Design and Analysis of Bilinear Pairing based Cryptosystems

Abstract

Pairings are basic building blocks in many cryptographic protocols such as identity newlinebased encryption, one round three party key agreement schemes, short signatures newlineand zero-knowledge proofs. The basic algorithm for pairing computation is provided by Victor S. Miller. The reduction of complexity of Miller s algorithm is a newlinesignificant research area in pairing based cryptography. We try to put some light newlinein this direction. We propose an algorithm for pairing computation by modifying newlinethe algorithm provided by Ionia and Joux.Elementary mathematical structures such as cyclic groups and pairings on genus 1 curves have been used very common in cryptography. Mathematically rich structures are also useful to realize various cryptographic primitives and protocols. Vector decomposition problem is a problem which can be defined on non-cyclic groups. We extend the use of Vector decomposition problem in different cryptographic primitives. We proposed a key agreement scheme based on vector decomposition. Managing digital identity is an important requirement in any network. Managing certificates newlineis too laborious in a large infrastructure network. The identity based encryption newline(IBE) is an alternative to this problem which uses the identity of the entity, to newlinegenerate public parameters and secret key. In IBE scheme, the secret key is generated newlineby a trusted third party called Private Key Generator (PKG). This permits newlinePKG to decrypt any messages sent in the network. Certificateless public key cryptography was another suggestion by Al-Riyami and Paterson [1]. But their system newlineuses two different encryption keys which results in double encryption. We propose newlinea scheme which uses shorter key and has reduced computational complexity. newlineThe advancement in computing facilities made an enormous increase in the amount newlineof digital information. This necessitates reliable and inexpensive ways to manage newlinethe huge storage requirement. Cloud data storage has drawn attention of people newlineas a solution to this requirement...