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I am interested to identify the effect of replacing $\oplus$ with $\boxplus$ on basic balanced Feistel structure over $r$-rounds. Given;

$F_\boxplus[L,R]= [S,T] = [R,L \boxplus f(R)]$ where $f$ is PRF

$[L,R] \in \left\{0,1\right\} ^{n} $

Q1 . In term of CPA and KPA security, does $\boxplus$ replacement add security over 3 rounds, with proof?

Q2 . If $\boxplus$-Feistel structure have better security bounds that $\oplus$-Feistel, why do not we see it common?

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    $\begingroup$ I'm assuming $\oplus$ denotes bitwise XOR here, but what's $\boxplus$? $\endgroup$ – Ilmari Karonen Nov 2 '18 at 11:28
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    $\begingroup$ @IlmariKaronen I would assume it to mean addition (modulo 2^(blocksize /2)) $\endgroup$ – SEJPM Nov 2 '18 at 11:49
  • $\begingroup$ You wrote "$F$ is a PRF". Do you mean "$f$ is a PRF"? $\endgroup$ – Future Security Nov 2 '18 at 16:06
  • $\begingroup$ I modified it to small f $\endgroup$ – hardyrama Nov 2 '18 at 16:18

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