Fuzzy Extractor: Order of elements in set

Does order of elements in two sets matters to authenticate using Fuzzy Extractor?

Using extractor as proposed in https://www.cs.bu.edu/~reyzin/fuzzy.html it seems the set difference is zero for this case:

$w= {1,2,3,4,5,6,7}$ and $w'={7,6,5,4,3,2,1}$ and other permutations where order of members are changed.

This is not favorable for our case because Eavesdropper can leak information even if has dissimilar set. In our protocol Eve has very low correlated data with Alice-Bob but in certain cases chances of getting $w$ at Eve is high since order is not taken care of.

If the result depends on construction, how to we identify responsible properties or formulations?

• It depends on the fuzzy extractor construction... what one are you looking at? – pg1989 Jun 17 '17 at 17:53
• I have a query then: 1. Why does it depend? Which construction features should use to decide? I am using one proposed by Dodis et.al and implemented here: cs.bu.edu/~reyzin/fuzzy.html – Jay Jun 17 '17 at 21:59
• OK, so now I'm thinking on how you can integrate your above comment into the question. If somebody (preferably Jay of course) has any ideas please edit the question. – Maarten Bodewes Jun 18 '17 at 9:05
• fuzzy extractors are usually used in applications where it is not the order that matters but how many (say minutiae in a fingerprint) correct features someone has. – kodlu Jun 18 '17 at 9:54
• A set is an unordered collection of elements; that contrasts to vector or tupple, which are ordered. So with proper use of standard terminology, if some function has a set as input (thus a set of sets as input set), then order of the elements in its input do not matter to its output. This is not an answer, because I entirely ignore the fuzzy extractor part of the question. – fgrieu Jun 18 '17 at 10:04