Efficient Implementation of Cancelable Optical Face Recognition Based on Elliptic Curve Encryption

doi:10.21203/rs.3.rs-1611155/v1

Most modern authentication systems adopt human biometrics to avoid any shortcomings that result from forgetting passwords and security codes utilized in traditional systems. To improve the security level of the original biometric traits from offensive attacks, cancelable biometric patterns are generated from the original biometric templates. This paper presents a new approach for cancelable face recognition based on the concept of elliptic curve cryptography (ECC). The ECC is classified as a public-key (asymmetric) encryption technique. In public-key encryption, each user (transmitter and receiver) has two keys: public key, and private-key. The proposed framework guarantees full distortion and encryption of the original biometric traits to be saved in the database to completely save the original biometrics away from intruders. To validate the performance of the proposed approacg, three face biometrics databases have been used. Receiver Operating Characteristic (ROC) curve and correlation scores are estimated to test the system quality. The simulation results prove that the proposed approach is efficient, robust, and it achieves high performance with three face databases.

Traditional authentication systems have their limitations for system access. These systems may fail to guarantee the exact and right password or personal identification number for each authentication process. The most general scheme of biometric authentication system involves a sensor module for image acquisition, a pre-processing module to provide alignment and noise removal, a segmentation module for region extraction, and a feature extraction module. Biometrics are classified into two categories: physical and behavioral. The physical category includes fingerprints, hand engineering, retina, iris scan, and faces. On the other hand, the behavioral category includes voice, signature, keystroke pattern, and walking style. These characteristics of the human body can be used to ensure that only the authorized individual has the permission to access the system [1–6].

To increase the security level of a stored biometric, a biometric cryptosystem can be used to build a cancelable biometric system. In traditional biometric cryptosystems, the original biometric templates can be encrypted and stored in encrypted form in the database. During the authentication phase, a decryption process is required. On the other hand, in cancelable biometric systems, the encrypted biometric templates are used in a statistical framework for identity verification. So, there is no need to decrypt the stored templates as in the traditional biometric cryptosystem [6–10]. Biometric authentication systems work based on two levels. The first level is the enrolment of the biometric of the users, and the second level is the authentication or verification [11, 12]. The main idea of cancelable biometrics is to make distortion of the original templates by certain transformation methods or encryption schemes to be stored in the database in the enrollment phase. In the authentication phase, the biometric of the corresponding user is transformed and distorted in the same transformation manner and stored in the database. According to some matching techniques, the verification of the user access is performed. So, cancelable biometrics can be classified as a means of privacy preservation. The basic concept of cancelable biometrics was introduced by N. K. Rath et al in 2007 [13]. Figure 1 displays the framework of the cancelable biometric recognition system.

As shown in Fig. 1, the cancelable biometric framework has two main processes: enrollment and authentication. In the enrollment stage, the users' cancelable biometric templates are obtained and stored in the database. In the authentication stage, the identification of the user is performed by measuring the similarity between new cancelable biometric templates and the stored ones [14–16]. Several researchers have developed and presented different techniques to implement user authentication systems based on biometrics [17]. Elliptic curve cryptography (ECC) was firstly used in encryption in [18, 19]. The ECC offers more security than classical image encryption techniques, because it is hard to solve the discrete logarithmic problem. Moreover, the ECC has a much lower key size than that of the Rivest–Shamir–Adleman (RSA) that achieves the same level of security. After that, several researchers focused on the ECC due to its strength [20–23]. The main problem faced with ECC implementation is the computational cost. The ECC multiplication operation is time-consuming, which makes it a challenge to implement encryption for real-time applications. Some researchers use the ECC to encrypt images by generating pseudo-random noise (PRN) to map pixel values according to the generated points in order to achieve a large degree of permutation [24]. Another important problem encountered with ECC is the increase in data size of the encrypted data compared to the size of the plaintext data. This increase is due to mapping of each pixel value in the plaintext image to a point on the elliptic curve that has two coordinates i.e.,${ p}_{x,y}$. In [25, 26], the authors proposed methods to reduce the encrypted data size by grouping multiple pixels values to share in one point. Their methods succeeded to decrease the size of the encrypted data, but it was still larger than that of the plaintext image.

