Authentication Attacks on Projection-based Cancelable Biometric
Schemes
Axel Durbet
1
, Paul-Marie Grollemund
2
, Pascal Lafourcade
1
, Denis Migdal
1
and Kevin Thiry-Atighehchi
1
1
Universit
´
e Clermont-Auvergne, CNRS, Mines de Saint-
´
Etienne, LIMOS, France
2
Universit
´
e Clermont-Auvergne, CNRS, LMBP, France
Keywords:
Cancelable Biometrics, Local-sensitive Hash, Sobel Filter, Reversibility Attacks, Biohash.
Abstract:
Cancelable biometric schemes aim at generating secure biometric templates by combining user specific tokens,
such as password, stored secret or salt, along with biometric data. This type of transformation is constructed as
a composition of a biometric transformation with a feature extraction algorithm. The security requirements of
cancelable biometric schemes concern the irreversibility, unlinkability and revocability of templates, without
losing in accuracy of comparison. While several schemes were recently attacked regarding these requirements,
full reversibility of such a composition in order to produce colliding biometric characteristics, and specifically
presentation attacks, were never demonstrated to the best of our knowledge. In this paper, we formalize these
attacks for a traditional cancelable scheme with the help of integer linear programming (ILP) and quadratically
constrained quadratic programming (QCQP). Solving these optimization problems allows an adversary to
slightly alter its fingerprint image in order to impersonate any individual. Moreover, in an even more severe
scenario, it is possible to simultaneously impersonate several individuals.
1 INTRODUCTION
Biometric authentication is seeing widespread use
due to the common integration of fingerprint sensors
and cameras on many smart objects. Since biometrics
is more convenient and quicker to use, and biometric
characteristics cannot be lost or forgotten, biometric
authentication solutions are in general preferred over
their password or physical token counterparts. De-
spite their many advantages, biometric solutions are
not exempt from vulnerabilities. As biometric-based
technologies are deployed at a larger scale, central-
ized biometric databases and devices become natural
targets in cyberattacks. These cyberattacks have the
potential to be harmful on the long term if they lead
to the theft of biometric data. Therefore, a biomet-
ric data may actually be vulnerable to impersonation
attacks and privacy leakage.
Several criteria essential to biometric authenti-
cation systems have been identified in (ISO, 2011)
and (ISO, 2018): irreversibility, unlinkability, revo-
cability and performance preservation of templates.
Fulfilling this set of criteria is now necessary to com-
ply with the privacy principles of the GDPR.
Faced with the mentioned vulnerabilities and re-
quirements, the community has proposed primitives
dedicated to biometrics, so-called biometric template
protection (BTP) schemes. In this paper, we focus on
cancelable biometrics (CB) which is an example of
BTP scheme claimed to meet the four criterias. For
more details on BTP schemes, the reader is referred to
two surveys (Nandakumar and Jain, 2015) and (Nat-
gunanathan et al., 2016). In CB, a biometric template
is computed through a process where the inputs are
biometric data (e.g., biometric image) of a user and
a user specific token (e.g., a random key, seed, salt,
or password). A CB scheme generally consists of a
sequence of processes (an extraction of features fol-
lowed by a parameterized transformation) that pro-
duces the biometric templates, and a matcher to gen-
erate a matching score between the templates. With a
CB scheme, templates can be revoked, changed, and
renewed by changing user specific tokens. Cryptanal-
ysis of CB schemes with strong adversarial models
commonly assume that the attacker knows both the
biometric template and token of the user. This as-
sumption is plausible in practice because a user token
may have low entropy (e.g., a weak password), or it
may just have been compromised by an attacker. This
is the stolen-token scenario (Teoh et al., 2008).
In (Ratha et al., 2001), the first CB scheme was
introduced in the case of face recognition. Since then,
several CB schemes have been proposed, including
the BioHash algorithm (Jin et al., 2004) applied on
568
Durbet, A., Grollemund, P., Lafourcade, P., Migdal, D. and Thiry-Atighehchi, K.
Authentication Attacks on Projection-based Cancelable Biometric Schemes.
DOI: 10.5220/0011277100003283
In Proceedings of the 19th International Conference on Security and Cryptography (SECRYPT 2022), pages 568-573
ISBN: 978-989-758-590-6; ISSN: 2184-7711
Copyright
c
 2022 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

