Research Article
Automatic Search for the Linear (Hull) Characteristics of ARX Ciphers: Applied to SPECK, SPARX, Chaskey, and CHAM-64
Table 6
The 11/10-round linear trails for SPARX-64/SPARX-128.
| | 11-round trail for SPARX-64 | 10-round trail for SPARX-128 | | r | | | | | r | | | | | | |
| | 1 | 0080400100C0F001 | 0 | 1 | 1 | 1 | 00000000000402000000000000000000 | 0 | 0 | 0 | 0 | 0 | | 2 | 000000010000C001 | 0 | 0 | 0 | 2 | 00000000081008100000000000000000 | 0 | 1 | 0 | 0 | 1 | | 3 | 0004000400070007 | 1 | 2 | 3 | 3 | 000000000C010E000000000000000000 | 0 | 3 | 0 | 0 | 3 | | 2C1020102C1C201 C | — | — | — | 4 | 00000000364834500000000000000000 | 0 | 5 | 0 | 0 | 5 | | 4 | 2C1C201C00000000 | 4 | 0 | 4 | | 00000000008A90E20000000000000000 | — | — | — | — | — | | 5 | 3140013000000000 | 3 | 0 | 3 | 5 | 000000000000000000000000008A90E2 | 0 | 0 | 0 | 2 | 2 | | 6 | 858D05CF00000000 | 4 | 0 | 4 | 6 | 000000000000000000000000078F138E | 0 | 0 | 0 | 4 | 4 | | 60117B1800000000 | — | — | — | 7 | 000000000000000000000000000E1600 | 0 | 0 | 0 | 2 | 2 | | 7 | 0000000060117B18 | 0 | 4 | 4 | 8 | 00000000000000000000000000001800 | 0 | 0 | 0 | 0 | 0 | | 8 | 0000000000812261 | 0 | 3 | 3 | | 00000000000000000000000060006000 | — | — | — | — | — | | 9 | 0000000080018280 | 0 | 1 | 1 | 9 | 00000000600060006000000000006000 | 0 | 1 | 1 | 0 | 2 | | 0000000000020202 | — | — | — | 10 | 00000000828182010280020080018001 | 0 | 2 | 1 | 1 | 4 | | 10 | 0002020200000200 | 1 | 0 | 1 | 11 | 0000000002150012081308140A060806 | — | — | — | — | — | | 11 | 1E08180808000800 | 3 | 1 | 4 | | | | | | | | | 12 | 38A8208020582040 | — | — | — | | | | | | | |
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