CRYPTOLOGY (CODING THEORY) AND LOGARITHM

sunflowerplateAI and Robotics

Nov 21, 2013 (3 years and 7 months ago)

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Cryptology


Cryptography


Inventing cipher systems; protecting
communications and storage



Cryptanalysis


Breaking cipher systems

What is used in Cryptology?


Cryptography:


Linear algebra, abstract algebra, number
theory


Cryptanalysis:


Probability, statistics,
combinatorics
,
computing


Caesar Cipher


ABCDEFGHIJKLMNOPQRSTUVWXYZ


Key = 3


DEFGHIJKLMNOPQRSTUVWXYZABC



Example



Plaintext: OLINCOLLEGE


Encryption: Shift by KEY = 3


Ciphertext
: ROLQFROOHJH


Decryption: Shift backwards by KEY = 3


Cryptanalysis of Caesar


Try all 26 possible shifts



Frequency analysis


Substitution Cipher


Permute A
-
Z randomly:

A B C D E F G H I J K L M N O P…
becomes

H Q A W I N F T E B X S F O P C…


Substitute H for A, Q for B, etc.


Example


Plaintext: OLINCOLLEGE


Key: PSEOAPSSIFI


Cryptanalysis of
Subtitution



Try all 26! permutations


Result is
bigger than Avogadro's Number



WWII Folly:

The Weather
-
Beaten Enigma

Cryptos


Jim
Sanborn

Who Cares?


You and me!


Shopping and e
-
commerce


ATMs and online banking


Satellite TV & Radio, Cable TV, CD players


Corporate/government espionage


Who else?


NSA, IDA, RSA, Aerospace, Bell Labs,
AT&T, NASA, Lucent, Amazon, iTunes…




Logarithm


Logarithms were originally developed
to simplify complex arithmetic
calculations.


What Is Logarithm


The

logarithm

of a number is
the

exponent

to which another fixed
value, the

base, must be raised to
produce that number.

log
b
n

p

if

and

only

if

b
p

n