Currently, biometric identifiers have been used to identify or authenticate users in a biometric system to increase the security in access control systems. Nevertheless, there are several attacks on the biometric system to steal and recover the user’s biometric trait. One of the most powerful attacks is extracting the fingerprint pattern when it is transmitted over communication lines between modules. In this paper, we present a novel fingerprint image encryption scheme based on hyperchaotic Rössler map to provide high security and secrecy in user’s biometric trait, avoid identity theft, and increase the robustness of the biometric system. A complete security analysis is presented to justify the secrecy of the biometric trait by using our proposed scheme at statistical level with 100% of NPCR, low correlation, and uniform histograms. Therefore, it can be used in secure biometric access control systems.
Nowadays, the biometric systems are widely used to authenticate and identify an individual, in order to recognize the user identity in a secure way. Nevertheless, these sophisticated recognition systems are prone to be attacked and the biometric identifier could be compromised. Identity fraud is a security problem in secure access systems controls. Therefore, there is an increasing interest in designing high and effective secure access systems based on biometric identifiers.
Techniques such as SHA-1, MD5, 3DES, RC5, AES, and IDEA are conventional encryption methods to protect information such as images and documents, when it is transmitted over on insecure communication channel. Nevertheless, they are not suitable for bulk and highly correlated data encryption such as images. On the other hand, there is an increasing research to design nonconventional encryption techniques such as chaotic and hyperchaotic encryption, since chaotic systems are related to cryptographic properties in confusion and diffusion process. In [
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Nowadays, in literature there are several approaches of implementation of chaotic systems in cryptography, because chaotic systems present cryptographic properties related to confusion and diffusion such as sensitivity to initial conditions and control parameters, mixing, determinism, and ergodicity [
In this paper, we present an image encryption scheme by using hyperchaotic Rössler map. We use the high pseudorandom sequences to generate excellent encryption effects and produce a highly secure encryption scheme, which present better results in some aspects compared with [
The organization of this work is as follows. In Section
There are several biometric identification systems, which are composed of two important stages, enrollment and identification. In enrollment stage, the user is registered in the database, while in the identification stage the user’s identity is determined by using a biometric identifier. The biometric identification systems can be divided into five subsystems: data collection, transmission, signal processing, decision, and data storage. In Figure
General biometrics system [
Currently, the biometric systems are a topic of high interest in the scientific community, because they provide a practical way for secure access control systems. Nevertheless, these systems have some vulnerable points, which are classified in two categories. One of these vulnerabilities is the attack on the communication lines. A snooper can spy the communication to steal confidential information of the biometric identifier, which can be used to extract the user identity. The second attack is on the modules (sensor, feature extraction, matching, database, etc.). The attacks use malicious programs such as a Trojan horse and it emulates the function of some modules of the biometric system and could reject an authorized user [
Due to the existence of attacks in the vulnerability points of the biometric systems, the scientific community and engineers have implemented some actions to protect the biometric system against these powerful attacks. Some of the proposed schemes are based on random data, withheld data, on-life detection, biometric multiple, cryptography, digital signature, network clean-up, and physical security [
In this paper, we propose an encryption scheme that provides security in the transmission subsystem, with the aim of protecting the communication line, where the image is sent to the storage subsystem and the signal processing subsystem; see Figure
Possible location of the encryption and decryption process on general biometric system.
Analogous or digital communication schemes need new cryptographic schemes to protect confidential information. Motivated by this fact, in recent years several researchers have reported great variety of advances related to chaotic encryption. These schemes exploit the pseudorandom properties of the states in a chaotic system; see, for example, [ Simple operation can generate complex dynamics, which provides a pseudorandom sequence where the confidential information can be hidden. Small variation in initial conditions in chaotic system provides great changes in the output dynamic, which benefits the number of keys that could be used for encryption. Encryption statistics preserve the uniform distribution for any chaotic sequence, which benefit the encryption against statistical attacks.
In this paper, we use the Rössler map for encryption purposes. This map generates hyperchaotic dynamics; that is, it presents greater complex behavior than a chaotic system. One distinctive characteristic of these systems is the existence of more than one positive Lyapunov exponent [
The hyperchaotic attractor generated by Rössler map is shown in Figure
Hyperchaotic attractor, generated by the Rössler map.
The encryption process is based on two important stages, the diffusing and permutation stage. On the other hand, the decryption process is constituted by the inverse permutation and inverse diffusing process (Figure
Block diagram of the proposed encryption algorithm.
Hyperchaotic Rössler map is used to generate a sequence of pseudorandom numbers, which are used in permutation and diffusion process.
Read the fingerprint plain image to generate
Generate an array of
By using
Add elements of the array
Generate a vector for the positions of the rows and a vector for the positions of the columns, which will be represented by the variables
Generate two vectors that contain the data resulting from chaotic states
Generate two vectors of pseudorandom sequences for column and row permutation by using the following expression:
sequence from the rows positions or sequence the columns positions.
( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (
The pixels from the diffused image will be permuted as follows:
The decryption process is based on the inverse steps of the encryption process. The hyperchaotic Rössler map is used with the same initial conditions and control parameters. Basically, the decryption steps are described as follows.
