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Showing Revision 1 created 10/24/2012 by Amara Bot.

  1. Welcome to Office Hours for this week.
  2. I'm here with Adam Sherwin. Job is sick today, so Adam has kindly stepped in.
  3. Adam is one of our new TAs.
  4. He is going to be TAing a statistics course that we'll be starting fairly soon.
  5. Thanks, Adam. What questions do we have for today?
  6. Alice asked about the math used in Unit 3, specifically what is z sub q?
  7. This is a good question. I have been fairly informal with the math that we use in this class.
  8. I want to focus on the fun parts of crypto, but really to understand things
  9. it's important to understand the math deeply.
  10. I will put a link to some great free notes from an MIT course that goes into a lot of detail
  11. on the math that will have a good definition of this.
  12. On the specific question of what z sub q is--
  13. this means the group of integers over multiplication.
  14. If q is a prime number that is all the numbers from 1 up to that prime number minus 1,
  15. and a group is defined by the set of elements and operations.
  16. So we use the numerals that we understand to show the members of the group,
  17. but they could be any symbol. What matters is what the operations do on those elements.
  18. The multiplicative groups on integers have the properties that correspond
  19. to what we think about integer multiplication having,
  20. except for modulo the size of the group.
  21. When it's a prime, these are very useful for cryptography.
  22. That's what I mean by z sub q.
  23. It's the multiplicative group of integers, so it's the numbers from 1 up to q - 1.
  24. When q us prime that's the same thing as z*q, which is what you'll sometimes see written.