Automatic Search for the Linear (Hull) Characteristics of ARX Ciphers: Applied to SPECK, SPARX, Chaskey, and CHAM-64

Algorithm 2

Constructing the m-bit cLAT for modular addition.

(1)	for each and input mask
(2)	, let and , for ;
(3)	for each input mask and output mask do
(4)	, , , ;
(5)	for to do
(6)	;
(7)	end for
(8)	if then //determining the connection status generated by the upper subblock.
(9)	, , ;
(10)	else
(11)	, ;
(12)	end if
(13)	for to do //determining the correlation weight.
(14)	;
(15)	if then
(16)	, ;
(17)	end if
(18)	end for
(19)	, ;
(20)	if and then //judgment conditions and .
(21)	;
(22)	;
(23)	; //the number of tuples correspond to and b.
(24)	; //connection status.
(25)	if then
(26)	; //the minimum correlation weight corresponds to and b.
(27)	end if
(28)	end if
(29)	end for
(30)	end for.