many modalities. CB schemes offer several advan-
tages such as efficient implementation, high match-
ing accuracy, and revocability. However, several at-
tacks on a variety of CB schemes have been pro-
posed: attacks against privacy by approximating fea-
ture vectors or linking several templates of an individ-
ual, and authentication attacks by elevating the false
acceptance rate (FAR). We refer the reader to (Nagar
et al., 2010; Topcu et al., 2016) for attacks on Bio-
Hash type schemes, (Li and Hu, 2014) for attacks us-
ing the Attack via Record Multiplicity (ARM) tech-
nique, (Lacharme et al., 2013; Dong et al., 2019) for
attacks using genetic algorithms, as well as attacks us-
ing constrained programming on CB schemes (Gham-
mam et al., 2020; Topcu et al., 2016).
Contributions. In this paper, we propose re-
versibility attacks against some projection-based CB
schemes, such as the BioHash. The particularity of
our attacks, as opposed to previous works, is that we
reverse the complete sequence of treatments includ-
ing the feature extraction algorithm. This allows us to
construct impostor fingerprint images, thus enabling
authentication (or presentation) attacks. In our au-
thentication attacks, an adversary, who already has
the knowledge of a user’s specific token and has at
least one fingerprint template of the same user, tries
to alter her own fingerprint image such that the ad-
versary can now use its own altered biometrics and
the stolen token to be falsely authenticated as a legiti-
mate user. The considered CB schemes are built upon
uniform random projection (URP) and a kernel based
feature extractor.To perform our attacks, we use In-
teger Linear Programming (ILP) as well as quadrat-
ically constrained quadratic programming (QCQP).
We state our results as follows:
1) Simple Authentication Attacks. A complete
reversal methodology of some projection-based CB
schemes, including the BioHash algorithm, is pro-
posed. The main ideas are to solve an integer lin-
ear program and a quadratically constrained quadratic
program to reverse both the projection and the feature
extraction. The solution provided by a solver is a fin-
gerprint image of the attacker whose the amount of
changes is minimized. Practical resolutions are pro-
vided for tiny synthetic images.
2) One Fingerprint Image for Several Imperson-
ations. The first attack is extended to produce a sin-
gle fingerprint image that impersonates the identity
of several users. This fingerprint image, when com-
bined with the distinct stolen tokens, produces tem-
plates that match exactly the stolen templates of the
respective users. To reach this objective, the attack
consists for the attacker to collect the pairs of (token,
template) of the target users to enlarge the set of con-
straints of a QCQP program.
Outline. Some background information and the ad-
versarial models are presented in Section 2. Section 3
provides our simple authentication attacks. Then, in
Section 4, it is shown how to impersonate several
users with different passwords. Finally, experimen-
tal evaluations and future works are discussed in Sec-
tion 5 and Section 5 respectively.
2 BACKGROUND
Cancelable biometric schemes generate secure bio-
metric templates by combining user specific tokens
such as password with a biometric data to create tem-
plates in respect of the four aforementioned criteria.
Biometric templates in CB schemes are constructed
in two steps: (i) Feature extraction: A feature vector
is derived from a biometric image; (ii) Transforma-
tion: A user specific token is used to transform the
user’s feature vector to a template.
In the following, we let (M
I
,D
I
), (M
F
,D
F
) and
(M
T
,D
T
) be three metric spaces, where M
I
, M
F
and
M
T
represent the fingerprint image space, the feature
space and the template space, respectively; and D
I
,
D
F
and D
T
are the respective distance functions. Note
that D
I
and D
F
are instantiated with the Euclidean dis-
tance, while D
T
is instantiated with the Hamming dis-
tance.
2.1 Feature Extraction
Let U be the set of users of the biometric system. We
identify a user with its biometric characteristic, and
define a function BC(·) that takes a biometric charac-
teristic usr ∈ U as input, and outputs a digital repre-
sentation of biometric data I; for instance, the scan
image of a fingerprint. Note that for two different
computations of I = BC(usr) and I
0
= BC (usr) (e.g.,
at different times, or different devices), we may have
I 6= I
0
due to the inherent noise in the measurement of
biometric data.
Definition 2.1. A biometric feature extraction scheme
is a pair of deterministic polynomial time algorithms
Π := (E,V ), where:
• E is the feature extractor that takes biometric
data I as input, and returns a feature vector
F ∈ M
F
.
• V is the verifier that takes two feature vectors F =
E(I), F
0
= E(I
0
), and a threshold τ as input, and
returns True if D(F,F
0
) ≤ τ, and False otherwise.
Authentication Attacks on Projection-based Cancelable Biometric Schemes
569

