East High School Math Week Jeff Kinne UW Computer Science.

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Presentation transcript:

East High School Math Week Jeff Kinne UW Computer Science

Math and Computer Science My job – “research”, i.e. think about cool Math and CS stuff My job – “research”, i.e. think about cool Math and CS stuff Today – one example of “cool stuff” Today – one example of “cool stuff” –Cryptography – sending secret messages –History and basic ideas involved –Where are the numbers? –RSA

Sending a Message AliceBob “What a bad Teacher!”“Yep”

Sending a Message - Problems Teacher can read the note Teacher can read the note Teacher can stop note from being sent Teacher can stop note from being sent Other Problems? Other Problems?

Sending Messages Assume: can send notes, but Teacher can read. Assume: can send notes, but Teacher can read. Goal of cryptography: prevent Teacher learning the secret! Goal of cryptography: prevent Teacher learning the secret!

What can we do? AliceBob “What a bad Teacher!”“Yep”

Secret coded language AliceBob “The Mouse defies the Hawk!” “Roger”

Foreign Language AliceBob “Qué mal profesor!”“Sí”

Pig Latin AliceBob “Atwhay away adbay eachertay!”“Epyay”

Better – Shift Cipher Take each letter and shift by 3 (aka Caesar Cipher) Take each letter and shift by 3 (aka Caesar Cipher) Alice: instead of “What a bad teacher”, Alice: instead of “What a bad teacher”, Write “Zkdw D Edg Whdfkhu”. Bob: receive “Zkdw D Edg Whdfkhu”, and undo the shift. Bob: receive “Zkdw D Edg Whdfkhu”, and undo the shift. Secret key: amount to shift by Secret key: amount to shift by

Shift Cipher What can teacher do to understand message? What can teacher do to understand message? Message: “Aerx xs womt gpeww”

Encryption schemes

How much is enough?

Defining “security”

Crypto uses

Security

Cryptosystem