

UNIT - I

A bird’s – eye view of modern Cryptography: Preliminaries, Defining Security in Cryptography Monoalphabetic Ciphers: Using Direct Standard Alphabets, The Caesar Cipher, Modular arithmetic, Direct Standard alphabets, Solution of direct standard alphabets by completing the plain component, Solving direct standard alphabets by frequency considerations, Alphabets based on decimations of the normal sequence, Solution of decimated standard alphabets, Monoalphabets based on linear transformation. Polyalphabetic Substitution: Polyalphabetic ciphers, Recognition of polyalphabetic ciphers, Determination of number of alphabets, Solution of individual alphabets if standard, Polyalphabetic ciphers with a mixed plain sequence, Matching alphabets, Reduction of a polyalphabetic cipher to a monoalphabetic ciphers with mixed cipher sequences

UNIT - II

Transposition: Columnar transposition, Solution of transpositions with Completely filled rectangles, Incompletely filled rectangles, Solution of incompletely filled rectangles – Probable word method, Incompletely filled rectangles general case, Repetitions between messages; identical length messages. Sieve algorithms: Introductory example: Eratosthenes’s sieve, Sieving for smooth composites

UNIT - III

Brute force Cryptanalysis: Introductory example: Dictionary attacks, Brute force and the DES Algorithm, Brute force as a security mechanism, Brute force steps in advanced cryptanalysis, Brute force and parallel computers. The birthday paradox: Sorting or not?: Introductory example: Birthday attacks on modes of operation, Analysis of birthday paradox bounds, Finding collisions, Application to discrete logarithms in generic groups.

UNIT - IV

Birthday- based algorithms for functions: Algorithmic aspects, Analysis of random functions, Number-theoretic applications, A direct cryptographic application in the context of blockwise security, Collisions in hash functions. Attacks on stream ciphers: LFSR- based key stream generators,

R19 M. TECH. CN/CNIS/CYBER SECURITY

Correlation attacks, Noisy LFSR model, Algebraic attacks, Extension to some non- linear shift registers, The cube attack.

UNIT - V

Lattice- based cryptanalysis: Direct attacks using lattice reduction, Coppersmith’s small roots attacks. Elliptic curves and pairings: Introduction to elliptic curves, The Weil pairing, the elliptic curve factoring method.

Text Books:

• 1. Elementary Cryptanalysis A Mathematical Approach by Abraham Sinkov, The mathematical Association of America (lnc).
• 2. Algorithmic Cryptanalysis” by Antoine joux, CRC Press’

References:

• 1. Algebraic Cryptanalysis, Bard Gregory, Springer, 2009
• 2. Cryptanalysis of Number Theoretic Ciphers, Sameul S. Wag staff, Champan & Hall/CRC.
• 3. Cryptanalysis: A Study of Cipher and Their Solution, Helen F. Gaines,1989 R19 M. TECH. CN/CNIS/CYBER SECURITY M. Tech. (CNIS/CN/Cyber Security) – I Year – I Semester Common to CNIS, CN and Cyber Security