Related-key boomerang attack on block cipher square

SQUARE 15 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 15 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 papei; we present a key recovery attack on full rounds of SQUARE using a related-key boomerang distinguisheL 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.