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Dec
9
comment Slow one-way pseudo-random permutation?
Why do you need to store the permutation as $2^m$ words of $m$ bits, rather than just using any short-block cipher on $m$-bit blocks? Also: what's the security gap you expect from this? (i.e., the ratio in workfactor to break vs the workfactor for the legitimate parties to compute this function.) My rough back-of-the-envelope estimate suggests you should expect a very small security gap. If we precompute the discrete log of all primes up to $2^{21}$ (about $2^{17}$) of them, the time to compute a single discrete log is about 200 smoothness tests (sieving + ECM on a $\le 84$-bit number).
Dec
8
comment Slow one-way pseudo-random permutation?
Right. This answer doesn't work. If the matrix is non-invertible, then this won't be a permutation. The original question asks for a one-way permutation. (If it didn't need to be a permutation, this question would be easy to solve: you could just use SHA256 truncated appropriately.)
Dec
7
comment PRP representation size
@Bush, your question still has the same problems. Have you tried answering the questions in the last paragraph of my question? They are intended to get you thinking along lines that enable you to clear up your confusion on your own.
Dec
7
comment Slow one-way pseudo-random permutation?
@fgrieu, excellent point. OK, I guess I don't know how to make this slow after all (unless each person will only use the key once -- but that's probably a relatively rare situation). Thank you for catching that.
Dec
7
comment Slow one-way pseudo-random permutation?
@RickyDemer, yup, either do that (i.e., iterate: a standard way to make something slow), or make the key expansion of $k \mapsto (k_0,k_1)$ slow (if each person will only use the key $k$ once -- which might not apply here, but I mention it just for completeness).
Dec
6
comment Keyed digest function with odds of collision below the birthday bound?
Is there any reason to think that the polynomial given here is hard to invert? It looks to me like that paper shows that these polynomials are easy to invert. In particular, it looks like the proofs of Propositions 1 and 2 give an explicit algorithm to find $x$ such that $p(x)=d$ (where $p$ is one of these permutation polynomials). For instance, equation (9) shows how to solve $(x^{2^k}+x+a)^{-l}+x=d$ for $x$, and the displayed equation at the end of Proposition 2 shows how to solve $(x^{2^k}+x+a)^s+x=d$ for $x$. (Cc:ing @fgrieu)
Dec
6
comment Slow one-way pseudo-random permutation?
I still don't think I understand the requirements, but I suspect if you took a step back and allowed yourself to admit other solutions you could find better, simpler solutions. For instance, something using a trusted server or HSM. P.S. I think there's a solution to the mobile app issue you mentioned. Suppose there's a 256-bit SHA256 hash. You can ask the user to enter in the first 64 bits of the hash, then look it up in the database of items and see if that's to uniquely identify the item; if it isn't, have them enter in the rest. It will be extremely rare that a user needs to enter more.
Dec
6
comment Can insecure algorithms be combined to form a secure algorithm?
Also, they are hoping it will be safe, but there is no proof that this is safe.
Dec
6
comment Slow one-way pseudo-random permutation?
Also, why does your application require such a complex construct? Why not just store a unique random serial number in the 2-D barcode, and have a back-end database that maps the serial number to whatever data is associated to that card (of course, the data can be encrypted under one merchant's key if you wish). Perhaps I haven't quite understood the application yet.
Dec
6
comment Slow one-way pseudo-random permutation?
Why do you need the output to be the same length as the input? If you're willing to have (say) a 256-bit output, your goals are easy to achieve; just use the SHA256 hash. If the output is going to be stored in a database but not stored on the card, that'd suffice. Also, why do you need it to be bijective (i.e., a permutation)? If collisions are non-trivial to find, is that good enough?
Dec
6
comment Enhance CSPRNG output
@user1028028, it doesn't matter if the PRNGs are independent. What matters is that their seeds (their keys) are independently chosen. That's how you can tell: check how you've generated them.
Dec
6
comment Enhance CSPRNG output
"Unrelated" is NOT the criterion. The criterion is that the keys be independently chosen, not that the algorithms be "unrelated" or "independent" (whatever that would mean). You can even use the same CSPRNG algorithm, as long as you have two independent keys.
Dec
6
comment Enhance CSPRNG output
How are they keyed? With two independent keys? Also, if one is a CSPRNG, then it cannot be biased (to be cryptographically secure means that it can't be biased).
Dec
6
comment If H(m) = 0 for some m, how can a DSA signature be forged?
As DrLecter says, when asking this sort of question, please make sure to describe what you've tried and where you got stuck. We expect you to make a serious effort before asking here and to show us what you've tried and where you got stuck.
Dec
6
comment Is an elliptic curve over $\mathbb{F}_p$ order preserving for the points $(x,y) \in \mathbb{Z}_p$?
Could you define what you mean by $E(x)=y$? If $E$ is the curve, then $E(x)$ is not well-defined. Do you mean $x,y$ such that $(x,y)$ is on the curve (i.e., $y^2=x^3+ax+b \pmod p$)?
Dec
6
comment Is there any analysis of freebsd's “geli” encrypted geometry provider?
Got any suggested links for reading about how geli works and how its crypto works? Any overviews or other resources that you think might be a helpful place to start for those who might want to start taking a look at it? If yes, that might be worth editing into your question.
Dec
4
comment Who uses Dual_EC_DRBG?
That patent does not appear to patent Dual_EC_DBRG. Nor does it appear to patent any backdoor. Rather, the patent lists Dual_EC_DBRG in the prior art, and claims to patent a method for generating the points P,Q in a way that is verifiably free of backdoors.
Nov
20
comment How to prove this LFSR equation?
I suggest you edit the question to include that information, to make this question self-contained, as well as to define the notation $(f,g)$ and $[f,g]$ for polynomials and $+$ for solution spaces. Also, I suggest you edit the question to show what you've tried so far and where you got stuck.
Nov
18
comment Should we sign-then-encrypt, or encrypt-then-sign?
@louism, that's a separate question. This isn't a discussion forum -- questions should be posted separately (see the Ask Question on the upper right). But make sure to first read the help center, and do your research (try to answer the question on your own using Google, Wikipedia, search on this site, etc.) before asking.
Nov
17
comment Bellovin 96' attack on IPsec ESP protocol on encryption only option
Did you read the description in the paper carefully, one step at a time? Where did you get lost? Are you familiar with other attacks on modes of operation?