Biclique-based cryptanalysis of the block cipher SQUARE

SQUARE, an eight-round substitution-permutation block cipher, is considered as a predecessor of the advanced encryption standard (AES). Recently, the concept of biclique-based key recovery of block ciphers was introduced and applied to full-round versions of three variants of AES. In this paper, this technique is applied to analyse the block cipher SQUARE. First, a biclique for three rounds of SQUARE using independent related-key differentials has been found. Then, an attack on this cipher is presented, with a data complexity of about 2⁴⁸ chosen plaintexts and a time complexity of about 2^125.7 encryptions. The attack is the first successful attack on full-round SQUARE in the single-key scenario.