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The RSA is a de-facto standard for public key cryptography, which provides, data confidentiality, data integrity, and authentication. However, RSA is computationally more expensive and needs longer key lengths which are very difficult to store on smaller computing devices e.g. smartphone, smartcards, palmtop, etc. Key generation using the matrix in RSA provides a way to reduce the key storage space but generating it randomly do not achieve any security goals. Biometrics can identify each person uniquely so here the matrix is generated using fingerprints. The matrix formed using fingerprints need to be stored in the database. In this paper to protect the matrix in the database from security breaches Fuzzy Vault is used which acts like a locker to provide confidentially to the matrix.
Since when RSA was first developed  it has been the most popular and widely used public key cryptosystems. The main drawbacks of RSA  compared to other cryptosystems is that it is computationally more expensive and need longer key lengths which are very difficult to store on smaller computing devices e.g. smartcards. These drawbacks have been overcome by proposing many variants of RSA  e.g. Multi-prime RSA , Common Prime RSA  and Dual RSA  to reduce the computational cost  or to reduce the key length storage space. Now, in this paper, the authors are working on  which provides a way to reduce the key storage space by generating the keys using a matrix. The security of any cryptographic algorithm depends upon the cryptographic keys. The keys must be strong and provide the uniqueness and randomness. Since biometrics uniquely recognize humans  based on physical traits like fingerprint, hand, ear, iris, and DNA or behavioral traits like talking, walking, and signature. Fingerprints are the most widely used parameter for personal identification amongst all biometrics . There are many methods available to generate RSA key using a single fingerprint  or using a combination of two or more fingerprints . In this paper, single fingerprint minutiae is used to generate the matrix elements which generate the RSA key pairs. First, the minutiae points are extracted from the fingerprint then the extracted minutiae points are used as the elements of the matrix. After the matrix is generated it must be stored so that it can be reused to regenerate the key pairs but doing so can cause the security breach. To overcome this problem a method known as the fuzzy vault is used to provide the security to the stored matrix. Fuzzy vault  is a crypto-biometric system which aims to secure the critical information with biometric data such as fingerprints so that only authorized user can access the data after providing the valid biometric data. The remaining part of the paper as follows: Section 2 gives an overview of fingerprint features and minutiae extraction from the fingerprint, section 3 gives the RSA overview with key generation using matrix, section 4 gives an overview of fuzzy vault proposed by Juels and Sudan . Section 5 gives implementation and conclusion of the paper
The purpose of the proposed model is to achieve cryptographic security goals i.e. Data Confidentially and User Authentication. Since the fingerprints are the most reliable method for personal identification hence we can achieve user authentication using fingerprints. Fuzzy Vault provides the confidentially to the stored matrix with the help of minutiae extracted. Random numbers are used at many levels during Keys generation to make the expected complexity of key generation high. The proposed model is very simple and can be used in small hand held devices to reduce the storage space of keys
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