Required key size for an ideal cipher with a 32 bit block size For an ideal block cipher, what size key would be required when the cipher has a 32-bit block size?
The size of the key depends on the security level you want, it is not possible to say "you need exactly $n$ key bits if you have a block size of $m$ bits".

Let's assume that for an ideal cipher, a block size of 32 bits means $2^{32}$ possible input values which can be permuted in $(2^{32})!$ ways. That means you would have at most $\log_2(2^{32}!)$ key bits, to avoid equivalent keys. This is a lot, and in practice only a (very!) tiny fraction of that amount of bits would be used. In fact, one could argue that this upper bound on the key size is so ridiculously large that it's almost meaningless.

For a lower bound (this is probably what you are interested in), you need to look at the required security level.
For example, a 10 bit key is easily bruteforced, but a 256 bit key is secure against brute force attacks (assuming of course there are no other attacks on the cipher).