New and Efficient ID-based Signature Scheme with Message Recovery using Bilinear Pairings over Elliptic Curves Salome James, N.B.Gayathri, P. Vasudeva Reddy * Department of Engineering Mathematics, Andhra University, Visakhapatnam, INDIA *Corresponding Author: vasucrypto@andhrauniversity.edu.in. Abstract: Digital signature is one of the most important cryptographic primitive and has many practical applications in the real world. In many signature schemes, messages are to be transmitted together with signature and thus these schemes requires a large communicational cost for which they may be cannot efficiently used in some resource constrained devices such as WSNs, Mobile phones etc., where the less computation and low band width for communication are of great concern. In this paper, we design and analyze a new signature scheme with message recovery in the Identity based setting using bilinear pairings over elliptic curves. We discuss the proof of correctness and the security of the proposed scheme. Finally, we compare our scheme with the related schemes in terms of computational and communicational point of view. Keywords: digital signature, Id-based cryptography, message recovery, bilinear pairings, CDH problem. 1. Introduction Digital signature is one of the most important cryptographic primitive, which can provide the data integrity, authentication and non-repudiation to digital communications and has many practical applications in the real world such as e-commerce, e-governance, e-voting etc,. Many signature schemes have been proposed in traditional and ID-based settings [18]. In many existing signature schemes, message is to be transmitted together with signature and thus these schemes requires a large communicational cost for which they may be cannot efficiently used in some special environments where low-communication and low-computation cost usually required. To solve this problem, signature scheme with message recovery technique is presented. In this these schemes, the original message of the signature is not required to be transmitted together with the signature. The message is embed in a International Journal of Pure and Applied Mathematics Volume 120 No. 5 2018, 1405-1422 ISSN: 1314-3395 (on-line version) url: http://www.acadpubl.eu/hub/ Special Issue http://www.acadpubl.eu/hub/ 1405