Cancelable biometrics methodology depends on the utilization of transformed or deformed versions of the biometrics in the verification stage [27]. The main goal of cancelable biometrics is to increase the privacy of users. So, several studies have been introduced to generate cancelable biometric templates. Soliman el al. [28] presented a cancelable biometric system based on double random phase encoding (DRPE) for both face and iris recognition. This system depends on the extraction of features from either face or iris to generate a matrix of features to be encrypted by the DRPE technique. Simulation results revealed an equal error rate (EER) of 0.17% and an area under receiver operating characteristic curve (AROC) of 99.3%. Gowthamim et al. [29] discussed fingerprint recognition using zone-based linear binary patterns. Their technique depends on feature extraction from fingerprint images using linear binary patterns. Each fingerprint image is divided into equal-size zones, and in each zone, the linear patterns are used for recognition. They achieved an average recognition accuracy of 94.28%. Attaullah et al. [30] proposed an authentication system based on fusion of behavioral biometrics. Their system works depending on extracting features by different types of sensors built in the smartphone, followed by a random forest classifier (RF) to verify the identity of the user. Their system achieves 99.3% in the true acceptance rate (TAR).

Loris and Alessandara [31] proposed an automatic ear recognition system based on the fusion of different color space representations of the ear. This system has five steps. The first step is the extraction of the person’s ear from the background of the whole image, followed by conversion of each image of the ear to 13 color space models, which produce 39 images. In the next step, pre-processing is performed on the 39 images with gamma correction, difference of Gaussian filtering, and equalization. Gabor features are used as discriminative features from all color space models. After that, feature selection and classification are performed based on sequential forward floating selection (SFFS) followed by a matching step based on the sum rule of several first nearest neighbor classifiers. The results of this technique give an AROC of 98.5%.

Malathi and Jeberson [32] introduced personal identification and verification techniques based on a discrete wavelet transform (DWT). Patterns of fingerprints, iris, and palm print have been used. The DWT is applied on a certain cropped area of each pattern. Then, secrete information is hidden in the vertical and horizontal high-frequency passband (HH). The inverse discrete wavelet transform (IDWT) is performed to reconstruct the 4 sub-bands. The RC4 is applied for encryption and decryption of the user information. Minutiae mapping technique is used to extract fingerprint, iris, and palm biometrics to compare with the patterns stored in the database. This authentication system achieved good results.

This paper introduces an ECC scheme to generate cancelable biometric templates that can guarantee the high-security level. The proposed approach guarantees full distortion and encryption of the original biometric traits to be saved in the database. The quantitative evaluations are performed using the EER, and AROC as metrics. The rest of this work is arranged as follows. Section 2 briefly describes the mathematical foundations of the elliptic curve and the ECC-based cancelable biometrics approach. Simulation results and comparative analysis are given in section 3. Section 4 gives the concluding remarks.

Cryptography is a branch of data and image security that can be implemented in cancelable biometric systems. Biometric traits can be encrypted firstly and stored in the database. Verification, in this case, must depend on distance metrics such as correlation coefficient. Different attempts for cancelable biometric systems have been presented based on encryption. We will follow the same trend, but with a new encryption technique. The encryption technique used in this paper is the ECC.

3.1 Elliptic Curve (EC) Mathematics

A finite elliptic curve (EC) $\in {\mathbb{Z}}_{p} ($integares mod$p)$ can be defined by a cubic equation as follows:

$${y}^{2}={x}^{3}+ax+b \left(mod P\right)$$

1

where $a,b \text{and} P$ are the EC parameters. $a \text{and} b$ are integer numbers $\in {\mathbb{Z}}_{p}$ and $P$ is a prime number. The parameter must satisfy the condition:

$$4{a}^{3}+27{b}^{2}\ne 0 \left(\text{mod} P\right)$$

2

Figure 2 shows an elliptic curve satisfying Eq. (1) and Eq. (2).

We briefly state some of the mathematical operations of EC. For more details, see [33, 34]. Point addition: if ${q}_{1}\left({x}_{{q}_{1}} , {y}_{{q}_{1}}\right)$ is added to the point ${q}_{2}\left({x}_{{q}_{2}} , {y}_{{q}_{2}}\right)$, the result is ${q}_{3}\left({x}_{{q}_{3}} , {y}_{{q}_{3}}\right),$ which is calculated as follows:

$${q}_{1}+{q}_{2}={q}_{3}$$

3

where${x}_{{q}_{3}}= {\eta }^{2}-{x}_{{q}_{1}}-{x}_{{q}_{2}} \left(\text{mod} P\right)$

$${y}_{{q}_{3}}=\eta \left({x}_{{q}_{1}}-{x}_{{q}_{3}}\right)-{y}_{{q}_{1}} \left(\text{mod} P\right)$$

$$\eta =\frac{{y}_{{q}_{2}}-{y}_{{q}_{1}}}{{x}_{{q}_{2}}-{x}_{{q}_{1}}}$$

Figure 3 illustrates the addition operation of two points [35].

