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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 ...


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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 ...


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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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