Download Cryptography and Inverse Linear Function Powerpoint

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