August 2024
Intermediate to advanced
1600 pages
108h 3m
English
Content preview from Computer and Information Security Handbook (2-Volume Set), 4th EditionBecome an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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GF(23) Is a Finite Field
We know that GF(23) is an abelian group because the operation of polynomial addition satisfies all of the requirements of a group operator and because polynomial addition is commutative. GF(23) is also a commutative ring because polynomial multiplication is a distributive over polynomial addition. GF(23) is a finite field because it is a finite set and because it contains a unique multiplicative inverse for every nonzero element.
GF(2n) is a finite field for every n. To find all polynomials in GF(2n), we need an irreducible polynomial of degree n. AES arithmetic is based on GF(28). It uses the following irreducible polynomial:
The finite field GF(28) used by AES obviously contains 256 distinct polynomials over GF(2). In ...
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