In this process,
The steps to perform the inverse blurring process are similar to those presented in the diffusion stage. Performing the reverse blurring equally will use the matrices
This section presents the experimental results of the proposed fingerprint encryption algorithm implemented in MATLAB simulation software 2008a (Figure
Program implemented in MATLAB 2008a version.
In Figure
Encryption and decryption process in permutation and diffusion process.
Figure
Decryption process with correct secret key.
If any of the stages is not implemented, that is, diffusion or permutation that is performed in the encryption or decryption process, the image will not retrieve. Figure
Decryption process with an omitted step.
To evaluate the security at statistical level of the proposed fingerprint hyperchaotic encryption algorithm, we considered different types of attacks. Attacks such as exhaustive attack, statistical attack, and differential attack are analyzed. In some cases, we show the results for both encryptions with and without permutation process.
In this analysis, the distribution and correlation are considered. The histogram of the image can give visual information of the distribution of the intensity levels of red, green, and blue component of a color image. In addition, the numerical correlation is calculated according to a specific expression to determine if the encrypted image presents low correlation, which is desired in a good encryption algorithm.
Histogram analysis of encryption process with and without permutation process, by using the key
Horizontal, vertical, and diagonal correlation distribution of the original image (
The correlation analysis is calculated as follows:
Correlation coefficient of encrypted image.
Image | Horizontal correlation | Vertical correlation | Diagonal correlation |
---|---|---|---|
Plain image | 0.8180 | 0.8670 | 0.8184 |
Encryption without permutation | 0.0392 | 0.0082 | 0.0392 |
Encryption with permutation | 0.0199 |
|
0.0199 |
By observing the results presented in Figure
This rudimentary but effective attack is known as brute force attack, in which all possible keys are tried until the correct secret key is found and the original message is decrypted. This type of attack is related to the key. Therefore, we check the efficiency of the key in the cryptographic scheme with a key space analysis and secret key sensitivity analysis.
Secret key sensitivity analysis.
In order to show the secret key sensitivity in the encryption process, the correlation (see (
Secret key sensitivity analysis: (a) MSE curves and (b) correlation curves.
The third analysis presented is against differential attack. If the encryption process is weak, an adversary could implement this attack to find a relation between similar plain images and determine the secret key. The analysis consists in encrypting two similar plain images with a small change in just one pixel. After that, the encryption algorithm is applied to both of them by using the same secret key. Then, a comparison between the encrypted images is performed. There are two parameters used to examine the resistance against differential attack, which are
A method to determine the error between original image and encrypted image is by using the mean square error MSE parameter, which is the existing qualitative squared error between both compared images [
The chosen/known plain image attack is a powerful cryptanalyst attack, which has broken several image encryption algorithms based on chaos. In a chosen plain image attack, the cryptanalyst chose a convenient image, for example, an image with all pixels in black to eliminate the function of the plain image over the algorithm (permutation and diffusion) and try to find the secret key (chaos), since its pixel values are zero.
In Figure
Chosen plain image attack: (a) chosen black plain image, (b) cryptogram of black image and possible secret key, (c) cryptogram of fingerprint image, and (d) decryption of encrypted fingerprint with the possible secret key.
In an occlusion attack, the transmitted encrypted image could lose blocks of information and not all the cryptograms can arrive to the receptor correctly. In this section, we present the robustness of the proposed encryption algorithm against 12.5%, 25%, and 50% of occlusion in an encrypted image. In Figure
Tolerance against occlusion attacks, considering data loss of 12.5%, 25%, and 50%.
This analysis shows the effectiveness of the proposed scheme against noise attack. In contrast to occlusion attack, the encrypted images can lose small portions of data over the encrypted image. In the analysis, encrypted data are distorted by zero-mean white additive Gaussian noise with a standard deviation from 0 to 0.3 with increments of 0.01. Figure
Decrypted image from cryptograms with Gaussian noise added.
MSE and correlation curves between original and retrieved image in noise attack.
The encryption and decryption processes are performed on a Laptop Toshiba Satellite E105-S1402 with operating system Windows Vista, processor speed of 2.26 Ghz, and 4 GB DDR2. The simulation is implemented in MATLAB R2008a software. “.bmp” plain image encryption of greyscale with
In this section, we present an important comparison with recent schemes reported in literature to show the effectiveness of the proposed scheme. The histogram generated by our scheme presents a uniform distribution, due to the highly uniform distribution of the values of the hyperchaotic sequences that benefit the encryption process at statistical level.
In Table
Comparison of space key.
Proposed | Reference [ |
Reference [ |
Reference [ |
Reference [ |
Reference [ | |
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Space key |
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Table
Speed of encryption/decryption.
Speed of encryption | Speed of decryption | Units | |
---|---|---|---|
Proposed | 0.2340 | 0.2105 | Seconds |
Reference [ |
0.52 | — | Seconds |
Reference [ |
1.5 | 2 | Seconds |
In this paper, we present a robust and fast fingerprint image encryption algorithm scheme by using a hyperchaotic map. The security analysis verifies the security capabilities of the proposed scheme to be used in real applications and enforce the security of the biometric systems. The encryption process presents high security when the permutation stage is omitted. However, the correlation is lower when the proposed permutation presses is applied, which benefits the strength of the encryption scheme against statistical attacks.
The authors declare that they have no competing interests.
This work was supported by the CONACYT, México, under Research Grant 166654.