Protecting Biometric Features by Periodic Function-Based Transformation and Fuzzy Vault - Transactions on Large-Scale Data-and Knowledge-Centered Systems - page 59

the authors presented two approaches to deal with this issue, including feature trans-
formation and biometric cryptosystem.
In the biometric cryptosystem approach, a key is derived from the biometric tem-
plate or bound with the biometric template. Both the biometric template and the key
are then discarded, and only the public helper data is stored in the database. Although
public helper data does not reveal any information about the biometrics and the key, it
is very useful to regenerate the key from another biometric sample which is closed to
the biometric template. The concepts of secure sketch and fuzzy extractor [10], a
combination of ANN and secure sketch [11] are kinds of biometric cryptosystem
approach. The fuzzy commitment scheme [12] and fuzzy vault [13] are two examples
of the key binding approach.
In the feature transformation approach, the biometric templates are transformed be-
fore being stored in the database. The transformed templates are hard to be recovered
to the original template even with some knowledge of transformation function. Then,
the transformed templates are safe to store in the database.

2.1 Fuzzy Vault

Juels and Sudan [13] introduced a construct called a fuzzy vault. The idea is that Al-
ice places a secret k in a fuzzy vault and locks it using a set A of elements from some
public universe U. To unlock the vault and retrieve k, Bob must present a set B closed
to A, i.e., B and A overlap substantially.
To construct a fuzzy vault, first, Alice selects a polynomial p of variable x that en-
codes k. Considering the elements of A as distinct x-coordinate values, she computes
the polynomial projections for the elements of A. Then, she adds some randomly
generated chaff points that do not lie on p. The final set includes real points which lie
on p and chaff points. The number of chaff points is far greater the number of real
points. It will make the attacker hard to find the real points.
When Bob want to unlock the vault and learn k (i.e., find p), he uses his unordered
set B. If B overlaps with A substantially, he will be able to locate many points in the
vault that lie on p. By using error-correction coding (e.g., Reed-Solomon), it is as-
sumed that he can reconstruct p and discover k.
There are many researches follow this scheme to construct the vault for fingerprint
[4, 5, 6], iris [7, 14], face [15], and some other biometric types.
However, several attacks against fuzzy vaults have been discovered [16, 17]. These
are: attacks via record multiplicity, stolen key inversion attack and blended substitu-
tion attack. In a stolen key inversion attack, if an adversary somehow recovers the key
embedded in the vault, he can decode the vault to obtain the biometric template. Be-
cause the vault contains a large number of chaff points, it is possible for an adversary
to substitute a few points in the vault with his own biometric features. In this case, the
system allows both the genuine user and the adversary to be successfully authenticat-
ed. This attack is called blended substitution. In record multiplicity attack, an adver-
sary can access to two different vaults generated from the same biometric data (from
two different applications). He can easily identify the genuine points in the two vaults
and decode the vault. Thus, the fuzzy vault scheme does not provide diversity and