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Table 5 Partial encryption and decryption on 24-round LBlock

From: Multidimensional linear cryptanalysis with key difference invariant bias for block ciphers

Step

Guess

Time

Obtained States

Size

1

\(K_{24}^{7}\)

N·24·2

\(X_{0}^{0}\left |X_{0}^{14}\right | X_{0}^{5}\left |X_{0}^{9}\right | X_{0}^{6}\left |X_{0}^{1}\right | X_{0}^{8}\left |X_{0}^{4}\right | X_{24}^{13} |\)

260·2

   

\(X_{22}^{7}\left |X_{24}^{2}\right | X_{24}^{8}\left |X_{24}^{11}\right | X_{24}^{0} | X_{24}^{9}\)

 

2

\(K_{24}^{0}\)

260·28·2

\(X_{0}^{0}\left |X_{0}^{14}\right | X_{0}^{5}\left |X_{0}^{9}\right | X_{0}^{6}\left |X_{0}^{1}\right | X_{0}^{8}\left |X_{0}^{4}\right | X_{24}^{13} |\)

256·2

   

\(X_{22}^{7}\left |X_{22}^{4}\right | X_{24}^{11}\left |X_{24}^{0}\right | X_{24}^{9}\)

 

3

\(K_{23}^{7}[0]\)

256·28+1·2

\(X_{0}^{0}\left |X_{0}^{14}\right | X_{0}^{5}\left |X_{0}^{9}\right | X_{0}^{6}\left |X_{0}^{1}\right | X_{0}^{8}\left |X_{0}^{4}\right | X_{21}^{7} |\)

252·2

   

\(X_{22}^{4}\left |X_{24}^{11}\right | X_{24}^{0} | X_{24}^{9}\)

 

4

\(K_{1}^{4}\)

252·29+4·2

\(X_{0}^{0}\left |X_{0}^{14}\right | X_{0}^{5}\left |X_{0}^{9}\right | X_{0}^{6}\left |X_{0}^{1}\right | X_{0}^{1}\left |X_{1}^{6}\right | X_{21}^{7}\left |X_{22}^{4}\right |\)

248·2

   

\(X_{24}^{11}\left |X_{24}^{0}\right | X_{24}^{9}\)

 

5

\(K_{2}^{6}\)

248·213+4·2

\(X_{0}^{0}\left |X_{0}^{14}\right | X_{0}^{5}\left |X_{0}^{9}\right | X_{0}^{6}\left |X_{2}^{7}\right | X_{21}^{7}\left |X_{22}^{4}\right | X_{24}^{11} |\)

244·2

   

\(X_{24}^{0} | X_{24}^{9}\)

 

6

\(K_{1}^{6}\)

244·217+4·2

\(X_{0}^{0}\left |X_{0}^{14}\right | X_{0}^{5}\left |X_{1}^{7}\right | X_{2}^{7}\left |X_{21}^{7}\right | X_{22}^{4}\left |X_{24}^{11}\right |\)

240·2

   

\(X_{24}^{0} | X_{24}^{9}\)

 

7

\(K_{1}^{5}\)

240·221+4·2

\(X_{0}^{0}\left |X_{1}^{4}\right | X_{1}^{7}\left |X_{2}^{7}\right | X_{21}^{7}\left |X_{22}^{4}\right | X_{24}^{11}\left |X_{24}^{0}\right | X_{24}^{9}\)

236·2

8

\(K_{2}^{4}\)

236·225+4·2

\(X_{3}^{14}\left |X_{1}^{7}\right | X_{2}^{7}\left |X_{21}^{7}\right | X_{22}^{4}\left |X_{24}^{11}\right | X_{24}^{0} | X_{24}^{9}\)

232·2

9

\(K_{3}^{7}\)

232·229+4·2

\(X_{3}^{14}\left |X_{3}^{5}\right | X_{21}^{7}\left |X_{22}^{4}\right | X_{24}^{11}\left |X_{24}^{0}\right | X_{24}^{9}\)

228·2

10

\(K_{24}^{1}, K_{4}^{5}[1]\)

228·233+5·4

\(X_{4}^{4}\left |X_{21}^{7}\right | X_{22}^{4}\left |X_{24}^{11}\right | X_{22}^{2}\)

220·2

11

\(K_{23}^{2}\)

220·238+4·2

\(X_{4}^{4}\left |X_{21}^{7}\right | X_{22}^{4} | X_{21}^{5}\)

216·2

12

\(K_{22}^{5}\)

216·242+4·2

\(X_{4}^{4}\left |X_{21}^{7}\right | X_{20}^{6}\)

212·2

13

\(K_{21}^{6}\)

212·246+4·2

\(X_{4}^{4} | X_{20}^{9}\)

28·2