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Genetic Algorithm Cipher Key Analysis

This document summarizes experiments on a genetic algorithm for cracking ciphers. It tested different crossover and mutation rates on ciphers with keys of length 26 and 50. For a cipher with a 26 character key, a 100% crossover rate with 0% mutation rate found fitness plateaued quickly, while 100% crossover and 10% mutation reached a fitness of 0.2638. A 50% crossover rate and 5% mutation rate evolved fitness further to 0.37. In general, higher mutation rates helped solutions escape fitness plateaus, but required larger populations, and strong crossover was important to evolve fitness without relying on mutation.

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31 views2 pages

Genetic Algorithm Cipher Key Analysis

This document summarizes experiments on a genetic algorithm for cracking ciphers. It tested different crossover and mutation rates on ciphers with keys of length 26 and 50. For a cipher with a 26 character key, a 100% crossover rate with 0% mutation rate found fitness plateaued quickly, while 100% crossover and 10% mutation reached a fitness of 0.2638. A 50% crossover rate and 5% mutation rate evolved fitness further to 0.37. In general, higher mutation rates helped solutions escape fitness plateaus, but required larger populations, and strong crossover was important to evolve fitness without relying on mutation.

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Assignment 2

Jacob Hyatt
#​
COSC, Brock University
1​
jh16gc@brocku.ca 
 

V. EXPERIMENTAL SETUP
I. INTRODUCTION FOR BOTH CIPHERS PROVIDED IN THE ASSIGNMENT PDF, A CROSSOVER
This document describes correlations between RATE OF100% AND MUTATION RATE OF 0%, A CROSSOVER RATE OF
different parameters and how they affect the output 100% AND A MUTATION RATE OF 10%, A CROSSOVER RATE OF 90%
AND A MUTATION RATE OF 0%, A CROSSOVER RATE OF 90%, AND
of a Genetic algorithm that aims to find a cipher key
MUTATION RATE OF 10%, WERE ALL TESTED ALONG WITH A CUSTOM
in different lengths of ciphers and lengths of SET OF 50% CROSSOVER RATE AND A 5% MUTATION RATE.
chromosomes/keys.
VI. RESULTS
II. PROBLEM
The problem with this specific problem is that the
parameters and how they affect the final fitness is VII. DISCUSSIONS AND CONCLUSIONS
slightly random which means that finding the
FINDINGS OF THE FIRST CIPHER WHICH USED A KEY/CHROMOSOME
optimal parameters is difficult without testing SIZE OF 26 FOUND RESULTS OF:
multiple parameters with a variety of problems.
III. SOLUTIONS
With optimal solutions this can help find
parameters that are on average the optimal solution
which then can be carried to other related problems.
IV. BACKGROUND

THE PROGRAM FOLLOWS THE TYPICAL SETUP OF A GENETIC


ALGORITHM. TOURNAMENT SELECTION IS DONE WITH A POPULATION
SIZE OF 5 IN WHICH IT SELECTS 5 RANDOM INDIVIDUALS FROM THE
CURRENT POPULATION AND FINDS THE FITTEST OF THE 5 AS THE (100% UF, 0% MR)
WINNER. CROSSOVER IS DONE WITH A SIMPLE 1 POINT CROSSOVER
LOOPING OVER THE CHROMOSOMES AND USING THE CROSSOVER RATE AS Found that evolution peaked and took long to find evolve to
THE CHANCE OF WHAT PARENT CHROMOSOME IS TO BE TAKEN FOR THE next solution
CHILD.

MUTATION FUNCTION IS SIMPLY USING THE MUTATION RATE FOR A


PERCENTAGE CHANCE OF A CHROMOSOME TO BECOME A RANDOM
CHARACTER.

ELITISM IS USED BY PLACING THE BEST INDIVIDUAL AT INDEX 0 OF THE


POPULATION ARRAY AND STARTING AT INDEX 1 WHEN LOOPING/EDITING
THE POPULATION TO PREVENT EDITING OF THE ELITE.
(100% UR, 10% MR) MINIMUM FINAL FITNESS

Found that the fitness found a best of 0.2638 MINIMUM FITNESS OF CIPHER ONE WAS RECORDED AT 0.1648991
WHILE THE MINIMUM FITNESS OF CIPHER TWO WAS 0.3786434
FINDINGS OF THE SECOND CIPHER FOUND THAT THE FITNESS WAS
GREATER THAN THE FIRST CIPHER, WHICH IS EXPECTED SINCE THE MAXIMUM FINAL FITNESS
POPULATION REMAINED THE SAME WHILE THE SIZE OF THE
KEY/CIPHER INCREASED. MAX FITNESS OF CIPHER ONE WAS RECORDED AT 0.6944101 WHILE
THE MAX OF THE SECOND CIPHER WAS RECORDED AT 0.6978943

ANALYSIS

THE RELATIONS OF 0% MR SEEMS TO POINT THAT THE


CROSSOVER FUNCTION CAN BE IMPROVED UPON WITH A DIFFERENT
CROSSOVER FUNCTIONS SUCH AS 3 POINT CROSSOVER OR UNIFORM 2
POINT.

100% UR ALONG WITH 10% MR SEEMED TO FOLLOW THE SAME


GENERAL PATTERN WITH BOTH CIPHERS EXCEPT WITH THE SECOND
CIPHER IT WOULD APPEAR THAT THE FITNESS TAKES A STEADIER CURVE
WHICH IS EXPLAINED SINCE THE SECOND CIPHER HAS A WIDER RANGE OF
(100% UR, 10% MR) CHARACTERS TO BETTER TEST FITNESS.

Found that the fitness evolved but started peaking at 0.467


VIII. DISCUSSIONS AND CONCLUSIONS

EXPERIMENTS INCLUDE TESTING OF SEVERAL DIFFERENT UNIFORM


RATES AND MUTATION RATES, WHERE FINDINGS FOUND THAT
HAVING A HIGHER MUTATION RATE MAY HAVE A CHANCE AT
GETTING THE FITNESS OUT OF A PLATEAU THIS ALSO MEANS THAT
YOU NEED TO CREATE A LARGER POPULATION SINCE IT WILL MOST
LIKELY TAKE LONGER TO FIND A PROPER CHROMOSOME THAT
INCREASES FITNESS.

MY FINDINGS WITH EXPERIMENTS AT 0% MUTATION RATE HAS


CONCLUDED THAT A STRONG CROSS OVER FUNCTION IS VITAL IN
(50% UR, 5% MR) EVOLVING THE FITNESS WITHOUT RELYING ON MUTATION.

Found the fitness evolved further although still flattened at


0.37

REFERENCES

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