An example of feature extraction is Sobel filter-
ing (Vincent and Folorunso, 2009). The resulting im-
age is obtained by computing two convolutions given
by the following matrices:
G
1
=


1 0 −1
2 0 −2
1 0 −1


and G
2
=


1 2 1
0 0 0
−1 −2 −1


.
Let ∗ denote the operator of convolution and I the
output matrix. Note that pixels at the edges of the
image are ignored and, their values are set to 0 in the
corresponding matrix I. The gradients, G
x
and G
y
,
are computed as follows G
x
= G
1
∗ I and G
y
= G
2
∗ I.
Then, the matrix of the output image S is computed as
kG
x
+ G
y
k
2
where k·k
2
denotes the Euclidean norm.
However, the norm does not apply in the usual way.
In this case, it is applied coordinate by coordinate.
2.2 Generation of Templates with URP
Definition 2.2. Let K be the token (seed) space, rep-
resenting the set of tokens to be assigned to users. A
cancelable biometric scheme is a pair of deterministic
polynomial time algorithms Ξ := (T ,V ), where:
• T is the transformation that takes a feature vector
F ∈ M
F
and the token parameter P as input, and
returns a biometric template T = T (P,F) ∈ M
T
.
• V is the verifier that takes two biometric tem-
plates T = T (P,F), T
0
= T (P
0
,F
0
), and a thresh-
old τ
T
as input; and returns True if D
T
(T,T
0
) ≤
τ
T
, and returns False otherwise.
The attacked CB instantiation, described in Al-
gorithm 1, is based on a uniform random projection
(URP). Such a projection serves as an embedding of a
high-dimensional space into a space of much lower
dimension while preserving approximately the dis-
tances between all pairs of points. Algorithm 1 as-
sumes the second factor, i.e., the token, is a password
and outputs a Biometric Compressed Vector (BCV).
Remark 2.2.1. BioHash instantiation is based on the
same type of projection, except that an additional step
of orthonormalization. This skipped step affects nei-
ther the accuracy nor the feasibility of the attacks.
2.3 Attack Models and Objectives
The objective of our attack is to impersonate one or
several users of a database. To perform this attack
some information are needed: the password of our tar-
get and the original BioHash of the target. We show
that anybody can perform a simple authentication at-
tack or a one fingerprint image for several imperson-
ations attack by building a template preimage if he
knows the above information.
Algorithm 1: [URP-SOBEL].
Inputs : biometric data I; token parameter P
Output : BCV vector T = (t
1
,...,t
m
)
1: Apply Sobel filter on I to produce an n-sized fea-
ture vector: F = ( f
1
,..., f
n
).
2: Generate with the token P a family V of m pseu-
dorandom vectors V
1
,...,V
m
of size n according
to a uniform law U([−0.5,0.5]).
3: Arrange the family V as a matrix M of size n×m.
4: Compute T as the matrix-vector product F × M.
5: for t
i
in T do
6: if t
i
< 0 then t
i
= 0 else t
i
= 1
7: end for
8: return T
The informal definitions of (Ghammam et al.,
2020) are tailored for the rest of the paper. Let I ∈ M
I
be a fingerprint image, and let T = Ξ.T (P,E(I)) ∈
M
T
be the template generated from I and the secret
parameter P. In our authentication attack, an adver-
sary is given T , P, and a threshold value τ
T
, and the
adversary tries to find a fingerprint image I
∗
∈ M
I
such that for T
∗
= Ξ.T (P,E(x
∗
)), T
∗
is exactly the
same as T , or T
∗
is close to T with respect to the dis-
tance function over M
T
and the threshold value τ
T
.
In this case, we say that I
∗
is a τ
T
-nearby-template
preimage of the template T .
A strategy for the adversary which have stolen the
secret parameter P is to alter her fingerprint image I
A
such that P along with her extracted feature vector F
A
enable the generation of the exact template T . This
motivates the notion of template fingerprint preimage
defined below.
Definition 2.3 (Template Fingerprint Preimage).
Let I ∈ M
I
be a fingerprint image, and T =
Ξ.T (P, Π.E(I)) ∈ M
T
a template for some secret
parameter P. A template preimage of T with re-
spect to P is a fingerprint image I
∗
such that T =
Ξ.T (P, Π.E(I
∗
)).
Another authentication attack consists in gener-
ating a fingerprint image that yields the exact tem-
plates of several distinct users with their correspond-
ing stolen tokens.
Definition 2.4 (n-template Fingerprint Preimage).
Let
I
1
,...,I
n
∈ M
I
be n fingerprint images of distinct
users, and n templates T
i
= Ξ.T (P
i
,Π.E(I
i
)) ∈ M
T
for distinct secret parameters P
i
∀i ∈ {0,...,n}. A
n-template preimage of (I
1
,...,I
n
) with respect to
(P
1
,...,P
n
) is a fingerprint image I
∗
such that:
∀i ∈ {0,...,n},T
i
= Ξ.T (P
i
,Π.E(I
∗
)).
SECRYPT 2022 - 19th International Conference on Security and Cryptography
570

