Abstract
WARP is a 128-bit lightweight block cipher presented by S. Banik et al. at SAC 2020. It is based on 32-nibble type-2 Generalised Feistel Network (GFN) structure and uses a permutation over nibbles to optimize the security and efficiency. The designers provided a lower bound on the number of active S-boxes but they did not provide the differential characteristics against these bounds. In this paper, we model the MILP problem for WARP and present the 18-round and 19-round differential characteristics with the probability of \(2^{-122}\) and \(2^{-132}\) respectively. We also present a key recovery attack on 21 rounds with the data complexity of \(2^{113}\) chosen plaintexts. To the best of our knowledge, this is the first key recovery attack against 21-round WARP using differential cryptanalysis.
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Notes
- 1.
Source code is available at https://github.com/tarunyadav/WARP-MILP.
- 2.
- 3.
In this calculation, we consider a pair (a, b) same as (b, a).
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Appendix
Appendix
1.1 A Differential Characteristics (108) of 18-Round WARP with Probability of \(2^{-122}\)
No. | Input difference | Output difference |
|---|---|---|
1 | 0x000af000faf000000a0000005f500050 | 0x00005000000a00070000000da7000dd0 |
2 | 0x00055000a75000000a000000aad00070 | 0x0000a000000f00050000000afd000aa0 |
3 | 0x000da000a5a000000a000000a5a00070 | 0x0000a000000f000f0000000fad0005a0 |
4 | 0x0005a000a5a0000005000000aa7000a0 | 0x00005000000a000a0000000a55000aa0 |
5 | 0x000aa000aa50000005000000aaa00050 | 0x00005000000a000a0000000aaf000ff0 |
6 | 0x000aa000aa5000000a000000daf00050 | 0x0000a000000a000500000005a5000da0 |
7 | 0x000ad000fa5000000a0000005ad000a0 | 0x0000a000000f000a0000000af7000a50 |
8 | 0x000aa000a5d000000a000000faa000d0 | 0x0000a000000f00050000000ff5000da0 |
9 | 0x0005a000aa70000005000000a55000a0 | 0x0000a0000005000a0000000faf000af0 |
10 | 0x000da000a5f00000050000007aa00070 | 0x0000a0000005000a000000057a000ff0 |
11 | 0x000da000a5a000000a000000a5a00070 | 0x0000a000000500050000000daf0005a0 |
12 | 0x0005a0005fa000000a000000adf000a0 | 0x0000a000000500050000000d750005a0 |
13 | 0x0005d000faa000000a000000aad00070 | 0x0000a000000a00050000000da5000aa0 |
14 | 0x0005a000ad50000005000000aa7000a0 | 0x0000a000000a000d0000000aaf000af0 |
15 | 0x000da000f5d000000a000000aaa00070 | 0x00005000000a00070000000dad000da0 |
16 | 0x0005f0007ad000000d000000aa5000a0 | 0x0000d000000a00070000000aa5000aa0 |
17 | 0x0005a000757000000d000000a57000a0 | 0x0000a000000a00050000000faf000da0 |
18 | 0x000aa000aaa000000a0000005a5000f0 | 0x0000a0000005000500000005aa000da0 |
19 | 0x0007d000a7a000000a000000dad00050 | 0x0000a000000a000a00000007da000aa0 |
20 | 0x000aa0005a5000000a000000aa5000f0 | 0x0000a000000a000500000005ad0005a0 |
21 | 0x000da000a5a000000d000000aaa000a0 | 0x0000a000000f00050000000ffa000ad0 |
22 | 0x000aa000a57000000d000000a5a000f0 | 0x0000a000000f000a00000005aa000da0 |
23 | 0x0005a000ad7000000d000000ad7000a0 | 0x000070000005000d0000000faa000da0 |
24 | 0x000aa000555000000a000000daa000a0 | 0x0000a000000d000500000005aa000ad0 |
25 | 0x000da000a5a000000a000000ada000a0 | 0x0000a000000f000500000005a5000aa0 |
26 | 0x000aa000aa7000000a000000dd500050 | 0x0000a000000d00050000000fad000aa0 |
27 | 0x000aa0007d70000005000000a5a00050 | 0x0000a000000a000f0000000da5000aa0 |
