patternModerate
Usefulness of binary extension field GF(2^n)
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fieldbinaryextensionusefulness
Problem
The binary extension field, usually denoted as $\textsf{GF}(2^n)$ or $\mathbb{F}_{2^n}$, is a finite field of characteristic 2.
Are there any applications of $\textsf{GF}(2^n)$ (or more broadly, $\textsf{GF}(p^n)$), for $n>1$, in computer science?
My impression is that most applications only require a sufficiently large domain. Therefore $\textsf{GF}(p)$ suffices. One exception is in cryptography: the design of some popular block ciphers uses binary extension fields. But more recent cryptographic designs seem to avoid $\textsf{GF}(2^n)$ operations.
Are there any applications of $\textsf{GF}(2^n)$ (or more broadly, $\textsf{GF}(p^n)$), for $n>1$, in computer science?
My impression is that most applications only require a sufficiently large domain. Therefore $\textsf{GF}(p)$ suffices. One exception is in cryptography: the design of some popular block ciphers uses binary extension fields. But more recent cryptographic designs seem to avoid $\textsf{GF}(2^n)$ operations.
Solution
$GF(2^n)$ is used in error correcting codes, in some elements of cryptography (e.g., message authentication with 2-universal hashing), and in the AES block cipher, which is very widely used.
Context
StackExchange Computer Science Q#165043, answer score: 14
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