The modular addition has been a main component in block cipher. The use of modular subtraction in block cipher is not common but there are some cipher such as Bel-T cipher which uses both modular addition and subtraction.

To find the xor differential probability of modular addition, the following equation is used :

$xdp^+ (\alpha,\beta,\gamma)= 2^{-\sum_{i=0}^{n-2}¬eq(\alpha[i],\beta[i],\gamma[i])}$

$\begin{equation} eq(\alpha[i],\beta[i],\gamma[i])=\begin{cases} 1, & \text{if $\alpha[i]=\beta[i]=\gamma[i]$}.\\ 0, & \text{otherwise}. \end{cases} \end{equation}$

Iam interested to find the xor differential probability equation of modular subtraction $xdp^-$

Q: How to derive the $xdp^-$ equation? or $xdp^+$ and $xdp^-$ are same

  • $\begingroup$ Define the operator $eq(.,.,.)$ and the symbols! $\endgroup$ – kodlu Oct 12 '18 at 23:16
  • $\begingroup$ eq() is added , $\alpha$ , $\beta $ are input differences , $\lambda $ is output difference $\endgroup$ – hardyrama Oct 13 '18 at 5:03
  • $\begingroup$ Still unclear. What is the symbol in front of $eq()$? If its a NOT how is it represented in the reals? Is there a modular inverse in the exponent? $\endgroup$ – kodlu Oct 14 '18 at 7:08
  • 1
    $\begingroup$ Same as addition. Probability that $(a \oplus \alpha) - (b \oplus \beta) = (a - b) \oplus \gamma$ is the same as that of $(a \oplus \alpha) + (-b \oplus \beta) = (a + -b) \oplus \gamma$. $\endgroup$ – Samuel Neves Oct 15 '18 at 13:10

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