!
Problem: Given k binary polynomials p1, p2, . , pk in n
variables x1 , . , xk, determine whether these polynomials
have a common zero (z1, . , zk).
!
As k and n increase, this problem rapidly becomes
intractable.
!
Theorem: The problem of deciding wheth
LECTURE February 8, 2011 A stick of unit length is split into two pieces. The breakpoint is randomly selected. On average, how long is the shorter piece? Simulation: Use code to imitate the physical experiment % one trial of the experiment breakPt= rand(1
LECTURE February 10, 2011 *If loop body contains an empty set [ ] the loop body won't execute, there is not an error Example1: Circumscribed/Inscribed Hexagon: Find n such that outerA and innerA converge First, itemize the tasks: - define how close is clo
LECTURE February 15, 20110 DrawRect(x of lower left corner, y of lower left corner, width, height, `color') DrawDisk(x center, y center, radius, `color') DrawStar(x center, y center, radius, `color') COLORS: `w' white `k' black `r' red `b' blue `g' green
LECTURE February 17, 2011 Rational approximation of : = 3.141592653. Can be closely approximated by fractions (i.e. 22/7) Rational number: a quotient of two integers Approximate pi as p/q where p and q are positive integers <= M Start with a straight forw
LECTURE March 1, 2011
*Review computer memory space, user defined function
*Review interpolation
Execute statement y= foo(x)
Matlab looks for a function called foo (m-file called foo.m)
Argument (value of x) is copied into function foos local
paramenter
LECTURE March 3, 2011
Example: Write a program fragment that calculates the cumulative
sums of a given vector v
Sums should be stored in vector of same length as v
1, 3, 5, 0
1, 4, 9, 9
v
cumulative sums of v
csum(1)= v(1);
for k= 2:1:length(v)
csum(k)=
LECTURE March 8, 2011
Two Dimensional Arrays:
Matrix
More like tables, not single row or column
Two indices identify the position of a value in a matrix
o mat(r,c)
o component in row r, column c of matrix mat
Array index starts at |
Rectangular: all
LECTURE March 15, 2011
Common formats of images
o JPEG: joint photographic experts group
o GIF: graphics interchange format
Data are compressed
We will work with jpeg files:
o imread: read a .jpg file and convert it to a normal numeric
array that we can
LECTURE March 17, 2011
Averaging the RGB values to get a gray value:
.3R + .59G+.11B (weighted average, more sensitive to certain
colors)
Divide each color by 3, add together to make another scalar
Scalar operation
Dirt in the image:
Pixel numbers wil
LECTURE March 29, 2011
A string is made up of individual characters, so a string is a 1-d
array of characters
cs1112 rocks is a character array of length 13; it has 7 letters, 4
digits, 1 space, and 1 symbol
Can have 2-d array of characters as well
char c
LECTURE March 31, 2011
See examples
Cell array- special array whose individual components may contain different
types of data
Use brace cfw_ for creating and addressing cell arrays
To address a specific component of array, also use braces
Creating cell a
LECTURE April 5, 2011
Simple array- each component stores one value (e.g., char, double,
uint8); all components have same type
Cell array- each cell can store something bigger than one value
(e.g., vector, matrix, string); cells may store items of differ
!
We assume the existence of an opponent that can do the following: ! block the flow of information ! record information and repeat it later in a spurious transmission ! change the content of a message through insertion or deletion of information or rearr
!
Computational complexity is a very important area in Computer
Science. It deals with questions of the following type.
*! When is a problem impossible to solve?
*! When is a solvable problem so difficult that the solution
would require too much effort?
!
!
Best Reference: Kahn, D., The Codebreakers: The Story of Secret
Writing, New York: MacMillan, 1967.
!
The earliest known cryptogram was chiseled into one of the
interior walls of the tomb of Khnumhotep II in Menet Khufu, Egypt
approximately 4,000 years
!
The systems that we have examined thus far are called "classical" or
"symmetrical" cryptosystems in that the same key is use for both
encryption and decryption.
!
Modern classical systems are characterized through the use of
extremely deep statistical a
! The systems that we have examined thus far are called "classical" or
"symmetrical" cryptosystems in that the same key is use for both
encryption and decryption.
! Modern classical systems are characterized through the use of
extremely deep statistical a
!
RSA was designed in an effort to create a public key
system whose secrecy was derived from the difficulty of
factoring large numbers.
!
RSA is the single most popular public key cryptosystem
in the world today.
!
RSA Inc. supports the design and impleme
!
RSA was designed in an effort to create a public key
system whose secrecy was derived from the difficulty of
factoring large numbers.
!
RSA is the single most popular public key cryptosystem
in the world today.
!
RSA Inc. supports the design and impleme
!
We assume the existence of an opponent that can do the following:
! block the flow of information
! record information and repeat it later in a spurious transmission
! change the content of a message through insertion or deletion of
information or rearr
!
Authentication is used for access control.
!
Encryption is used to ensure privacy and
protection of user information.
!
Both functions are usually combined in
the derivation of a session key for a given
call.
!
The combined process is called the
Authent
ENGRI 1280
Stephen Wicker
!
!
!
!
!
English jurist, philosopher
Advocate of utilitarianism
Legal positivist
considered natural rights
to be nonsense on stilts
Avid materialist: To make
a point, he had himself
stuffed and put on display
when he died.
Prop
PROJECT: PRIVACY-AWARE
DESIGN PRACTICES
Steve Wicker
ENGRI 1280
YOUR ASSIGNMENT!
Select a system that collects some form of user
information.
! Characterize the information collected
!
!
!
!
What can they learn about you?
Is the data collection absolutely
!
Cryptology: The general study of methods for securing information
against disclosure to unauthorized parties. This study includes
Cryptography and Cryptanalysis.
!
Cryptosystem: A machine that obscures the contents of a message
so that only the intended
Searching for an item in an unorganized collection: *May need to look through the whole collection to find the target item (ex. linear search through vector) *For linear search, work is proportional to the length of vector The "bubble" process - sorting p