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I want an algorithm design that works with galois theory and rings of polynomials on finite fields. Can someone suggest me a design that works with these concepts?

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    $\begingroup$ Can you be more specific? What research have you already done? Why are you asking for these particular constraints? $\endgroup$ – Squeamish Ossifrage Apr 30 '18 at 22:00
  • $\begingroup$ For presenting in university $\endgroup$ – Farzin hj May 1 '18 at 5:38
  • $\begingroup$ Such a question is too open-ended for this site (maybe better for chat), but how about elliptic curves over an extension field, like FourQ uses? Let $p = 2^{127} - 1$, a nice Mersenne prime; note that $x^2 + 1$ is irreducible over $\mathbb F_p$, which makes a nice representation for $\mathbb F_{p^2} \cong \mathbb F_p[i]/(i^2 + 1)$. FourQ is the curve $E/\mathbb F_{p^2}\colon -x^2 + y^2 = 1 + d x^2 y^2$ for a certain nonsquare $d \in \mathbb F_{p^2}$. You have Galois theory, polynomials at several levels, nontrivial finite fields. $\endgroup$ – Squeamish Ossifrage May 1 '18 at 15:08
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You almost certainly are looking for AES.

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  • $\begingroup$ Any other algo ? $\endgroup$ – Farzin hj Apr 30 '18 at 17:19
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The Whirlpool cryptographic hash has those features. It's somewhat related to AES, yet different.

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