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Public Keys, One Way Functions and Hard Problems

Enfoque de la lección 
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.

Edades:

11 - 14
Objetivos 

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
Resultados anticipados del aprendizaje 

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.
Actividades de la lección 

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.

Concordancia con los programas escolares

La hoja sobre concordancia con el programa escolar se incluye en PDF.


Concordancia con los programas escolares
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