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

Table 2

The 9/10/13 round optimal linear trails for SPECK32/48/64.

r	SPECK32		SPECK48		SPECK64
	0	00A0062 F	1	000180B80001	1	0100012014010021	2
1	78B818B9	4	000000C00001	0	0001810020000101	1
2	00906021	1	00000E00000 E	2	0000010000000001	0
3	60804081	1	7A0070700070	5	0000000100000000	1
4	00800001	0	C2C080829380	6	0D0000000C000000	2
5	00010000	1	D00000108300	2	60610000606C0000	3
6	0B000800	3	800000809800	1	00024D0300620C03	6
7	20402050	2	00000400C004	1	181070141B107358	6
8	008380C3	1	200020260020	2	0013001818031840	3
9	170B130A	—	013100310100	2	1818000000181200	2
10			8800A8880109	—	0018000000001000	1
11					0000100000000000	1
12					0000009800000080	2
13					5000040480000404	—