A Genetic Algorithm for Cipher text-Only Attack in Cryptanalysis

1. A Genetic Algorithm for Cipher text-Only Attack in Cryptanalysis Agenda: Genetic Algorithms Cryptanalysis Proposed Algorithm

2. Genetic Algorithm Genetic Algorithms are good at taking large, potentially huge search spaces and navigating them, looking for optimal combinations of things, solutions you might not otherwise find in a lifetime. Genetic algorithms (GA) are a computational paradigm inspired by the mechanics of natural evolution, including survival of the fittest, reproduction, and mutation. A genetic algorithm for cipher text only attack in cryptanalysis

3. Children Reproduction Modification Modified children Parents Evaluated children Population Evaluation Deleted members Discard Genetic Algorithm contd…. • Simple Genetic Algorithm { initialize population; evaluate population; while TerminationCriteriaNotSatisfied { select parents for reproduction; perform recombination and mutation; evaluate population; } } A genetic algorithm for cipher text only attack in cryptanalysis

4. Real Time Example The Optimization Problem: - The problem is simply stated. Find the maximum value of the following function: Y = - X^2 + 8X + 25 How would you do that on paper? A genetic algorithm for cipher text only attack in cryptanalysis

5. Real Time Example contd…. • Fitness Function would be: - • Fitness factor ( for evaluation): - fi / ∑ f. • Initial Population is taken randomly as: - • 2 – 00010 • 7 – 00111 • 22 – 10110 • 11 – 01011 • Next we will calculate the fitness and then based on fitness would mate those members to get a new generation. A genetic algorithm for cipher text only attack in cryptanalysis

6. Real Time Example contd…. A genetic algorithm for cipher text only attack in cryptanalysis

7. Real Time Example contd…. A genetic algorithm for cipher text only attack in cryptanalysis

8. Real Time Example contd…. • With zero knowledge except the fitness value, GA begun to converge on optimum value. • GA is effectively blind but ……. • Measure of goodness makes it powerful. • After couple of iterations we get the correct answer as x = 4. A genetic algorithm for cipher text only attack in cryptanalysis

9. Cryptanalysis • Cryptanalysis is the study of mathematical techniques for attempting to defeat cryptographic techniques, and, more generally, information security services. [Menezes et.al] • Types of attacks on various encryption schemes are: - • ciphertext-only attack • known-plaintext attack • chosen-plaintext attack • adaptive chosen-plaintext attack • chosen-ciphertext attack • adaptive chosen-ciphertext attack A genetic algorithm for cipher text only attack in cryptanalysis

10. Proposed Algorithm • Here we are going to discuss a cryptanalysis method based on genetic algorithms to break the Vernam cipher. • Let M = mi, m2. ... denote a plaintext bit stream. • K = kl, k2, ... a key bit stream. • Vermam cipher generates a ciphertext bit stream C = Ek(M) = c1, c2, ..., where ci = (mi + ki) mod p. p is a base. • First, we find out the key K and then decrypt the cipher text to get plain text. • So the algorithm goes here…………….. A genetic algorithm for cipher text only attack in cryptanalysis

11. Proposed Algorithm contd…. • First make a dictionary of words that show up frequently in a general English document, such as the following words: Dictionary = {this, it, has, have, do, does, as. been, what, when, how, why, who, such, the, while, when. ...} • Each chromosome represents a vectors of K = (k1,k2, …..kn). • Good chromosome? ………….Good fitness value. • Such good chromosomes then cross over to make new chromosomes. This things iterates until we get the best chromosome. • How to define this fitness value then so that we can get the possible answer? A genetic algorithm for cipher text only attack in cryptanalysis

12. Proposed Algorithm contd…. • Let K’ represent a key k’1,k’2,…..k’n. M represent the m1,m2,…..mn and C represent the ciphertext c1,c2,…….cn. • We calculate M’ using a chromosome m’1,m’2 using m’i = (ci-ki)mod p. • Define an array Match[1…r] called match counters of key string. • Match[i] is the number of times of the key string k'i k'i+l whose decrypted string m'[i] m'[i+l] appears in the DIC. • To calculate the fitness of a chromosome we simply square the value of each Match[i] and take their summation. i.e. fitness = fitness + Match[i] * Match[i], for 1<= i <= r A genetic algorithm for cipher text only attack in cryptanalysis

13. Proposed Algorithm contd…. • Plain text is M = ATTACK AT DAWN. • Key string K = {22, 3, 15,35,28}, length of string r = 5, and base p = 25. • The intercepted ciphertext C = {WWJKFHCPECADMX). • If one of chromosome is K' = {22, 3, 15, 16, 28) then, • decrypted text M' = {ATTTCK AN DAWH}. • Match counters are Match[l] = 3, Match[2] = 3, Match[3] = 2, Match[4] = 0, and Match[5] = 2. • Thus, fitness of K' is 3^2 + 3^2 + 2^2 + 0^2 + 2^2 = 26. • Other chromosome K" = {12, 3, 15, 20, 28). Here fitness value is 9 only. A genetic algorithm for cipher text only attack in cryptanalysis

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