Performance and Security Issues of Elliptic Curve Cryptography

Abstract

The current era has seen an explosive growth in communications. Applications like newlineonline banking, personal digital assistants, mobile communication, smartcards, etc. newlinehave emphasized the need for security in resource constrained environments. newlineElliptic curve cryptography (ECC) serves as a perfect cryptographic tool because newlineof its short key sizes and high security comparable to that of other standard public key newlinealgorithms. ECC is a key based technique for encrypting data. ECC focuses on pairs newlineof public and private keys for encryption and decryption of messages. newlineECC schemes are based on the scalar multiplication of elliptic curve points and newlinethe computational intractability of the inverse operation, the Elliptic Curve Discrete newlineLogarithm Problem (ECDLP). A survey on existing ECC solutions was conducted with newlinea thorough analysis of the challenges in developing ECC based systems. The challenges newlineidentified in the survey are domain parameter selection, scalar multiplication, point newlinemultiplication, elliptic curve selection, elliptic curve generation, key generation, key newlinesize selection, security measurements, applications etc. newlineThe objective of this thesis is to focus on key generation issue of elliptic curve newlinecryptography. Biometrics has been used for secure identification and authentication for newlinemore than two decades since biometric data is unique, non transferable, unforgettable, newlineand always with us. newlineWith fast evolution of mobile devices and mobile network, the need of protecting newlineuser sensitive information locally and performing secure user authentication remotely newlinebecome ever more increasing. Bio-cryptography is emerging as a powerful solution newlinewhich can combine the advantages of conventional cryptography and biometric security. newlineIn the first contribution, focus is given on key generation from user s biometric. newlineA private key is generatd from user s fingerprint minutiae. The minutiae points are newlineextracted from the fingerprint image based on image processing algorithms, then the extracted newlinefingerprint minutiae are used for generating