Biometric Encryption using Elliptic Curve

International Journal of Research and Reviews in Computer Science (IJRRCS) Vol. 2, No. 5, October 2011, ISSN: 2079-2557 © Science Academy Publisher, United Kingdom www.sciacademypublisher.com

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Biometric Encryption using Elliptic Curve G. Mary Amirtha Sagayee1, S Arumugam2, and S. Anandha Mala3 1

Department of Information Systems and Communications, Anna University, Chennai Department of Computer Science and Engineering, Nandha Engineering College, Erode, Tamil Nadu, India 3 Department of Computer Science and Engineering, St Joseph College of Engineering, Chennai, India 2

Email: [email protected], [email protected], [email protected]

Abstract – The greatest strength of biometrics is that it does not change over time. But at the same time while using it directly for enhancing the security in network system, if that data has been compromised, it’s compromised forever [1]. Biometrics, cryptography and data hiding will provide good perspectives for information security. Many mathematicians proved that Elliptic Curve is the best solution for Cryptography [10]. We proposed an algorithm for deriving the key from biometric for ECC based applications which will provide high security with good performance in terms of computational and bandwidth requirements.

Keywords – Finger Print Image, Minutiae, Cryptography, ECC, Prime Field

1.

Introduction

In recent development of Information Technology, secured communication has become necessary. Cryptography is a kind of secret writing by which two parties can communicate with secret messages [17]. Most of the researches were demonstrating that Biometric is the ultimate solution for identification and authentication, since it is proved as reliable and universally acceptable identification/authentication methods in many application areas [15]. Due to the popularity of biometrics and cryptography, the information security is becoming as a common demand in all applications area. Biometric is referred as automatic system that uses measurable, physical or physiological characteristics or behavioral traits to recognize the identity of an individual. While comparing with traditional identify / authentication systems, biometrics offers greater security. Enhancing the identification and authentication system using cryptography and biometrics are providing high assurance [14]. In the past decades, a lot of efforts have been taken in the combination of biometric and cryptography. There issues in this combination, is the security/privacy concerns in enhancing information security [2]. We proposed an algorithm to extract the key from biometric image for ECC. In many researches, it is confirmed that the finger print is widely used than iris or face and more over it is the primary choice for most privacy concerned applications. In this paper, we derived a mathematical approach for generating the key for ECC from the fingerprint image. The rest of the paper is organized as follows. In Section 2, the related works are discussed. Section 3 provides the method for extracting the minutiae from fingerprint image and in Section 4, a mathematic approach to generate the cryptographic key from the resultant image template is derived which is cable of providing better authentication/ identification with security. Finally the conclusions are summarized in Section 5.

2.

Literature Survey

In 1970s, private keys, which are not known to others, are used by both parties. In 1976, another method was devised by Rivest, Shamir and Adleman[6] for using cryptography with public key distribution. Both methods made fundamental use of the arithmetic in some algebraic object. In 1997, Victor S.Miller[10] has suggested that the Elliptic Curves gives solutions to many issues in providing high security by finding the curves whose group orders are divisible by a small prime in order to provide a fast algorithm. Also it could reduce the problem of calculating discrete logarithms to the Diffe-Hellman problem.[5] Many algorithms are proposed in Cryptography, which are based on symmetric and asymmetric key. In asymmetric cryptography system, private and public keys are involved, which is based on mathematical functions rather than on substitution and permutation. Elliptic Curve Cryptography (ECC) is a public-key cryptography system [10], in which a key pair is selected so that the problem of deriving the private key from the corresponding public key is equivalent to solve a computational problem that is believed to be intractable. In general, the keys are protected by user passwords, which will compromise the integrity of sensitive data due to poor selection of the password by the user. Combining biometric with cryptography could be the solution by generating deterministic bit sequences for generating a reliable key. [12]. But it is essential to generate the key with minimum possibility of uncertainty due to poor image quality of the fingerprint which is used for feature extraction. [14]. Also the digital signature from the fingerprint should be adopted with the cryptography algorithm in such a way that security and infrastructure requirements should not be changed. [13].

G.M. Amirtha Sagayee et al. / IRRCS, Vol. 2, No. 5, pp. 1112-1115, October 2011

3.

Minutiae point extraction from Finger print.

