Security Cryptanalysis of NUX for the Internet of Things

Algorithm 2

Algorithm for linear approximations on NUX.

Input: S-box , Bias threshold .

Output: A linear approximation with the best bias.

Data: The number of active S-boxes in i rounds .

   The number of active S-boxes of the i-th round .

Generate the LAT of S-box.

Store all 2, 4 and the corresponding input/output masks in LAT in the table

  for Each of 8 S-boxes in the first round do

  for all non-zero entities in LAT do

   if S-box is in   then

     , .

     Store them in .

    else

     , .

      Store them in .

    Calculate , , , , and store them in .

    Calculate , , , , and store them in .

    Update to be 1.

    The bias is recorded as .

  for   to   do

    if    then

     Travel to get , and its corresponding bias

    else if    then

      Travel to get , and the corresponding bias

    Compute the total bias, and keep ones greater than threshold

    Calculate , , , , and store them in .

    Update the number of active S-boxes and bias

  for Each of 8 S-boxes in the first round do

  for all non-zero entities in DDT do

    Find the largest and store it in

    Output linear approximations with bias