Quantum algorithms are raising concerns in the field of cryptography all over the world. A growing number of symmetric cryptography algorithms have been attacked in the quantum setting. Type-3 generalized Feistel scheme (GFS) and unbalanced Feistel scheme with expanding functions (UFS-E) are common symmetric cryptography schemes, which are often used in cryptographic analysis and design. We propose quantum attacks on the two Feistel schemes. For
$ d $
-branch Type-3 GFS and UFS-E, we propose distinguishing attacks on
$(d+1)$
-round Type-3 GFS and UFS-E in polynomial time in the quantum chosen plaintext attack (qCPA) setting. We propose key recovery by applying Grover's algorithm and Simon's algorithm. For
$ r $
-round
$ d $-branch Type-3 GFS with
$ k $
-bit length subkey, the complexity is
$O({2^{(d - 1)(r - d - 1)k/2}})$
for
$r\ge d + 2$
. The result is better than that based on exhaustive search by a factor
${2^{({d^2} - 1)k/2}}$
. For
$ r $-round
$ d $-branch UFS-E, the attack complexity is
$O({2^{(r - d - 1)(r - d)k/4}})$
for
$d + 2 \le r \le 2d$
, and
$O({2^{(d - 1)(2r - 3d)k/4}})$
for
$r > 2d$
. The results are better than those based on exhaustive search by factors
${2^{(4rd - {d^2} - d - {r^2} - r)k/4}}$
and
${2^{3(d - 1)dk/4}}$
in the quantum setting, respectively.
