Related-Key Boomerang Attack on Block Cipher SQUARE

Abstract

Square is an 8-round SPN structure block cipher and its round function and key schedule have been slightly modified to design building blocks of Rijndael. Key schedule of Square is simple and efficient but fully affine, so we apply a related-key attack on it. We find a 3-round related-key differential trail with probability 2-28, which has zero differences both on its input and output states, which is called local collision in [6]. By extending of this related-key differential, we construct a successful attack on full rounds of Square. In this paper, we present a key recovery attack on full rounds of Square using a related-key boomerang distinguisher. We construct a 7-round related-key boomerang distinguisher with probability 2-119 by finding local collision, and calculate its probability using ladder switch and multiple path estimation techniques. As a result, one round on top of the distinguisher is added to construct an attack on full rounds of Square which recovers 16-bit key information with 2123 encryptions and 2121 data.