# CRYPTOLOGY (CODING THEORY) AND LOGARITHM

AI and Robotics

Nov 21, 2013 (4 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