CRYPTOGRAPHY

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CRYPTOGRAPHY

• BY
• Jesse Jablonski
• Steve Zakulec
• (Jay) I Fu-Ching

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Cryptography in WWII

• German Encryption Method Enigma
• American Encryption Method Navajo
• William F Friedman

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The Enigma 1930-45

• Designed for military communications
• Designed by Professor David Lovelock
• 3 major changes made in
• 1930-38
• 1938-40
• 1941-45

Photo Courtesy of http//www.image-in.co.il/HTML/S
EC4NET/images/aes_enigma.jpg
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Navajo Language Encryption

• Original language spoken on Navajo reservation in
  southwestern US
• Until recently, an unwritten language
• Idea for use as a cryptosystem proposed by Philip
  Johnstone

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William F. Friedman

• Leader in American Cryptology for half a century
• Head of S.I.S.
• Broke PURPLE, Japanese diplomatic cryptosystem
• Member of NSA

Photo courtesy of http//www.liceofoscarini.
it/studenti/crittografia/bio/friedman_pic.jpg
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WHY CRYPTOGRAPHY?

• Need for secure communication in non-secure medium

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Basic Ciphers Shift

• Encrypting
• Ek (x) (xk) mod 26 y
• Decrypting
• Dk (y) (y-k) mod 26 x
• (x,y eZ)

Mono-Alphabetic System
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Shift Cipher Example
Plain Text Cryptology Key 7 Cipher Text
JYWAVSVNF
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Basic Ciphers Substitution

• Encrypting
• E(x) Y
• Decrypting
• D(y) X

Mono-Alphabetic System
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Substitution Cipher Example
Plain Text Cryptology Cipher Text XIBKGLOLTB
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Basic Ciphers Vigenere

• Key (k1, k2, k3 kn)
• Encrypting
• Ek(x)(x1k1, x2k2)Y
• Decrypting
• Dk(y)(y1-k1, y2-k2)X
• All operations performed in Z26

Poly-Alphabetic System
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Vigenere Cipher Text Shift Plain Text
Cryptology Key Dog Cipher Operation C r y
p t o l o g y D o g D o g
D o g D f f
e s h u o c m b Cipher textFFESHUOCMB
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Symmetric vs. Asymmetric

• Symmetric involves a single key that is used
  for both encryption and decryption
• Thus, the key must be kept secret- except that
  the other party must have it in order to read
  messages for them
• Asymmetric involves two keys- one public and one
  private
• Public known by everyone, used to encrypt a
  message
• Private only known by author- used to decrypt

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How RSA public crypto works

• Pick prime P Pick prime Q

Calculate mpq
Calculate n(p-1)(q-1)
E relatively prime to N
Find d ed1(mod n)
With this done, Alice has a public key (e and m)
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Advantages of Public Key

• Based on (theoretically) difficult math problems
• Solves the problem of distributing keys
• Can be used to digitally sign documents

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Bibliography

• Barr, Thomas H. Invitation to Cryptology. Upper
  Saddle River, NJ Prentice Hall, 2002.

http//www.answers.com/topic/william-f-friedman ht
tp//library.thinkquest.org/J002073F/thinkquest/ho
me.htm http//www.math.nmsu.edu/crypto/public_hrml
/Enigma.html http//www.theargon.com/articles/cryp
tology20lessons/hocryp.html