AiS Challenge Team Interim


Team Number: 53

School Name: Moriarty High School

Area of Science: Cryptology

Project Title: Cryptoanalysis



	Cryptology is the art of encoding and decoding messages and has 
been important throughout history.  In ancient days people used 
concealment ciphers.  The message was there but somehow hidden. Another 
way of encrypting in the early days was transposition ciphers.  You would 
write a message in columns and you would read it in a diagonal direction. 
Another way of encrypting is substitution ciphers.  In substitution 
ciphers, numbers and symbols replace the letters.  Today, cryptology has 
become a very important topic. In the world there is a high security need 
to encrypt and decode messages. Through this expanding field of study, a 
project is formed. 

For our project we plan to create a program that will encrypt a message in 
a new way. In our design we will attempt to incorporate the use of 
fractals to encrypt the message.  Presently, we are starting small and 
learning to encrypt messages using substitution - a method of encryption 
long known and used.  After we have experience with encrypting and 
knowledge about fractals, we will combine our research to make a 
fractal-encoding program.  The project could be advanced further by 
decrypting the newly formed message by the reverse process in which it was 

Proposed Method of Solution
Although this project will be difficult it can be accomplished. We will 
begin by studying encryption and messages that are encrypted. Then we will 
need to set up a math model to encrypt messages in a new and, or, more 
efficient way. Next, we will implement parallel processing to speed up 
encryption time. Finally, the project can be extended by setting up a way 
to decode encryptions such as the one created. 

Project Significance
This project will be important in today's National Security Issues. There 
would be a great advantage if our country were able to encode information 
in ways impossible to decode while decoding secret information that we 
need to know. We find cryptology to be very interesting.  As young 
children, the element of making something only a select few can understand 
has been very exciting. Now, as young adults, we are still fascinated with 
this idea, and want to continue it through the encryption program we are 
generating.  We want to create a code that will present a unique way of 
encrypting messages.

Our team attended the Supercomputing conference in Glorieta near the end 
of October.  While there, we asked many scientists for help with refining 
our project to a more doable one.  One expert instructed us that we should 
focus our project on a new way to encrypt messages.  He suggested using 
fractals as the new way of encryption.  We have followed his advice and 
looked up information on fractals as well as general encryption.  The 
Challenge also set us up with a mentor who reviewed our abstract.  He 
contacted us and we are making a list of questions for him.  We would like 
to know if he has any background with fractals to add to our research or 
any better ideas for encryption.  He instructed us to focus our project 
and we want to ask him for suggestions about a simple fractal/encryption 
program we can start to focus with.   We know that mentors are an 
essential part of a successful project. We are also getting help form a 
mentor at Sandia National Lab who suggested that we should start with a 
simple method of encryption such as a substitution cipher. Once the 
substitution cipher worked with our fractal encryption we should then try 
a more complex cipher in its place. 

Math Model / Research
Substitution cipher is very simple to understand.  A substitution cipher 
is when you substitute the regular alphabet for a "cryptobet."  This 
cryptobet is a regular alphabet where the letters are replaced with other 
letters or numbers.  Although there are no set equations for substitution 
ciphers, one equation we tried was as follows.  Since each letter has a 
corresponding ASCII number, we added 25 to the ASCII number.  This would 
make A Z and R l.  Another substitution method is to put a formula to 
change the first letter.  For example, with the first letter being in the 
variable x changing into the variable y one could use a formula such as y 
= (12*x - 17/8)^2.  This formula would also find a number correlating to a 
letter, but it would be more difficult to decrypt because the formula is 
so complex.  There are many substitution ciphers. We are currently writing 
a simple program that switches the alphabet with a cryptobet so that we 
will know how to implement substitution into our program with fractals.
 To add to our project, we plan to use fractals as a new way to encrypt 
messages.  We need to discuss this with our mentor after completing other, 
simpler encryption methods.  The information we have presently is as 
follows. Fractals are usually simple equations that, when reiterated 
numerous times, create chaotic pictures that sometimes look like real 
life.  One very simple fractal is the Sierpinski Triangle.  This triangle 
can be formed through many different ways.  One is in the form of a game.  
The idea is to mark three points in three different colors and then color 
two sides of a dice each color. You have to start with a spot and then 
roll the die.  Move halfway towards the color you rolled and mark a point 
of that color.  Continue to roll moving halfway towards the color you roll 
each time.  Rather than a mess of points, this game forms a triangle like 
the one shown at left.  Other fractals are formed through diverse ways. 
The Mandelbrot set iterates the equation (z^2+c) with z fixed at 0 and c 
varying.  It is a set of all of the sets of a different fractal set, the 
Julia set.  The Julia set is the function f(z)=z^2+c when z is a point and 
c is a complex number of any value.  There are an infinite number of 
equations and thus an infinite number of fractals.  The fractals are 
created by plotting each point on a screen using the formula.  The points 
that end up going out of the screen are one color, depending on how many 
iterations it takes to leave the screen.  The points from which the 
formula never leaves the screen are a different color.  This creates a 
picture.  The twist is that each point has a real x coordinate and an 
imaginary y coordinate.  This makes numbers needing great accuracy, which 
is why computers are so convenient to use to make fractals. 
From this information we plan to create a program to use fractals in 
cryptology.  Some ideas we have today include substituting the ASCII 
number for each letter as the variable in the equation (this is usually 
"c").  We could also first use a substitution method and then from our 
results we would replace the variable with our substitution.  We need to 
ensure our formula is random enough it is difficult to crack.
Although there is the possibility we will use a different math concept to 
encrypt, fractals are an interesting subject that would be fun to work 
with.  The options are endless with fractals because of their basis in 

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