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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
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