Finite field: Difference between revisions
From Elliptic Curve Crypto
fields |
and no others |
||
| Line 8: | Line 8: | ||
:“''When n>1, GF(p<sup>n</sup>) can be represented as the field of equivalence classes of polynomials whose coefficients belong to GF(p). Any irreducible polynomial of degree n yields the same field up to an isomorphism''” <ref>''Wolfram Mathworld'': Finite Field. https://mathworld.wolfram.com/FiniteField.html</ref>. | :“''When n>1, GF(p<sup>n</sup>) can be represented as the field of equivalence classes of polynomials whose coefficients belong to GF(p). Any irreducible polynomial of degree n yields the same field up to an isomorphism''” <ref>''Wolfram Mathworld'': Finite Field. https://mathworld.wolfram.com/FiniteField.html</ref>. | ||
No other finite fields exist. | |||
Latest revision as of 18:53, 28 December 2024
The simplest finite fields and those of most interest for elliptic curve cryptography are of prime order, and isomorphic to the integers modulo some prime number.
Other Galois fields also exist of order
for any prime number p and power k > 1.
- “When n>1, GF(pn) can be represented as the field of equivalence classes of polynomials whose coefficients belong to GF(p). Any irreducible polynomial of degree n yields the same field up to an isomorphism” [1].
No other finite fields exist.
- ↑ Wolfram Mathworld: Finite Field. https://mathworld.wolfram.com/FiniteField.html
