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

Table 3

Linear hulls for SPECK32/48/64.

2n	r							Time	Reference
32	9	0010, 1400	0B00, 0800	15	25		69737	N/A	[18]
	9	0380, 5224	066A, 0608	14	14		1	N/A	[16]
	9	00A0, 062F	170B, 130A	14	20		14	25 s	This paper
48	10	000131, 050021	2484F2, 2480F6	22	N/A		1	N/A	[16]
	10	800121, 158021	DE84DC, C684DC	22	N/A		1	N/A	[18]
	10	000180, B80001	8800A8, 880109	22	28		50	157.3 h	This paper
64	13	18600010, 10724800	00024982, 00420802	30	30		1	N/A	[16]
	13	00101800, 00001812	00006065, 00006068	30	30		1	N/A	[18]
	13	01000120, 14010021	50000404, 80000404	30	32		178	7.3 h	This paper
	14	01000120, 14010021	26902000, 20802006	33	35		194	5.8 h	This paper

All experiment code in this work are run on a single high-performance server with Intel(R) Xeon(R) CPU E5-2680 v4 @ 2.40 GHz. All masks are represented in hexadecimal.