3.1. Finger Print A finger print is made of a series of ridges and furrows on the surface of the fingertip, the formation of which is determined during the first seven months of fetal development. Fingerprints of identical twins are different. The uniqueness of a fingerprint can determine by the pattern of ridges and furrows as well as the minutiae points. A total of 150 different local ridge characteristics (islands, short ridges, enclosure etc) have been identified. Among the variety of minutia types reported in the literatures, two are mostly significant and in heavy usage: one is called termination (Ridge Ending), which is the immediate ending of a ridge; the other is called bifurcation (Branch), which is the point on the ridge from which tow branches derive. A good quality fingerprint typically contains about 40-100 minutiae. The problem of maintaining the secrecy of the private key in cryptography can be solved by generating the keys from minutiae. 3.2. Algorithm for Minutiae Extraction from Finger Print Minutiae points serve as an important means of biometric recognition system. The ridges of the fingerprint form the socalled minutiae points. The implement the minutia extractor, a three stage approach is widely used researchers. They are (i) preprocessing (ii) minutia extraction and (iii) post processing stage. The fingerprint image preprocessing stage includes, normalization, ridge orientation estimation, ridge frequency estimation and filtering [2]. The most commonly employed method of minutiae extraction is the Crossing Number (CN) concept [6]. It takes enhanced image as input and does thinning and minutiae marking. Output of this stage is the list of minutiae. False minutiae may be introduced into the image due to factors such as noisy images and image artifacts created by the thinning process. Hence, after the minutiae are extracted, it is necessary to employ a post processing stage in order to validate the minutiae [11]. The quality of the ridge structures in a fingerprint image is an important characteristic, as the ridges carry the information of characteristic features required for minutiae extraction. Generally for a given digital fingerprint image, the region of interest can be divided into three categories[2] as (i) Well defined region (ii) Recoverable region (iii) Unrecoverable Region. The algorithm of preprocessing consists of four main stages as follows: a) Normalization is used to standardize the intensity values in an image by adjusting the range of gray– level values so that it lies within a desired range of values. b) Orientation Estimation in which the orientation field defines the local orientation of the ridges contained in the fingerprint. c) Estimation of Ridge Frequency which is used in the construction of the Gabor filter. It is represents the local frequency of the ridges in a fingerprint, which is a sinusoidal shaped wave along a direction normal to the local ridge orientation.

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d) Gabor Filtering is used to tune the ridges at a specific orientation and frequency in the fingerprint image. After a fingerprint image has been enhanced, the next step is to extract the minutiae from the enhanced image. The different steps for minutiae extracting are as follows: a) Thinning is the morphological operation and successively erodes away the foreground pixels until they are one pixel wide. The obstacles and noise are eliminated by this process [10]. It preserves the connectivity of the ridge structures while forming skeletons version of the binary image. The resultant of thinning algorithm will improves the visibility of the ridges and enables to extract effective minutiae points. b) Minutiae Extraction can be done by the Crossing Number (CN) [6] concept. The minutiae are extracted by scanning the local neighborhood of each ridge pixel in the image using a 3x3 window. The CN value is then computed which is defined as half the sum of the differences between pairs of adjacent pixels in the right-neighborhood. Using the properties of CN, the ridge pixel can then be classified as ridge ending, bifurcation or non-minutiae point. Table 1. Properties of Crossing Number CN 0 1 2 3 4

Prosperity Isolated Point Ridge Ending Point Continuing Ridge Point Bifurcation Point Crossing Point

The extracted minutiae points are recorded with the information (i) x and y co-ordinates (ii) Orientation of the associated ridge segment and (iii) Type of minutiae (ridge ending or bifurcation. In image post processing, the extracted minutiae are validated due to factors such as nosy images, and image artifacts created by the thinning process. 3.2.1. Algorithm for validating the ridge ending point Step 1: Label with a value of 1 for all the pixels in M which are eight connected with the ridge ending point. Step 2: Count in a clockwise direction, the number of 0 to 1 transitions (T01) along the border of image M. If T01 = 1, then the candidate minutiae point is validated as true ridge ending. 3.2.2. Algorithm for validating the bifurcation point Step 1: Examine the eight neighboring pixels surrounding the bifurcation point in a clockwise direction. For the three pixels that are connected with the bifurcation point, label them with the values of 1,2 and 3 respectively. Step 2: Next label the rest of the ridge pixels that are connected to these three connected pixels. Step 3: Count in a clockwise direction, the number of transitions from 0 to 1 (T01), 0-2 (T02) and 0 to 3 (T03) along the border of image M. If T01 = 1 power T02=1 poser T03 = 1, then the minutiae point is validated as a true bifurcation.

G.M. Amirtha Sagayee et al. / IRRCS, Vol. 2, No. 5, pp. 1112-1115, October 2011

4.

Cryptographic key generation from Finger print image.

4.1. Cryptographic Key Generation Elliptic curves are mathematical constructs that have been studied by mathematicians since the seventeenth century. The following section will provide the general architecture of implementation and details about the algorithms for embedding minutiae on elliptic curve and the biometric based key generation method.

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image. The algorithm FPCONCAT for the above processes follows as below: Step 1: Get the binary values XBi, YBi and θBi of Xi, Yi and θi for given ith θ θ number of minutiae. Step 2: Concatenate all the binary values in the following order. MBi = X Location (9bits) | | (3 bits)

| |

Step 3: Convert the above concatenated binary string MBi to decimal to get the single co-ordinate value M1i. Let K be a large enough integer so that the failure probability of 1 out of 2k will be satisfied when the plaintext m is attempted to imbed; in practice k=30. Suppose message units are integers 0