Quantum cryptanalysis of ciphers based on generalized Feistel and Lai-Massey schemes

This paper investigates generalizations of the Lai-Massey scheme, including unified constructionscombining it with the Feistel scheme (MD GLM, UFLM, L-Feistel, and quasi-Feistel). New reductionsto the quasi-Feistel scheme are provided. Known efficient quantum attacks are analyzed, includingchosen-plaintext attacks on 3 rounds and chosen-ciphertext attacks on 4 rounds for a special case of thequasi-Feistel cipher using Simon’s algorithm. It is demonstrated that restrictions in that work led to thedegeneration of the quasi-Feistel scheme into the standard Feistel scheme, replicating known quantumattacks on the Feistel scheme. New two-round distinguishing attacks are presented for the L-Feistel andMD-1 GLM schemes, enabling round key recovery.