Shared Secrets Keeping secrets on the web. Encryption Goal : hidden in plain sight.

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Presentation transcript:

Shared Secrets Keeping secrets on the web

Encryption Goal : hidden in plain sight

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

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

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

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

Breaking a Cipher Guess and check

XOR XOR with 0 = don't change XOR with 1 = change In0In1Out In0In1Out

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

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!

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

XOR key with encrypted message to reproduce message ??? Ä ý w W i k i More info: Binary Keys

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

Secret Colors Deriving a secret color:

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

Secret Colors Deriving a secret color: – Pick private colors

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

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

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

Attempting with Math Not so secret…

Attempting with Math Not so secret…

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

Clock Math

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

Calculating Mods Wolfram Alpha

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

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 …

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

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

Diffie Hellman Derive a secret number

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

Powers of 2 Mod 11 Powers of 2 mod 11: Mod 11 means 10 possible values then cycle… Power of 2ValueMod

Powers of 2 Mod 4 Powers of 2 mod 4: Prime clock sizes work better… Power of 2ValueMod

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

Diffie Hellman Derive a secret number – Pick private numbers

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

Public Private Number

Diffie Hellman

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

Shared Secret Number

Diffie Hellman

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

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

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

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)