Representing sboxes by using smaller GF multiplications

asked 2020-04-26 04:07:10 -0500

updated 2020-04-27 07:49:44 -0500

slelievre gravatar image

Hello,

Up to now, I work on representing the PRESENT sbox in different ways. I tried to compute the algebraic normal form (ANF) which returns 4 output equations. Each output equation processes 4 input variables in GF(2) and returns one output variable in GF(2) while using single AND gates. After that, I used Lagrange interpolation which returned one function with one GF(2^4) input and one GF(2^4) output while using GF(2^4) multipliers. Since both equations are not very helpful for solving my problem, I look for a method to represent the sbox as two polynomials with two GF(2^2) input variables and two GF(2^2) outputs. So more detailed I want to redesign the PRESENT by only using GF(2^2) multiplications and linear components. Is there any method in SAGE to get such a representation?

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