Target’s template
Password
Initialize the linear
system to obtain a good
output for the filter
Random attacker
filtered image
Modified filtered image
Initialize quadratic
system to find a preim-
age of our modified
output of the filter
Return an image
for authentication
DB
Random attacker
original image
Set objective
Solve
Solve
Set objective
Figure 1: Principle of the attack’s first approach.
Target’s template
Password
Initialize the
quadratic system
Random
attacker image
Return an image
for authentication
DB
Set objective
Solve
Figure 2: Principle of the attack’s second approach.
3 SIMPLE AUTHENTICATION
ATTACK
There are two ways of performing this attack. The
first one includes two steps described in Section 3.1.
First, given an attacker feature vector, we seek the
slightest modification of it such that its transforma-
tion by Ξ yields exactly the template of the victim.
Then, using the filter constraints of the convolution,
we seek the slightest variation of the attacker’s im-
age such that the filtering of this variation produces
exactly the modified feature vector. The second ap-
proach described in Section 3.2 consists in generat-
ing all constraints at once and directly generating the
modified attacker’s image.
3.1 Two-phase Approach Formulation
The attack takes as input: the target’s password (P
t
),
the target’s template (T
t
) and the attacker’s image (I
A
).
This attack computes and uses these intermediate in-
formation: the attacker’s derivative features (F
A
) and
the modified attacker’s features (F
0
A
). The output is
a modified attacker’s image X whose complete trans-
formation using P
t
matches exactly T
t
.
First, the attacker (A) uses I
A
to compute the
derivative F
A
using the filter. Then, A computes her
modified image’s features F
0
A
whose derived template
using P
t
matches exactly the target template T
t
. As
described in Section 3.1.1, this is done by solving an
under-constrained linear system and seeking the near-
est modified features whose derived template using P
t
matches exactly T
t
. Next, using F
0
A
and I
A
, A com-
putes her modified image X whose image derivative
by Sobel filter matches exactly the modified features
F
0
A
. As described in Section 3.1.2, this is done by solv-
ing an under-constrained quadratic system and seek-
ing the nearest modified image X whose Sobel deriva-
tive matches exactly the features F
0
A
. Figure 1 gives an
overview of this first method step by step, where in-
puts are in circles and different steps in boxes.
3.1.1 Getting a Correct Output for the Filter
For this part, we assume that we are after the filter. We
want to reverse target’s template by using the pass-
word. To do that, let X = (x
0
,...,x
n
), M the projec-
tion matrix derivated from target’s password and f the
quantization function which takes XM to create a bi-
nary template.
We know the projection matrix and the template
T . Thus, a pre-image of the projected vector can be
find by solving a system under constraints. Notice
that the proposed attack works for many projections
system such as BioHash.
Let K
1
be all indices where T is equal to 0 and
K
2
all other indices. So, we seek a solution to the
following system:





