PK &iAOޠ " Q_&_A_Session__3/01-Welcome.en.srt1
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Welcome to Office Hours for this week.
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I'm here with Adam Sherwin. Job is sick today, so Adam has kindly stepped in.
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Adam is one of our new TAs.
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He is going to be TAing a statistics course that we'll be starting fairly soon.
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Thanks, Adam. What questions do we have for today?
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Alice asked about the math used in Unit 3, specifically what is z sub q?
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This is a good question. I have been fairly informal with the math that we use in this class.
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I want to focus on the fun parts of crypto, but really to understand things
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it's important to understand the math deeply.
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I will put a link to some great free notes from an MIT course that goes into a lot of detail
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on the math that will have a good definition of this.
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On the specific question of what z sub q is--
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this means the group of integers over multiplication.
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If q is a prime number that is all the numbers from 1 up to that prime number minus 1,
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and a group is defined by the set of elements and operations.
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So we use the numerals that we understand to show the members of the group,
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but they could be any symbol. What matters is what the operations do on those elements.
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The multiplicative groups on integers have the properties that correspond
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to what we think about integer multiplication having,
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except for modulo the size of the group.
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When it's a prime, these are very useful for cryptography.
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That's what I mean by z sub q.
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It's the multiplicative group of integers, so it's the numbers from 1 up to q - 1.
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When q us prime that's the same thing as zq, which is what you'll sometimes see written.
PK &iA!