28 | 0x0005a000757000000d000000a5a000a0 | 0x0000a000000a000a00000005ad000aa0 |
29 | 0x000aa000aa70000005000000ad5000a0 | 0x0000f000000a000f00000007dd0005a0 |
30 | 0x0005a000daa000000a000000a55000a0 | 0x0000a000000f000d0000000daf000af0 |
31 | 0x000aa000dda000000a000000aa700050 | 0x0000a000000d000a0000000d7f000af0 |
32 | 0x000aa000a5a000000a000000daa000f0 | 0x0000a000000f00050000000fff000af0 |
33 | 0x000af0005aa000000a0000005a500050 | 0x0000a000000d000500000005a7000a50 |
34 | 0x000da000755000000d0000007aa00070 | 0x0000a0000005000f0000000aad000aa0 |
35 | 0x000aa000ada0000005000000aa700050 | 0x0000a000000a00050000000dad000aa0 |
36 | 0x0005a000ad50000005000000aaa000a0 | 0x0000a0000005000d0000000aaf000ff0 |
37 | 0x0005a0007da000000d000000ad7000a0 | 0x0000a000000f000a0000000aad000da0 |
38 | 0x000aa000aa70000005000000add00050 | 0x0000a0000005000500000005aa000aa0 |
39 | 0x000aa0007df0000005000000af7000a0 | 0x0000f000000f000a00000005aa000aa0 |
40 | 0x000aa000adf000000a0000005a700050 | 0x0000a000000a00050000000a5a000aa0 |
41 | 0x000aa000aaa000000a0000005f500050 | 0x0000a000000a000f00000005a50005a0 |
42 | 0x0007a000d5a00000070000005a700050 | 0x000050000007000a00000007dd000aa0 |
43 | 0x000aa000fa7000000a000000ddd00050 | 0x0000a000000a000500000005aa0005a0 |
44 | 0x000da0005aa000000a000000aa500070 | 0x0000a000000f000500000005aa000aa0 |
45 | 0x000a5000da5000000a000000aa500050 | 0x0000a0000005000d0000000fa7000ad0 |
46 | 0x000aa0005a7000000a0000005d500050 | 0x0000700000050005000000057f000af0 |
47 | 0x000aa000d5f000000a0000005aa00050 | 0x0000a000000f000500000005af000aa0 |
48 | 0x000aa000ada000000f000000f5a00050 | 0x0000f000000f000a0000000afd000aa0 |
49 | 0x000aa0005aa000000a000000a5a00050 | 0x0000a0000005000a0000000d7f000aa0 |
50 | 0x0005a000a5a000000d000000ada000a0 | 0x0000a0000005000d0000000d7d000d70 |
51 | 0x0005a000aa5000000f000000aad000a0 | 0x0000a000000a000a0000000daa000a50 |
52 | 0x000ad000da5000000a0000005aa00050 | 0x0000a000000a000a0000000af7000ad0 |
53 | 0x000da000a5f00000050000007a700070 | 0x0000a000000f000a00000005af000af0 |
54 | 0x000aa00055a000000a0000005a700050 | 0x0000a000000f000d0000000ff5000da0 |
55 | 0x000aa000aa5000000f000000fad000a0 | 0x0000f000000a000f0000000a55000aa0 |
56 | 0x000fa000a570000005000000ad7000f0 | 0x0000d000000a00070000000a57000a50 |
57 | 0x0005a000aff000000a000000aaa000a0 | 0x0000a000000d000f0000000d75000aa0 |
58 | 0x000aa000a550000005000000aaa000d0 | 0x0000a000000a000d0000000ad50005a0 |
59 | 0x0005a000a57000000a000000ad7000a0 | 0x0000a0000005000f0000000d77000ad0 |
60 | 0x0005a0005aa000000a000000aa5000a0 | 0x0000a000000d000a0000000d77000ad0 |
61 | 0x0005a000a5a000000f000000afa000a0 | 0x0000a0000005000d0000000daa000fd0 |
62 | 0x0005a00075a000000d000000aaa000a0 | 0x0000a000000500050000000fa70005d0 |
63 | 0x000aa000a5d000000a0000005aa00050 | 0x0000a000000d000d0000000d7a000a50 |
64 | 0x000aa000d5d0000007000000daa00050 | 0x0000f000000a000a0000000aaa000a50 |
65 | 0x000fa000aa7000000d000000ada000f0 | 0x0000a0000005000d00000005ad0005a0 |
66 | 0x000aa000f57000000a0000005da00050 | 0x0000d000000a00070000000755000fa0 |
67 | 0x000dd000aaa000000a000000aaa000a0 | 0x0000a000000f000d0000000daa000a50 |
68 | 0x000a5000a7a000000d000000aad000f0 | 0x00005000000a000a0000000aaa000a50 |
69 | 0x0005a000a570000005000000ada000a0 | 0x0000a000000500050000000faf000aa0 |
70 | 0x000aa000ffa000000a000000d5f00050 | 0x00005000000a000a0000000a5a000a50 |
