Identity Based Cryptography Using Matrices

A new method of identity (ID) based Elgamal type encryption/decryption is described. The technique uses rectangular integer matrices in finite field Z_p, as the private keys. Adoption of modular arithmetic limits the size of the elements of the key matrices while maintaining reasonably high security levels. The principle of the method is extended to design a new ID based Proxy Re-Encryption (PRE) scheme that converts the cipher text (CT) intended for one user into a different CT which can be decrypted by another user. In present work, all mathematical operations like addition, subtraction, multiplication, and inversion of matrices are carried out using modular algebra. Further, ID based encryption/decryption as well as PRE has protection against chosen plain text and chosen CT attacks. Computational expensive techniques like, bilinear maps and modular exponentials are not used in the proposed scheme. Therefore, present technique is computationally less expensive compared to similar existing methods as confirmed by experimental results. Proposed PRE scheme is implemented within a cloud service system is well suited for secure data sharing among multiple end users.