Cryptography Applied to
Linear Functions
Louena L. Manluctao
East Early College High School
Houston Independent School District
Dr. Guofei Gu
Assistant Professor
College of Computer Science and
Engineering
Texas A & M University
Roadmap
• Introduction
•
•
•
•
- Bridging Research to Lesson
- STAAR/TEKS Objective
The Classroom Project
Samples of Pre-Test/Post-Test
Acknowledgements
Q&A
Research Interest
•Network and system security such as
Internet malware detection, defense,
and analysis
• Intrusion detection, anomaly detection
• Network security
• Web and social networking security
Relevance of the Research
• http://www.youtube.com/watch?v=Mh1tf
KyC-bY
Sony Pictures hacked by Luiz Security,
1,000,000 passwords claimed stolen
(update)
http://consumerist.com/2011/06/how-hackers-stole-200000-citiaccounts-by-exploiting-basic-browser-vulnerability.html
Bridging Research to Lesson in
Algebra 1
Research Lab
Cryptography
Probability and Statistics
Number Theory
Abstract Algebra
Programming
Algebra 1
Linear
Functions
and Sequences
STAAR/TEKS OBJECTIVES
A1.3
& A1.4 (C) Linear Functions:
(A) use symbols to represent unknowns and
variables; and
(B) look for patterns and represent eneralizations
algebraically.
(C)
connect equation notation with function
notation, such as y = x + 1 and f(x) = x + 1.
STAAR/TEKS OBJECTIVE
(7) Linear functions. The student
formulates equations and inequalities
based on linear functions,
(A) analyze situations involving linear
functions and formulate linear equations
or inequalities to solve problems;
THE CLASSROOM PROJECT :
CRYPTOGRAPHY APPLIED TO LINEAR
FUNCTION
• Day 1:
• Pre-Test
• Hook
• Power Point Presentation on Computer
Network Security and Cryptography
• Explain ( How to encrypt and decrypt)
• Worksheets on finding the function key
HOOK
• Find the sum of 5 sets of 4-digit numbers
without using the calculator.
• I am texting this message, -4, -13, 2, -22,
-1, -46, -46, -73
what do you think is it?
• Do you think your computers are safe
from cyber attack in your own homes?
Power Point on Cryptography
• What is cryptography?
• Different Kinds of Cryptography
• How to Encrypt and Decrypt
Encrypt/Decrypt
Finding The Key (Linear Equation)
• The key will be the equation from a given
sequence:
• Consider: 3, 6, 9, 12, 15
5,9,13,17,21
9,7,5,3,1,-1
-3,3,9,15,21
Cont.
• The common difference is the multiplier of
n (the position of the term)
• To find out what should be added or
subtracted, find the zero term
• We are now going to develop a formula
• First let us define our variables:
• T = the nth term
z = the zero term
• d= the common difference
• n = position in the sequence
Cont.
Sequence
Difference
of terms
Difference
Multiplied by
Position n
The zero
The
term
Equation
(1st term-d)
3,6,9,12,15
3
3n
3-3=0
T = 3n+0
5,9,13,17,21
4
4n
5-4=1
T = 4n+1
9,7,5,3,1,-1
-2
-2n
9—2=11
T = -2n+11
-3,3,9,15,21
6
6n
-3-6=-9
T = 6n - 9
The equation is T = dn + z or
y = mx + b
Write an equation to describe
the following sequences
1. 9, 8, 7, 6, 5
2. 13, 17 , 21, 25, 29
3. 6, 11, 16, 21, 26
4. 112, 100, 88, 76
Day 2:
• Review of Previous Lesson
• Discussion of Finding the Inverse of the
equation of the line.
• Decoding Activity
• Post-Test
To Find the Inverse of an
Equation
• Exchange x and y
• Solve for y in terms of x
Ex. Y = 3x
x = 3y
x/3 = y
Find the inverse of the following
equations
• 1.
• 2.
• 3.
• 4.
y
y
y
y
=
=
=
=
3x + 5
-2x -4
4x – 6
3/4x + 2
The Decoding Activity
• Students will be grouped by two’s
• Each pair will be given a sequence where
they will need to find the key.
• Use the key to find the encrypted code
• Decipher using inverse equation.
• Use : Space = 0 ; A = 1; B=2; C=3…Z=26
• Give the message.
What is the text message?
-4, -13, 2, -22, -1, -46, -46, -73
• Key: -1, -4, -7, -10, . . .
• What is the encrypted key? y = -3x+2
• What is the decrypted key? Y = -(x-2)/3
• What is the deciphered message?
2, 5 , 0, 8, 1, 16, 16, 25
Plaintext message is:
BE HAPPY
Decoding Activity: What is the message?
• -21 3 -35 -11 5 -13 -33 5 - 37 -33 -5 -7 -37 -15
•
5 3 -23 -3 5 -7 -37 -23
KEY: 3, 1, -1, -3, …
• What is the encrypted key? ( y = mx+b)
•
•
•
•
___________________
What is the decrypted key? ________
What is the deciphered message?__________
Remember : Space = 0 A = 1 B =2 C =3…
Z = 26
Plaintext Message:
_________________________________
Assessment: Pre-Test/Post Test
Sample Questions
1. The nth term of a sequence is defined
to be 3n +7. The 35th term is how much
less than the 39th term?
A)4
B) 12 C) 19
D) 33
2. Given the sequence -5, -2, 1, 4 … which
equation best represents the sequence?
A) y =3x-5
C) y = 3x-8
B) y = -3x-5
D) y = -3x-8
Acknowledgements
Dr. Robin Autenrieth, Dr. Cheryl Page, Dr. Arun Srinivasa
Matthew Pariyothorn, Ashwin Rao, Roberto Dimaliwat,
Stephen Hudson
Dr. Guofei Gu, Chao Yang,
Jialong Zhang , Wilber Rivas
Question and Answer
Thanks to Chao Yang’s Presentation