Tag Archives: field

The Frobenius endomorphism with finite fields

February 9, 2009 – 00:17

The Frobenius endomorphism is defined as: where p is the characteristic of the ring you’re working with. Simple, right? If you’re working with a field with prime order, then Frobenius is actually the identity map. Since the order of the multiplicative subgroup is p, when you raise to the power of p you get back [...]

By Conrado | Posted in Cryptography, Math | Also tagged , | Comments (3)

Visualizing group structure with colored addition/multiplication tables

December 7, 2008 – 01:32

When working with finite fields, if the number of elements is a prime power with m > 1, you can represent the elements as polynomials with degree m-1 and do the field addition and multiplication modulo a irreducible polynomial with degree m. The field GF(5) is composed by the numbers 0 to 4. We don’t [...]

By Conrado | Posted in Cryptography, Math | Also tagged , , , | Comments (5)