XM
i
< 0,∀i ∈ K
1
XM
i
≥ 0,∀ j ∈ K
2
x
i
∈ R
+
,∀i ∈ (K
1
∪ K
2
)
With M
i
the i-th column of M. We seek to mini-
mize the distance between F and F
A
. By doing so, the
attacker can be authenticated by modifying the small-
est number of information of her own biometric fea-
ture vector.
This part of the attack solves the following prob-
lem. By taking F
A
= (o
1
,...,o
n
) the attacker’s bio-
metric features, M the projection matrix we have:
• Minimize: kX − F
A
k
2
• Under the following constraints:





XM
i
< 0,∀i ∈ K
1
XM
i
≥ 0,∀ j ∈ K
2
x
i
∈ R
+
,∀i ∈ (K
1
∪ K
2
)
With M
i
the i-th column of M.
Authentication Attacks on Projection-based Cancelable Biometric Schemes
571

3.1.2 Get a Preimage to Avoid Filter Effect
The filter leads to a loss of information. But we can
write a quadratic system to create a collision and get
a correct preimage. Let the image matrix be
I =



o
0,0
... o
0,width-1
.
.
.
.
.
.
.
.
.
o
length-1,0
... o
length-1,width-1



Applying the filter to that formal matrix yields a
new matrix D which has quadratic components. But,
we know that D must be equal to F
A
. Thus, we can
solve a quadratic system with (length × width) equa-
tions and (length × width) variables to find a preim-
age.
Let I
A
= (o
i, j
) denote the attacker’s original im-
age, F
A
= (a
i, j
) its modified features, I
0
= (x
0
i, j
) the
modified original image and X = (x
i, j
) its augmented
form. We consider the augmented form as the original
matrix where zeroes are added all around the matrix
to compute the convolution without overflowing.
In the case of Sobel filter, we solve the following
problem:
• Minimize:
∑
i, j
(o
i, j
− x
i, j
)
2
• Subject to the following constraints:



























α
i, j
= x
(i−1, j−1)
+ 2x
(i, j−1)
+ x
(i+1, j−1)
− x
(i−1, j+1)
− 2x
(i, j+1)
− x
(i+1, j+1)
β
i, j
= x
(i−1, j−1)
+ 2x
(i−1, j)
+ x
(i−1, j+1)
− x
(i+1, j−1)
− 2x
(i+1, j)
− x
(i+1, j+1)
a
2
i, j
= α
2
i, j
+ β
2
i, j
,∀(i, j)
x
i, j
= 0 if i = 0 or i = length + 1
x
i, j
= 0 if j = 0 or j = width + 1
x
i, j
∈ J0,255K,∀(i, j)
3.2 Formulation as a Single Program
The attack takes as input the same parameters (P
t
,
T
t
and I
A
) and returns a modified attacker’s im-
age X whose complete transformation matches the
target template. The main idea is to merge both
steps described in Section 3.1. A unique constrained
quadratic system is solved to find the nearest mod-
ified image whose complete transformation matches
exactly the template (see Figure 2). Note that this sin-
gle program avoids some problems such as having an
intermediate feature vector which is not in the range
of the filter function.
Assume that I
A
= (o
i, j
)
n×m
is the attacker’s origi-
nal image, I
0
= (x
0
i, j
)
n×m
the modified original image
and X = (x
i, j
)
n×m
its augmented form. Let K
1
be all
indices where the template is equal to 0 and K
2
all
other indices. Let M = (a
i, j
)
(n∗m)×`
be the projection
matrix. Let Y
f lat
be the flattened form of the matrix Y
where rows are concatenated in a single vector.
Thus, using the notations from the sections 3.1
and 3.2 we define the following problem for Sobel
filter:
• Minimize: kX − I
A
k
2
• Subject to the following constraints:









Y
2
=

(G
1
∗ X)
2
+ (G
2
∗ X)
2

Y
f lat
M
i
< 0,∀i ∈ K
1
Y
f lat
M
j
≥ 0,∀ j ∈ K
2
x
i, j
∈ J0,255K,∀(i, j)
Where the squaring stands for the coordinate by coor-
dinate squaring and M
i
the i-th column of M.
4 MULTIPLE COLLISIONS
ATTACK
In this attack, the attacker knows the templates and
passwords of the victims. Then, her goal is to use
all these information to generate one image that al-
lows her to impersonate all the victims using their
own password. The attack takes as input: the tar-
get’s templates (T
t
)
i∈µ
, the attacker’s image (I
A
) and
the target’s passwords (P)
i∈µ
. The output is a modi-
fied attacker’s image X which matches all templates
for the corresponding password.
As in the single authentication attack, we define a
quadratic system with more constraints and a function
to minimize. Let M
i
be the projection matrix for the
i-th user. Assume that (K
1
)
i
is the list of all indices
where (T
t
)
i
is equal to 0 and (K
2
)
i
all other indices.
The other notations are the same as in Section 3.2.
The problem can be defined as:
• Minimize: kX − I
A
k
2
• Under the following constraints where (M
i
)
j
is the
j-th column of M
i
:









Y
2
=

(G
1
∗ X)
2
+ (G
2
∗ X)
2

Y
f lat
(M
i
)
j
< 0,∀i ∈ µ, ∀ j ∈ (K
1
)
i
Y
f lat
(M
i
)
k
≥ 0,∀i ∈ µ, ∀k ∈ (K
2
)
i
x
i, j
∈ J0,255K,∀(i, j)
As matrices M
i
are fully random, the probability
of them forming an indexed family of linearly de-
pendent vectors is negligible, thus making the sys-
tem solvable. Assume that L(V
1
,...,V
k
) is the event
that (V
1
,...,V
k
) is an indexed family of linearly in-
dependent vectors, with n the size of vector and η
the number of precision bits for our numbers. It can
be shown that P(L(V
1
,...,V
k
)) = (
∏
k
i=2
2
η(n−i+1)
−
SECRYPT 2022 - 19th International Conference on Security and Cryptography
572

1)/(
∏
k
i=2
2
η(n−i+1)
). Since this probability is near 1,
the usurpation of
b
n/w
c
persons with w the size of the
template is a likely event.
5 EVALUATION AND
CONCLUSION
We evaluate our attack (Section 3.2) through our
Python implementation. Gurobi 9.1.2 is used to
solve the quadratic non-convex programs, on a com-
puter running on Debian 11, with an EPYC 7F72
dual processor (48 cores) and 256GB RAM. We have
launched resolutions of the programs 50 times, each
with a time limit of 150 seconds. Table 1 reports the
running times for the different settings along with the
amount of changes done in the attacker fingerprint,
using Euclidian distance. With a 4×4-pixel image
and a 50-bit template, 150 seconds starts to be insuf-
ficient to solve the system and optimize the criterion.
In 500 seconds, we solve the system with a 10×10-
pixel image for a better ratio amount of changes over
image size. Thus, the experiments are encouraging
for a NP-hard problem (Sahni, 1974).
Table 1: Summary of the experiments for a 50-bit template.
Image Size Template Size Mean Distance Mean Time (s)
2 × 2 99 0.14
2 × 3 117 32.76
3 × 3 50 133 150.0
4 × 3 144 146.67
4 × 4 177 150.0
In this paper, we present several authentication at-
tacks on a popular CB scheme consisting in a compo-
sition of a kernel-based filter with a projection-based
transformation, in the stolen token scenario. Their
particularity is to completely reverse a CB scheme to
impersonate any or several users. To the best of our
knowledge, this is the first time that attacks are con-
ducted on a complete chain of treatments, including a
non-linear filter. The proposed methodology is to for-
malize the attacks as constrained optimization prob-
lems. As long as the attacker has access to one or
several templates with the corresponding passwords
or not, our attacks can be performed. Future work
will focus on finding optimizations and relaxations of
the systems to ensure the scaling of our attacks.
ACKNOWLEDGEMENT
The authors acknowledges the support of the French
Agence Nationale de la Recherche (ANR), under
grant ANR-20-CE39-0005 (project PRIVABIO).
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