Hashing files is an expensive thing for CPU. I am tasked to write a secure digital signature scheme. For that, I decided to check the integrity of files using Hash/Digest.
To be more secure, my plan is to use two or three hashes instead of one. Rough diagram looks like following.
Generating Hash which will be signed by a private key
[plain.txt] ---- algoX ----> [sha512(plain.txt) + sha256(plain.txt)]
Calculate sha512, sha256 of plain.txt and verify it by matching with the output of algoX. Verify is OK if and only if all hashes match.
I know that it is as hard as most difficult hash, but will it yield significant security improvement keeping in view the expense of hash calculations.
What are possible attacks which can be carried out against this type of scheme?