Point inverse: the inverse of point ${q}_{1}\left({x}_{{q}_{1}} , {y}_{{q}_{1}}\right)$ is ${q}_{2}\left({x}_{{q}_{2}} , {y}_{{q}_{2}}\right),$ which is calculated as follows:

$${q}_{2}\left({x}_{{q}_{2}} , {y}_{{q}_{2}}\right)={q}_{2}\left({x}_{{q}_{1}}, P-{y}_{{q}_{2}}\right)$$

4

Point multiplication: the product of an integer number $n$ times a point ${q}_{1}\left({x}_{{q}_{1}} , {y}_{{q}_{1}}\right)$ is calculated as follows;

$${q}_{2}\left({x}_{{q}_{2}} , {y}_{{q}_{2}}\right)=n\bullet {q}_{1}\left({x}_{{q}_{1}} , {y}_{{q}_{1}}\right)={q}_{2}\left(P, \left(n-1\right)P\right)$$

5

Practically, the multiplication operation is performed by additive operations with $n$ times as follows:

$${q}_{2}\left({x}_{{q}_{2}} , {y}_{{q}_{2}}\right)=\sum _{n}{q}_{1}\left({x}_{{q}_{1}} , {y}_{{q}_{1}}\right)$$

6

Discrete logarithm problem: in EC public key encryption, each user randomly chooses his private key, i.e., ${k}_{p}$ and shares $\gamma ={k}_{p}G,$ where $G$ is a generating point, which is shared through the channel. An intruder tries to gather information about the used key. It is very easy to calculate $\gamma$ by multiplying${k}_{p}G$, but it is infeasible to calculate ${k}_{p}$ form $\gamma , \text{a}\text{n}\text{d} G$. This is known as the discrete logarithm problem.

3.2 Image Encryption Using ECC

Different from symmetric key encryption, the ECC is public-key encryption. In public-key encryption, each user has two keys: public and private. The private key is secret, and no one can decrypt an encrypted message without knowing the private key. Diffie and Hellman in 1976 proposed a solution to securely share the key between users. They introduced a public-key protocol to exchange keys with EC, securely [36].

For message encryption, El Gamal cryptosystem with EC was firstly introduced in 1984 [36]. El Gamal is a public key encryption algorithm, which uses two keys. The two users denoted $\alpha \text{and} \beta$ agree on predetermined curve parameters ($a, b, \text{and} P$), and pick a pint on the curve $G$. A pixel value of the plaintext image represents information mapped to a point $M$ on the curve and encoded for transmission over the channel. The protocol of encryption and decryption is performed as follows:

1- Users randomly choose their private keys, ${k}_{\alpha }$ and ${k}_{\beta }$, and keep them secret.

2- Users calculate their public key, ${Q}_{\alpha }={k}_{\alpha }G$ and ${Q}_{\beta }={k}_{\beta }G$, and share it over the channel.

3- If user $\alpha$ wants to send a message $M$ to user $\beta$, it calculates:

$$S=M+{k}_{\alpha }{Q}_{\beta }$$

7

4- User $\alpha$ sends $S$ to user$\beta .$

5- User $\beta$ wants to decrypt the message by calculating:

$$S+\left(-{k}_{\beta }\right){Q}_{\alpha }=$$

$$M+{k}_{\alpha }{Q}_{\beta }-{k}_{\beta }{Q}_{\alpha }=$$

$$M+{k}_{\alpha }{k}_{\beta }G-{k}_{\beta }{k}_{\alpha }G=M$$

8

Any intruder aims to calculate ${k}_{\alpha }$ or ${k}_{\beta }$ form ${Q}_{\alpha }$ or ${Q}_{\beta }$ will face the discrete logarithm problem, which is computationally infeasible.

To encrypt an image using the ECC, each pixel value is mapped to a point on a predefined EC. The EC parameters play an important role in the pixel scrambling process to satisfy the required confusion level. The number of points of the selected EC parameters should be greater than the size of the plaintext image to achieve high encryption and security levels. In this paper, we select the technique that is implemented in [37] to encrypt the images. In [37], the authors proposed a mapping method to distribute the pixel value on the points of a selected EC. For example, they selected an EC with 123456 points, and the image pixel value 0 is mapped to 482 points specified according to repetitions of the pixel value 0 in the image. For more details, see [38, 39]. We have chosen this method, because it is simple and suitable for our application. Figure 4 shows the results of the ECC encryption for three different images. Figure 5 shows the block diagram of the proposed ECC-based cancelable biometric scheme. The correlation coefficient is considered as the metric of matching.

