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# '''Why is Modular Arithmetic Important for Crpytography''' | # '''Why is Modular Arithmetic Important for Crpytography''' | ||
We are used to dealing with problems in math classes that deal with infinite sets of numbers, such as the real numbers and integers. Cryptosystems however are often based on finite and discrete sets and modular arithmetic is at the heart of many cryptosystems. We need to know about modular arithmetic in order to compute within these systems. However, everyone has some experience with modular arithmetic whether they are aware of it or not. Telling time, though time possibly is infinite, is a finite system. If we are talking about the time, we don't have an infinite number of hours to work with, we only have 12 (or 24 in military time). So this is a finite system and we need modular arithmetic to deal with it. Let's look at an easy example. | We are used to dealing with problems in math classes that deal with infinite sets of numbers, such as the real numbers and integers. Cryptosystems however are often based on finite and discrete sets and modular arithmetic is at the heart of many cryptosystems. We need to know about modular arithmetic in order to compute within these systems. However, everyone has some experience with modular arithmetic whether they are aware of it or not. Telling time, though time possibly is infinite, is a finite system. If we are talking about the time, we don't have an infinite number of hours to work with, we only have 12 (or 24 in military time). So this is a finite system and we need modular arithmetic to deal with it. Let's look at an easy example. | ||
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''Example 1.1'': Say it's 10 am and your friend wants to meet up with you after lunch. They tell you to meet them in 5 hours. What time are you going to meet them? | ''Example 1.1'': Say it's 10 am and your friend wants to meet up with you after lunch. They tell you to meet them in 5 hours. What time are you going to meet them? | ||
| + | Obviously, you will meet your friend at 1 pm. But <math>\ 10+5=15 </math>. How we write this is <math> 15 \equiv 1 \bmod 12 </math>. | ||
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| + | <math> | ||
| + | \begin{definition}{Modulus Operator} | ||
| + | \end{definition} | ||
| − | + | </math> | |
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==[[2015_Summer_Cryptography_Paar_Introduction to Cryptography_Kathryn Marsh and Divya Agarwal _comments | Questions and comments]]== | ==[[2015_Summer_Cryptography_Paar_Introduction to Cryptography_Kathryn Marsh and Divya Agarwal _comments | Questions and comments]]== | ||
Revision as of 05:53, 9 June 2015
Modular Arithmetic
A slecture by Kathryn Marsh and Divya Agarwal
based on the Cryptography lecture material of Prof. Paar.
Link to video on youtube
Notes
- Why is Modular Arithmetic Important for Crpytography
We are used to dealing with problems in math classes that deal with infinite sets of numbers, such as the real numbers and integers. Cryptosystems however are often based on finite and discrete sets and modular arithmetic is at the heart of many cryptosystems. We need to know about modular arithmetic in order to compute within these systems. However, everyone has some experience with modular arithmetic whether they are aware of it or not. Telling time, though time possibly is infinite, is a finite system. If we are talking about the time, we don't have an infinite number of hours to work with, we only have 12 (or 24 in military time). So this is a finite system and we need modular arithmetic to deal with it. Let's look at an easy example.
Example 1.1: Say it's 10 am and your friend wants to meet up with you after lunch. They tell you to meet them in 5 hours. What time are you going to meet them?
Obviously, you will meet your friend at 1 pm. But $ \ 10+5=15 $. How we write this is $ 15 \equiv 1 \bmod 12 $.
$ \begin{definition}{Modulus Operator} \end{definition} $
Questions and comments
If you have any questions, comments, etc. please post them here.
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