Do you think the format preserving encryption(FPE) schemes have any limitation with respect to other conventional block ciphers?
Actually, one can view an FPE scheme as a generalization of a conventional block cipher. After all, a conventional block cipher is fixed to a specific block size; with FPE, we can use any block size we find convenient (for example, the entire message).
Do FPE have a wide range of applications to be a future research area?
I believe so. One nice thing about FPE (with a tweak; most FPE schemes allow one) is that it is easy to construct an AEAD scheme that is quite misuse tolerant:
To encrypt, you'd take the message $M$, and append $k$ zeros and $\ell$ random bits (or nonce; the decryptor will recover these bits and so they can be used as a sequence number if needed). Encrypt that with the FPE scheme, using the AAD as the tweak.
To decrypt, you decrypt with the FPE scheme using the AAD as the tweak; parse the result, and check if the $k$ zeros appear at the end.
It should be obvious that this is a secure AAD scheme (assuming that the FPE scheme is secure). In addition:
If the sender uses bad randomness for its $\ell$ random bits, it becomes a deterministic scheme where the adversary can determine if the same message was sent twice, but can't determine anything beyond that.
If the receiver forgets to check the $k$ zeros, then this becomes a fully garbling scheme, where the adversary can change the decrypted message into something random, but can't do anything beyond that. This is in contrast to many AEAD schemes, where if the decryptor forgets to check the tag, then the encryption becomes malleable (and the AAD is essentially ignored).
So, if this is so wonderful, what's the drawback? Well, one major one is performance - the current FPE schemes are quite slow, and so this straight-forward design isn't used. A better performing (but still secure) FPE scheme would make this far more attactive.
Another obvious drawback is that FPE cannot be implemented in a "one-pass" manner (where we process the message in parts); this is convenient when we need to handle large messages; however it should be obvious that being able to do misuse-tolerant encryption (where lack of nonce entropy leaks only whether the messages were identical) is incompatible with one-pass encryption, and that being able to do misuse-tolerant decryption (where forgetting to check the integrity check allows an active attacker only to randomize the plaintext) is incompatible with one-pass decryption.
