![]() The field Fp The finite field Fp (p a prime number)
consists of the numbers from 0 to p - 1. Its operations are addition and
multiplication, which are defined as for the groups Zn
and Zp* respectively: all calculations end with
reduction modulo p. The restriction that p be a prime number is
necessary so that all non-zero elements have a multiplicative inverse (see
Zp* for details). As with Zn and
Zp*, other operations in Fp (such as
division, subtraction and exponentiation) are derived from the definitions
of addition and multiplication. Calculations in the field F23 include 10* 4 - 11 mod 23 = 29 mod 23 = 6 7-1 mod 23 = 10 since 7*10 mod 23 = 70 mod 23 = 1 (83) / 7 mod 23 = 512 / 7 mod 23 = 6* 7-1 mod 23 = 6*10 mod 23 = 14. |