Research Article
Automatic Search for the Linear (Hull) Characteristics of ARX Ciphers: Applied to SPECK, SPARX, Chaskey, and CHAM-64
Table 5
Linear characteristics for SPARX-128.
| | r | | | | | | | | | |
| | 1 | 0 | 0 s | 0000000000000000 | 0000000000000000 | | | | | | | | | | 0000000000804001 | 0000000000000001 | 0 | 0 | 1 | 1 | 0 s | | 2 | 0 | 0 s | 0000000000000000 | 0000000000000000 | | | | | | | | | | 0000000000804001 | 0000000000040004 | 0 | 0 | 1 | 1 | 0 s | | 3 | 1 | 0 s | 0000000000000000 | 0000000000000000 | | | | | | | | | | 0000000000804001 | 000000002C102010 | 1 | 3 | | 1 | 0 s | | 4 | 3 | 0 s | 0000000000000000 | 000000000B000800 | | | | | | | | | | 0000000000906021 | 0B03000300030803 | 3 | 10 | | 1 | 0 s | | 5 | 5 | 2 s | 0000000000A03021 | 0000000000000000 | | | | | | | | | | 0000000000000000 | 0000000085C28442 | 5 | 10 | | 3 | 0 s | | 6 | 7 | 1 s | 0000000000805021 | 0000000000000000 | | | | | | | | | | 0000000000000000 | 0000000042854284 | 7 | 12 | | 3 | 1 s | | 7 | 9 | 4 s | 0000000000906021 | 0000000000000000 | | | | | | | | | | 0000000000000000 | 00000000170B130A | 9 | 15 | | 5 | 13 s | | 8 | 12 | 13 d | 0000000000811381 | 00000000170B130A | | | | | | | | | | 0000000000000000 | 160F01040104120E | 12 | 18 | | 11 | 101 s | | 9 | | — | 0000000000004020 | 0000000002150012 | | | | | | | | | 27 m | 0000000000000000 | 081308140A060806 | 18 | 22 | | 53 | 6 h | | 10 | | — | 0000000000804001 | 000000000B810800 | | | | | | | | | 4.4 d | 0000000000000000 | 09840A0402050204 | 23 | 23 | | 1 | — |
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