Square Attack on Reduced-Round Zodiac Cipher

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Zodiac is a block cipher with 128-bit blocks and designed for the Korean firm SoftForum in 2000. This paper discusses the security of Zodiac against the Square attack. We first construct two 8-round distinguishers to build a basic Square attack against the reduced 9-round Zodiac with 128-bit keys, and then extend this attack to 12, 13, 14, and 15-round Zodiac, which finds their round keys with the complexities 292.3, 2124.8, 2157.2, and 2189.5, respectively. Moreover, our attack can find the round keys of the full 16-round Zodiac with 256-bit keys with a complexity of 2221.7 which is better than the exhaustive search and in this attack we just need 216.5 chosen plaintexts. This result shows that the Square attack is not only applicable to Square-like ciphers but also to ciphers with Feistel structure once more.