In this section, the evaluation of the proposed approach is presented. Firstly, the security of the proposed ECC is assessed in terms of visual analysis, histogram analysis, correlation analysis, entropy analysis, differential attack analysis, and key sensitivity analysis as given in Figs. 6–8 and Table 1. It is known that the encryption system must break the correlation between the adjacent pixels. Therefore, it is noticed from the results that the encryption system succeeds in destroying the very strong correlation of the plain pixels in the biometric templates. In addition, the encryption system should produce a different encrypted image even with a correlated key. Figure 8 shows an original image and its encrypted versions using very related private keys K₁(8, 3), K₂(8, 4), and K₃(7, 3). The histograms are almost uniform, which indicates an equal probability of the encrypted pixel levels.

Furthermore, Table 1 shows the values of correlation, NPCR, and UACI between two encrypted biometrics using the related keys: K₁, K₂, and K₃. The results indicate that the cryptosystem is very sensitive to the encryption key. All the obtained results prove that the proposed ECC technique can be implemented, efficiently for designing a secure and efficient cancelable biometric recognition system. So, this motivated us to utilize it in our proposed work.

To evaluate the performance of the proposed cancelable biometric system using the ECC encryption technique, three different databases have been used [41–43]: Research Laboratory for Olivetti and Oracle (ORL) database [41], NiST Face Recognition Technology (FERET) dataset [42] and Mass Labelled Faces in the Wild (LFW) dataset of the University of Massachusetts’ Computer Vision laboratory [43]. Twenty images have been used for each database and the correlation coefficient and ROC curve have been estimated for each case. All the used encrypted biometrics and their histograms are shown in Figs. 9–11 for the three databases.

Table 1

The correlation, NPCR and UACI values of encrypted biometrics using different related keys.
Evaluation metric	K₁(8, 3) & K₂(8, 4)	K₁(8,3) & K₃(7, 3)	K₂(8,4) & K₃(7, 3)
Correlation	0.0042	0.0107	0.0053
NPCR	0.9956	0.9963	0.9962
UACI	0.3369	0.3339	0.3357

The block diagram shown in Fig. 5 has been used to obtain the ECC images from the original ones for the three databases. These ECC images are stored in the database module for biometric system applications. For checking the recognition and security levels, the correlation coefficient and the AROC are calculated. The correlation scores for genuine and the imposter distributions for the studied case are shown in Figs. 12–15. The noise variances are changed to be 0.01, 0.02, 0.03, 0.04, and 0.05.

The results shown in the figures ensure the feasibility to add the ECC images in the databases and use them for biometric authentication. The evaluation metrics with different levels of the noise variance for the proposed ECC-based cancelable face recognition approach for ORL, FERET, and LFW database are shown in Table 2.

Table 2

Evaluation metrics with different levels of the noise variance for the proposed ECC-based cancelable face recognition approach for ORL, FERET, and LFW database.
Darabase	ORL		FERET		LFW
Variance	EER	ROC	EER	ROC	EER	ROC
0.01	0	1	0	1	0	1
0.02	0	1	0	1	0	1
0.03	0	1	0	1	0	1
0.04	0	1	0	1	0	1
0.05	0	1	0	1	0	1

This paper presented an improved approach for cancelable face recognition based on the concept of ECC. The main achievement of this approach is the utilization of ECC for biometric data in order to achieve biometric security from intruders. The ECC is classified as public-key encryption (asymmetric) technique. The proposed approach guarantees full distortion and encryption of the original biometric traits to be saved in the database in order to ensure that no accessing of original biometrics can be achieved by intruders. Investigation tests validated the inspiring attainment of the suggested approach in well ciphering and distortion of the stored biometrics. Thus, it is more suitable for secure biometric patterns compared to traditional encryption methods. The capability of the proposed approach to satisfactorily cipher and distort a variety of biometric datasets has been proved. So, the suggested cancelable biometric recognition approach is a good candidate for modern access technology. In the future work, we plan to design a multi-level cryptosystem based on a cancelable biometric concept that includes steganography, encryption, and watermarking for achieving a new level of security. Also, a further improved deep learning model for cancelable biometric recognition will be introduced for cloud-based applications.

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Efficient Implementation of Cancelable Optical Face Recognition Based on Elliptic Curve Encryption

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Journal Publication

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Abstract

Figures

1. Introduction

2. Proposed Ecc-based Cancelable Biometric Approach

3.1 Elliptic Curve (EC) Mathematics

3.2 Image Encryption Using ECC

3. Simulation Results

4. Conclusions And Future Works

References

Status:

Journal Publication

Version 1