Protecting Biometric Features by Periodic Function-Based Transformation and Fuzzy Vault - Transactions on Large-Scale Data-and Knowledge-Centered Systems - page 60

revocability properties. In this paper, we proposed a hybrid scheme where biometric
templates are first transformed based on a periodic function to guarantee diversity and
revocability properties.

2.2 Feature Transformation

Transformation functions are classified into two types: invertible (or salting) and non-
invertible transformation.
Salting is a method in which the biometric features are transformed using a func-
tion defined by a user-specific key or password [9]. With the key, we can invert the
transform template to the original one. Therefore, the key needs must be kept secret.
Salting can be considered as two-factor authentication in which the users must present
both secret key and biometric trail to the authentication system. In [18], the authors
generate a user-based random orthonormal matrix A , where n is the size of
biometric feature vectors. Then, the original template feature vector x is transformed
to a secure domain using matrix product: yAx . The random orthonormal matrix is
generated from a user-based key or token using Gram-Schmidt algorithm 1 . The secu-
rity in this scheme is relied on the user-specific random matrix which plays a role as a
secret key. Another example of salting is using a user-based shuffling key to trans-
form an iris code in [19]. User-based shuffling key which is generated based on users'
key or password is an n-bit string. An iris code is also divided into n blocks. The
transformation works as follows: beginning from the first to the last block, if the bit
i is 1 (or 0), block i will be moved to the first (or last) place of the code.
In non-invertible transformation, the biometric template is transformed by a one-
way transformation function. A one-way function F is “easy to compute” (in poly-
nomial time) but “hard to invert” [9]. The function F can be public. Non-invertible
transformation for fingerprint is proposed in [20]. The authors presented three meth-
ods to transform fingerprint. In the first method, the fingerprint image is divided into
rectangular grid cells. A shifting map is defined as a transformation function. The
minutiae in each cell are moved to a new position which is defined in a shifting map.
There may be some minutiae to be shifted to the same cell. Thus, even if the shifting
map is public, the attacker cannot infer that a minutia in the transformed template is
belonged to which cell in the original template. This is the characteristic of non-
invertible transformation. Similarly, in the second method, the fingerprint image is
divided into sectors, and the minutiae are shifted among sectors which have the same
or nearly the same radius. The third method considers not only the position but also
the direction of the minutiae. Scutu et al. [21] proposed a secure authentication based
on robust hashing. The idea is to embed each component of a feature vector into a
Gaussian function. After that, a number of fake Gaussians are added to hire the true
Gaussian.
To all of noninvertible transformation, the most challenge is that how to preserve
the similarity of distances among transformed templates and among original tem-

1 Gram-Schmidt algorithm from Wikipedia: http://en.wikipedia.org/wiki/Gram%E2%80%
93Schmidt_process (Oct 2014).