Public Keys, One Way Functions and Hard Problems

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Lesson synopsis

Public KeySecurity has always been a major focus of computer science research, and with the explosion of Internet use by commerce, the need for secure transactions has taken on more urgency. Most recently, cyber-thieves demonstrated that true security on the Internet is going to require a new level of understanding of how to protect personal data, and more importantly, financial transactions. This lesson introduces two important concepts: public key encryption and one-way functions. It provides an opportunity for students to understand the underpinnings of almost all Internet security: they will come to appreciate that any lock can be eventually broken, and that theoretical computer scientists study ‘hard’ problems to lengthen the time it will take to break a lock. Note that this is not a lesson in encryption, but in how mathematics is used to secure information.

Age Levels

11 - 14 years

Objectives

Introduce students to:
The concept of a public key
How the modulo function is a one-way function
How the Diffie-Hellman key exchange uses a one-way function
What computer scientists mean by ‘hard’ problems

Anticipated learner outcomes

Students will be able to
Practice creating public keys with the classic color model.
Exchange information with the Diffie-Hellman method using modulo arithmetic.
Explain why no lock can be completely secured, and that given time, any mathematical ‘lock’ can be broken.
Use exponentiation and modulo arithmetic to create cyber-keys.

Internet Connections

Exploring Careers in Engineering and Technology Video
http://ieeetv.ieee.org/educational_activities/solving-real-world-problems-with-computing-exploring-careers-in-engineering-and-technology
Public Key Full Video
https://www.youtube.com/watch
Modulo calculator
http://www.miniwebtool.com/modulo-calculator
One way function calculator
https://www.mtholyoke.edu/courses/quenell/s2003/ma139/js/powermod.html

Recommended Reading

https://en.wikipedia.org/wiki/Public-key_cryptography
https://en.wikipedia.org/wiki/Modulo_operation
https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange
https://en.wikipedia.org/wiki/One-way_function

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