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Shared Secrets Keeping secrets on the web

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Encryption Goal : hidden in plain sight

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Encryption Goal : hidden in plain sight – Internet is plain sight

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Encryption Goal : hidden in plain sight – Internet is plain sight – Encryption is only form of privacy

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Caesar Cipher Shift each letter in a message a certain amount:

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Caesar Cipher Right shift of three: – Key: is +3 Encrypted message:

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Breaking a Cipher Guess and check

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XOR XOR with 0 = don't change XOR with 1 = change In0In1Out 101 110 In0In1Out 000 011

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Binary Keys 1 or 0 with XOR = 1 bit encryption – 1 or 0 is key… 2 possibilities

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Binary Keys 1 or 0 with XOR = 1 bit encryption – 1 or 0 is key… 2 possibilities For stronger key, need more bits: – 32 bit key = 4 billion possibilities – Real encryption uses 128/256/512/1025/2048 bits!

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Binary Keys XOR key with message to produce encrypted message W i k i ??? Ä ý w

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XOR key with encrypted message to reproduce message ??? Ä ý w W i k i More info: https://fr.khanacademy.org/math/applied-math/cryptography/ciphers/e/bitwise-operators https://fr.khanacademy.org/math/applied-math/cryptography/ciphers/e/bitwise-operators Binary Keys

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Shared Keys Need to share a key – How do we do it if someone is always listening?

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Secret Colors Deriving a secret color:

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Secret Colors Deriving a secret color: – Pick a public color

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Secret Colors Deriving a secret color: – Pick private colors

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Secret Colors Deriving a secret color: – Make public mixtures with private colors

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Secret Colors Deriving a secret color: – Mix other person's public with your private

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Secret Colors Eve can't reproduce color – too much red

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Attempting with Math Not so secret…

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Attempting with Math Not so secret…

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One Way Function One way function: – Can not be reversed Multiplication two way x ∙ 7 = 42

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Clock Math http://www.shodor.org/interactivate/activities/ClockArithmetic/

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Modulo Modulo ( mod or % ) – Divide and keep remainder 14 mod 12 = 2 8 mod 12 = 8 19 mod 12 = 7 24 mod 12 = 0 26 mod 12 = 2

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Calculating Mods Wolfram Alpha

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One Way Math Clock Math/Modulo is One Way X mod 12 = 2 …what is X???

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One Way Math Clock Math/Modulo is One Way X mod 12 = 2 …what is X??? 14 mod 12 = 2 26 mod 12 = 2 38 mod 12 = 2 …

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Hard Math Some problems are relatively slow to solve: – Factoring numbers – Taking logarithms

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Hard Math Some problems are relatively slow to solve: – Factoring numbers – Taking logarithms Slow is good for encryption – Avoid brute force attacks

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Diffie Hellman Derive a secret number

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Diffie Hellman Derive a secret number – Pick two public numbers – clock size and base Clock size: 11 Base : 2

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Powers of 2 Mod 11 Powers of 2 mod 11: Mod 11 means 10 possible values then cycle… Power of 2ValueMod 11 122 244 388 4165 53210 6649 71287 82563 95126 1010241 1120482 1240964

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Powers of 2 Mod 4 Powers of 2 mod 4: Prime clock sizes work better… Power of 2ValueMod 4 122 240 380 4160 5320 6640 71280 82560 95120 1010240 1120480 1240960

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Diffie Hellman Derive a secret number – Pick two public numbers – clock size and base Clock size: 11 Base : 2

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Diffie Hellman Derive a secret number – Pick private numbers

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Diffie Hellman Derive a secret number – Calculate public-private numbers…

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Public Private Number

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Diffie Hellman

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Derive a secret number – Use other ppn as base to calculate shared secret

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Shared Secret Number

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Diffie Hellman

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Sue's dilemma Sue knows: 2 x mod 11 = 6 2 y mod 11 = 3 6 y mod 11 = ssn 3 x mod 11 = ssn Where y = your private number And x = Arnolds

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Sue's dilemma Sue knows: 2 x mod 11 = 6 2 y mod 11 = 3 6 y mod 11 = ssn 3 x mod 11 = ssn Mod is one way – must guess and check

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Sue's dilemma Sue knows: 2 x mod 11 = 6 2 y mod 11 = 3 6 y mod 11 = ssn 3 x mod 11 = ssn Solving for x or y involves logarithms – very slow for computers

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What is our secret? Calculate our shared secret: clock size = 13, base = 4 Then go to: faculty.chemeketa.edu/ascholer/SSN.html Your Private Number: 8 My Private Number: ?? Your PPN: 4 8 mod 13 = 3 My PPN: 4 ?? mod 13 = 10 SSN = (myPPN) (your private number) mod (clock size)

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Diffie-Hellman Key Exchange first public-key type scheme proposed by Diffie & Hellman in 1976 along with the exposition of public key concepts – note:

Diffie-Hellman Key Exchange first public-key type scheme proposed by Diffie & Hellman in 1976 along with the exposition of public key concepts – note:

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