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AES Cryptosystem Overview: Security, Efficiency & Key Generation

Understand the Advanced Encryption Standard (AES) evaluating criteria like security, efficiency, and key generation. Explore AES operations: byte substitution, shift row, mix column, add round key. Study AES key length, block size, and the relationship between DES and AES. Algorithm background in computer security with concepts of time complexity, space complexity, and polynomial-time algorithms. Learn about bin packing and partitioning problems in algorithm design.

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AES Cryptosystem Overview: Security, Efficiency & Key Generation

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  1. Lecture 6 Overview

  2. The minimum requirements • A symmetric-key cryptosystem • A block cipher • Capable of supporting a block size of 128 bits • Capable of supporting key length of 128, 192, and 256 bits • Available on a worldwide, non-exclusive, royalty-free basis CS 450/650 Lecture 6: AES

  3. Criteria for Evaluation • Security • Soundness of the mathematical basis for an algorithm’s claimed strength • Research community search for flaws • Computational Efficiency • Memory Requirements • Flexibility • Simplicity CS 450/650 Lecture 6: AES

  4. Advanced Encryption Standard • 10, 12, 14 rounds for 128, 192, 256 bit keys • Regular Rounds (9, 11, 13) • Final Round is different (10th, 12th, 14th) • Each regular round consists of 4 steps • Byte substitution (BSB) • Shift row (SR) • Mix column (MC) • Add Round key (ARK) CS 450/650 Lecture 6: AES

  5. AES Overview Plaintext (128) ARK Subkey0 9 rounds BSB SR Ciphertext (128) ARK Subkey10 CS 450/650 Lecture 6: AES

  6. Round i operations 128-bit substitution boxes confusion transposition step of circular shift confusion Left shift and XOR of bits diffusion and confusion portion of key is XORed confusion Subkeyi CS 450/650 Lecture 6: AES

  7. Shift Row (128-bit) CS 450/650 Lecture 6: AES

  8. Mix Column = * Multiplying by 1  no change Multiplying by 2  shift left one bit Multiplying by 3  shift left one bit and XOR with original value More than 8 bits  100011011 is subtracted CS 450/650 Lecture 6: AES

  9. Add Key = b’x bx kx XOR CS 450/650 Lecture 6: AES

  10. 4 bytes 4 bytes 4 bytes 4 bytes 4 bytes 4 bytes 4 bytes 4 bytes Key Generation Circular left shift 1byte S-box XOR XOR Round constant XOR XOR CS 450/650 Lecture 6: AES

  11. DES vs AES CS 450/650 Lecture 6: AES

  12. Lecture 8 Algorithm Background CS 450/650 Fundamentals of Integrated Computer Security Slides are modified from Hesham El-Rewini

  13. Analysis of Algorithms • Algorithms • Time Complexity • Space Complexity • An algorithm whose time complexity is bounded by a polynomial is called a polynomial-time algorithm. • An algorithm is considered to be efficient if it runs in polynomial time. CS 450/650 Lecture 8: Algorithm Background

  14. Time and Space • Should be calculated as function of problem size (n) • Sorting an array of size n, • Searching a list of size n, • Multiplication of two matrices of size n by n • T(n) = function of n (time) • S(n) = function of n (space) CS 450/650 Lecture 8: Algorithm Background

  15. Growth Rate • We Compare functions by comparing their relative rates of growth. 1000n vs. n2 CS 450/650 Lecture 8: Algorithm Background

  16. Definitions • T(n) = O(f(n)): T is bounded above by f The growth rate of T(n) <= growth rate of f(n) • T(n) = W (g(n)): T is bounded below by g The growth rate of T(n) >= growth rate of g(n) • T(n) = Q(h(n)): T is bounded both above and below by h The growth rate of T(n) = growth rate of h(n) • T(n) = o(p(n)): T is dominated by p The growth rate of T(n) < growth rate of p(n) CS 450/650 Lecture 8: Algorithm Background

  17. Time Complexity • C • O(n) • O(log n) • O(nlogn) • O(n2) • … • O(nk) • O(2n) • O(kn) • O(nn) Polynomial O(2log n) Exponential CS 450/650 Lecture 8: Algorithm Background

  18. P, NP, NP-hard, NP-complete • A problem belongs to the class P if the problem can be solved by a polynomial-time algorithm • A problem belongs to the class NP if the correctness of the problem’s solution can be verified by a polynomial-time algorithm • A problem is NP-hard if it is as hard as any problem in NP • Existence of a polynomial-time algorithm for an NP-hard problem implies the existence of polynomial solutions for every problem in NP • NP-complete problems are the NP-hard problems that are also in NP CS 450/650 Lecture 8: Algorithm Background

  19. Relationships between different classes NP NP-hard NP-complete P CS 450/650 Lecture 8: Algorithm Background

  20. Partitioning Problem Given a set of n integers, partition the integers into two subsets such that the difference between the sum of the elements in the two subsets is minimum 13, 37, 42, 59, 86, 100 CS 450/650 Lecture 8: Algorithm Background

  21. Bin Packing Problem • Suppose you are given n items of sizes s1, s2,..., sn • All sizes satisfy 0  si  1 • The problem is to pack these items in the fewest number of bins, • given that each bin has unit capacity CS 450/650 Lecture 8: Algorithm Background

  22. Bin Packing Problem Example (Optimal; Solution) for 7 items of sizes: 0.2, 0.5, 0.4, 0.7, 0.1, 0.3, 0.8. CS 450/650 Lecture 8: Algorithm Background

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