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| − | A finite field exist if and only if it has size <math> p^m | + | '''A finite field exist if and only if it has size <math> p^m </math> where <math> p </math>is prime and <math> m \in \N </math> ''' |
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| + | This is to say, there exist a Galois field with 11 elements (11 is prime, m=1) called <math> GF(11) </math> but you can not construct a Galois field with 12 elements. | ||
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==[[2015_Summer_Cryptography_Paar_Introduction to Galois Fields for AES_Katie Marsh_comments | Questions and comments]]== | ==[[2015_Summer_Cryptography_Paar_Introduction to Galois Fields for AES_Katie Marsh_comments | Questions and comments]]== | ||
If you have any questions, comments, etc. please post them [[2015_Summer_Cryptography_Paar_Introduction to Galois Fields for AES_Katie Marsh_comments|here]]. | If you have any questions, comments, etc. please post them [[2015_Summer_Cryptography_Paar_Introduction to Galois Fields for AES_Katie Marsh_comments|here]]. | ||
Revision as of 05:12, 11 June 2015
Introduction to Galois Fields for AES
A slecture by student Katie Marsh
Based on the Cryptography lecture material of Prof. Paar.
Link to video on youtube
Accompanying Notes
Finite Field/Galois Field: a finite set together with operations + and * with the following properties:
1. The set forms an additive group with neutral element 0
2. The set without 0 forms a multiplicative group with neutral element 1
3. The distributive law $ a(b+c)= (ab)+(ac) $
A finite field exist if and only if it has size $ p^m $ where $ p $is prime and $ m \in \N $
This is to say, there exist a Galois field with 11 elements (11 is prime, m=1) called $ GF(11) $ but you can not construct a Galois field with 12 elements.
Questions and comments
If you have any questions, comments, etc. please post them here.
Back to 2015 Summer Cryptography Paar