71 | 0x000a5000aa5000000a000000da500050 | 0x0000f000000f000a0000000da7000ad0 |
72 | 0x0005a000f5a000000a000000a5a000a0 | 0x0000a000000a00050000000a5a000a50 |
73 | 0x0005a000ad5000000a000000aa7000a0 | 0x0000a000000f000d00000005aa000aa0 |
74 | 0x000aa00055a000000a000000dda00050 | 0x00005000000a00070000000add000aa0 |
75 | 0x000aa000a57000000a0000005da00050 | 0x0000a0000005000f00000005af000af0 |
76 | 0x000aa000d57000000a000000a5a000a0 | 0x0000a000000a000f00000005a7000f50 |
77 | 0x0005f000afa0000005000000aff000a0 | 0x00005000000a000a00000005aa000ad0 |
78 | 0x000aa000aaa000000a000000d5a00050 | 0x0000a00000050005000000057a000aa0 |
79 | 0x000aa000aa5000000f000000fa500050 | 0x0000a0000005000d0000000faf000af0 |
80 | 0x000aa00055a000000a0000005da00050 | 0x0000f000000f000a0000000daa0005d0 |
81 | 0x000aa000ad7000000d000000ad700050 | 0x000070000005000d0000000d7a0005a0 |
82 | 0x000aa0007aa0000005000000a5500050 | 0x0000a000000f000f00000005aa000da0 |
83 | 0x000aa000aaa000000a0000005a500050 | 0x0000a000000a000a0000000daa000ad0 |
84 | 0x000aa000d5a000000a000000daa000f0 | 0x0000d000000a00070000000ad7000a50 |
85 | 0x000aa0005aa000000a000000d5500050 | 0x0000a0000005000500000005ad000fa0 |
86 | 0x000aa0005aa000000a000000d5500050 | 0x0000a000000f000a0000000aaf0005a0 |
87 | 0x0005a000aaa0000005000000a55000a0 | 0x0000a0000005000a00000005af000aa0 |
88 | 0x000aa000ada000000d000000a57000d0 | 0x0000a0000005000f00000005aa000da0 |
89 | 0x0005a000aaa0000005000000a5d000a0 | 0x0000a000000a00050000000a5a000aa0 |
90 | 0x000aa000dd5000000a000000daa000d0 | 0x0000f000000a000a00000005ad000aa0 |
91 | 0x000aa000a5a000000a000000aaa00050 | 0x0000a000000a000f00000007d5000aa0 |
92 | 0x000aa0005f7000000a00000055a00050 | 0x0000a000000500050000000d77000fd0 |
93 | 0x0007a000dff000000a000000daa000d0 | 0x0000a0000005000d0000000aa7000a50 |
94 | 0x000aa000dda000000a000000fa700050 | 0x0000a000000a000a0000000fa5000da0 |
95 | 0x000ad000aa50000005000000aa500050 | 0x0000a000000a00050000000a5d0005a0 |
96 | 0x0005a0007d700000050000007d7000a0 | 0x0000a0000005000a00000005a50005a0 |
97 | 0x000aa000ad5000000a0000005aa00050 | 0x0000a000000a000a0000000a5a000aa0 |
98 | 0x000df000aaf000000d000000afd00070 | 0x0000a000000500050000000d75000aa0 |
99 | 0x000aa000a57000000a000000dda00050 | 0x0000a000000a000a0000000ada000af0 |
100 | 0x0005a000a57000000d000000a5a00070 | 0x00005000000a000a0000000a5a000aa0 |
101 | 0x000da000a5a000000a000000afa000a0 | 0x0000a0000005000f00000005ad000aa0 |
102 | 0x000a500057a000000a000000aad000a0 | 0x0000a000000a000f0000000aa5000aa0 |
103 | 0x00055000aaa000000d0000007af000a0 | 0x0000a000000a00050000000a55000fa0 |
104 | 0x0005f000aaf000000a000000af5000a0 | 0x0000a0000005000d0000000faa000aa0 |
105 | 0x0005a000a5f000000a000000afa000a0 | 0x00005000000a000a00000007da000aa0 |
106 | 0x000aa000aaa000000a00000055500050 | 0x0000a000000a000a0000000a55000aa0 |
107 | 0x0005a00075a000000d000000ada000a0 | 0x0000a000000f00050000000af5000aa0 |
108 | 0x000aa000a5a000000a0000005aa00050 | 0x0000a000000a00050000000755000aa0 |
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Kumar, M., Yadav, T. (2022). MILP Based Differential Attack on Round Reduced WARP. In: Batina, L., Picek, S., Mondal, M. (eds) Security, Privacy, and Applied Cryptography Engineering. SPACE 2021. Lecture Notes in Computer Science(), vol 13162. Springer, Cham. https://doi.org/10.1007/978-3-030-95085-9_3
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