In cryptography, prime fields play major role in its mathematical problems. Below you can see a simple example of a prime field 29 which denoted by F29.
The elements of F29 are {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27 28}
For any integer a, a mod p shall denote the unique integer remainder r , 0 ≤ r ≤ p − 1, obtained upon dividing a by p; this operation is called reduction modulo p.
(i) Addition: 17 + 20 = 8 since 37 mod 29 = 8
(ii) Subtraction: 17 − 20 = 26 since −3 mod 29 = 26
(iii) Multiplication: 17 · 20 = 21 since 340 mod 29 = 21
(iv) Inversion: 17−1 = 12 since 17 · 12 mod 29 = 1
