This study proposes a new classical key recovery attack against schemes such as Feistel, Misty, and Type-1/2 generalized Feistel schemes (GFS), which creatively combines the birthday attack with the periodic property of Simon’s algorithm. Although Simon’s algorithm can recover the periodic value in polynomial time, this study requires the birthday bound to recover the corresponding periodic value in the classical setting. By this new attack, the key to a 5-round Feistel-F scheme can be recovered with the time complexity of O(2^3n/4) under the chosen plaintexts and ciphertexts of O(2^n/4), and the corresponding memory complexity is O(2^n/4). Compared with the results of Isobe and Shibutani, the above result not only increases one round but also requires lower memory complexity. For the Feistel-FK scheme, a 7-round key recovery attack is constructed. In addition, the above approach is applied to construct the key recovery attacks against Misty schemes and Type-1/2 GFS. Specifically, the key recovery attacks against the 5-round Misty L-F and Misty R-F schemes and those against the 6-round Misty L-KF/FK and Misty R-KF/FK schemes are given; for the d-branch Type-1 GFS, a d²-round key recovery attack is presented, and when d≥6, the number of rounds of the key recovery attack is superior to those of the existing key recovery attacks.