Collision attack on reduced-round Camellia

Camellia is the final winner of 128-bit block cipher in NESSIE. In this paper, we construct some efficient distinguishers between 4-round Camellia and a random permutation of the blocks space. By using collision-searching techniques, the distinguishers are used to attack on 6, 7, 8 and 9 rounds of Camellia with 128-bit key and 8, 9 and 10 rounds of Camellia with 192/256-bit key. The 128-bit key of 6 rounds Camellia can be recovered with 210 chosen plaintexts and 215 encryptions. The 128-bit key of 7 rounds Camellia can be recovered with 212 chosen plaintexts and 254.5 encryptions. The 128-bit key of 8 rounds Camellia can be recovered with 213 chosen plaintexts and 2112.1 encryptions. The 128-bit key of 9 rounds Camellia can be recovered with 2113.6 chosen plaintexts and 2121 encryptions. The 192/256-bit key of 8 rounds Camellia can be recovered with 213 chosen plaintexts and 2111.1 encryptions. The 192/256-bit key of 9 rounds Camellia can be recovered with 213 chosen plaintexts and 2175.6 encryptions. The 256-bit key of 10 rounds Camellia can be recovered with 214 chosen plaintexts and 2239.9 encryptions.