![]() What is a field? A field is a set of elements with two custom-defined
arithmetic operations: most commonly, addition and multiplication. The
elements of the field are an additive abelian group, and the non-zero
elements of the field are a multiplicative abelian group. This means that
all elements of the field have an additive inverse, and all non-zero
elements have a multiplicative inverse. As is true for groups, other
operations can be defined in a field, using its main two
operations.
A field is called finite if it has a finite number of elements. The most commonly used finite fields in cryptography are the field Fp (where p is a prime number) and the field F2m. |