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The problem can be simplified to the following problem, since the standard argument doesn't really take into account that you can't generate all the polynomials of the given maximum degree : Assume that we have sampled a random point $\vec{x}\in \mathbb{F}_p^n$. We let an adversary adaptively choose polynomials of degree at most $d$ and after each choice ...


It's much easier to add a cost factor to the key derivation from the password than to add a lot of data to an encrypted container. See the PBKDF's PBKDF2, bcrypt and scrypt for more information, or see this Q/A for GPG. In general, an iteration to derive the key is of course much more efficient than adding overhead at the start of the file. If a key with an ...


I'm not aware of any implementations, but I'm also not aware of any patents on this algorithm. Also, one can generically make such schemes tweakable via tFPenc(key,tweak,plaintext) = FPenc(PRF(key,tweak),plaintext) and tFPdec(key,tweak,ciphertext) = FPdec(PRF(key,tweak),ciphertext) .

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