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CyberPDX Crypto 3: Modern Ciphers

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Wu-chang Feng

on 13 July 2018

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Transcript of CyberPDX Crypto 3: Modern Ciphers

CyberPDX Cryptography
Modern Ciphers

Key distribution problem simplified
No shared secret key to distribute (unlike Enigma)

Two parts
Public key that is published by recipient
Private key that is kept secret by recipient
Public-key
encryption

The Worksheet
Start with 'H'
We'll just do a number
Recall ASCII encoding
String “Hello There”
Decimal (Base 10)
Bob encodes the message
Public key

Private key

Alice creates a private and public key
Encrypting messages
Recipient broadcasts public key and keeps private key secret

Sender encrypts data using public key

Recipient decrypts data using private key

Decoding message without private key prohibitively expensive
Relies upon a difficult mathematical problem to ensure
…or does he?
To decode messages
Evan intercepts, but can't easily determine the original message
Bob sends the encrypted message to Alice
For each node:
Add up all the numbers connected to it (including the node itself)
Bob encrypts the message
Bob fills nodes with (random) numbers

Bob makes sure the nodes add up to the desired number 72

“Worksheet” is the UNENCRYPTED message
Not transmitted
Creates a worksheet
He has a message for his mayor, Alice.
This is Bob
Homework: Find the private key
Why can’t it be 7?
How many?
9
8
7
Also known as the dominating set problem

Map of a city
Circles are neighborhoods
Lines are roads








Problem
Cover map with minimal # of ice cream trucks
Each neighborhood either has an ice cream truck or is next to exactly one neighborhood that does
Ice Cream Truck Problem
Caesar, Substitution, Transposition ciphers
Apply simple functions to encrypt data
Easily reversed using analysis or brute force

Vigenère, Enigma
More difficult functions applied
Key distribution problem

Factoring products of large prime numbers
Private Key
Public Key
Which difficult problem does the Internet rely upon?
Construction
Alice's private key
Alice's public key
...by adding up numbers on private key: 30+18+24 = 72 = 'H'
Why does it work?
Alice decrypts original message
with her private key
She wants to hear from concerned citizens like Bob

But Alice and Bob have never met...
This is Alice
He wants to listen to the messages Bob sends to Alice

Neither Bob nor Alice want him to listen
This is Evan
72 101 108 108 111 32 84 104 101 114 101
72
The story of Bob and Alice (and Evan)
Now It's Your Turn!
Evan needs to know Alice's private key (i.e. her dominating set)
Previously
Public-key cryptography
What if it became easy?
Ice-cream
truck problem

Ice-cream
truck encryption

Operation
Ice Cream Truck Group Activity
Analogous to issuing open lockboxes to people to put their messages in that only you can open
Need something resistant to quantum attacks ("post-quantum")
Lattices?
Elliptic curve?
Initially, yes. Recent PSU hire now says no.
In 2015, yes. NSA now says no.
Public key cryptography activity
An important message has just arrived from outer-space.
Each of you will get one of the 52 characters in the message
Find dominating set, add up numbers, generate ASCII character
Help others do the same and collect all characters of the message
Tell me what the message says, then reorganize back to your team tables
Bob gets a copy of Alice's public key
Each neighborhood either has an ice cream truck or is next to precisely one neighborhood that does
Give me your solution tonight or tomorrow to collect wristbands for your team
Full transcript