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

Table 1

Summary of the linear characteristics on SPECK, SPARX, Chaskey, and CHAM-64, where “s,” “m,” “h,” and “d” represent seconds, minutes, hours, and days, respectively.

Variants	Round					Reference
SPECK32	9		N/A		N/A	[18]
	9		N/A		N/A	[16]
	9		9 s		25 s	This paper
SPECK48	10		N/A		N/A	[18]
	10		N/A		N/A	[16]
	10		3.2 h		157.3 h	This paper
SPECK64	13		N/A		N/A	[18]
	13		N/A		N/A	[16]
	13		8.6 h		7.3 h	This paper
	14		25.6 h		5.8 h	This paper
SPARX-64	10		3 d		1 h	This paper
	11		5 m		—	This paper
SPARX-128	9		27 m		6 h	This paper
	10		4.4 d		—	This paper
Chaskey	3		N/A		N/A	[18]
	4		15.7 m		—	This paper
	5		6.6 h		—	This paper
CHAM-64	34		N/A		N/A	[7]
	34		1.1 d		—	This paper
	35		4.8 d	—	—	This paper