A Star-based Independent Biclique Attack on Full Rounds SQUARE

Abstract. SQUARE is an iterated block cipher proposed by Daemen et.al. in FSE1997. Inspired by Bogdanov et.al.’s recent works [12], we first present an improved biclique attack, i.e. stat-based independent biclique attack on full rounds SQUARE in this paper. We construct a one round stat-based independent biclique for the initial round, and utilize matching with precomputation techniques to recover the whole key from the remaining rounds. The computing complexity of our attack is 126.17 2 encryptions and required data can be reduced to a single plaintext-ciphertext pair. To be the best of our knowledge, our attack has an optimal computing complexity and data complexity of biclique attack on full rounds SQUARE.