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Public Keys, One Way Functions and Hard Problems

Lesson Focus 
Security 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
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.
Lesson Activities 

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.

Alignment to Curriculum Frameworks

Curriculum alignment sheet is included in PDF.


Alignment to Curriculum Frameworks
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