Automatic Search for the Linear (Hull) Characteristics of ARX Ciphers: Applied to SPECK, SPARX, Chaskey, and CHAM-64
Algorithm 1
Const (): constructing the input-output mask tuples with linear correlation weight of for modular addition, .
Input: and . Each pattern of the Hamming weight distribution of can be calculated by the combination algorithm in [28], which is the combination pattern of , where for .
(1)
Func_LSB: //constructing the LSBs of
(2)
if then
(3)
Output the tuple of () with (1, 1, 1) or (0, 0, 0);
(4)
end if
(5)
if then
(6)
For each ,, and , call Func_Middle ();
(7)
else
(8)
For each ,, and , call Func_Middle ();
(9)
end if
(10)
Func_Middle (): //constructing the middle bits of
(11)
if then
(12)
call Func_MSB ();
(13)
end if
(14)
if then
(15)
if then // recorded whether the value of is 1 or not.
(16)
For each and , call Func_Middle ();
(17)
else
(18)
For each and , call Func_Middle ();
(19)
end if
(20)
else //. The value of determines whether belongs to or .
(21)
if then
(22)
For each and , call Func_Middle ();
(23)
else
(24)
For each and , call Func_Middle ();
(25)
end if
(26)
end if
(27)
Func_MSB (): //constructing the bits of with position higher than .
(28)
if then //the value of determines whether equals to 0 or 7.
