Suppose I have the values $a$, $b$, and $V = H(a) \oplus H(b)$ with inputs $a \neq b$ and $H$ being SHA-224. None of these values are a secret. How secure is it to assume that no other possible values $a'$ and $b'$ (except the case of $a'=b$ and $b'=a$) can be generated that result in the same $V = H(a') \oplus H(b')$?
Are there recommended procedures to combine two hashes into a single value and meet the following properties:
- $V$ has same (or nearly same) size as each of both input hashes
- Any single unknown value ($V$, $H(a)$, or $H(b)$) can easily be deduced from two known values.
- Cryptographically hard to obtain different pre-images $a'$ and $b'$ with same $V$