# Does unbalancing a feistel cipher always improve security? Does it improve security at all?

So according to Wikipedia unbalanced feistel ciphers provide greater provable security. Specifically, they state:

The Thorp shuffle is an extreme case of an unbalanced Feistel cipher in which one side is a single bit. This has better provable security than a balanced Feistel cipher but requires more rounds.

Which is a summary of the paper "How to Encipher Messages on a Small Domain — Deterministic Encryption and the Thorp Shuffle".

Forgive the simplicity of the question I'm about to ask, but as an amateur, to me this seems counter intuitive. If for each plaintext block we have:

$$L_{i+1} = R_i$$

and

$$R_{i+1} = L_i \oplus F(R_i, K_i)$$

Where F is the round function, then doesn't constraining either $L_i$ or $R_i$ to a single, or fewer bits (given whichever side is smaller, they will swap in the next round) mean that each xor is easier to reverse since only single bits are being altered at a time (and we know this reliably since algorithms aren't secret...)? Does that not make the cipher more susceptible to side channel attacks, essentially becoming more of a stream-like operation?

So, is this actually the case and if so why? Is there any particular implementation of an unbalanced feistel cipher one should avoid - for example, are there optimum sizes for the data size bigger than a single bit?

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