ShaunApps/finite-fields.md

Last active May 28, 2019 11:55

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Why prime fields?

F17 = {0, 1,..., 16}

G = 6

G * x % 17:

6 * 0 = 0
6 * 1 = 6
6 * 2 = 12
6 * 3 = 1
6 * 4 = 7
6 * 5 = 13
6 * 6 = 2
6 * 7 = 8
6 * 8 = 14
6 * 9 = 3
6 * 10 = 9
6 * 11 = 15
6 * 12 = 4
6 * 13 = 10
6 * 14 = 16
6 * 15 = 5
6 * 16 = 11

F12 = {0, 1,..., 11}

G = 6

G * x % 12:

6 * 0 = 0
6 * 1 = 6
6 * 2 = 0
6 * 3 = 6
6 * 4 = 0
6 * 5 = 6
6 * 6 = 0
6 * 7 = 6
6 * 8 = 0
6 * 9 = 6
6 * 10 = 0
6 * 11 = 6
6 * 12 = 0
6 * 13 = 6
6 * 14 = 0
6 * 15 = 6
6 * 16 = 0