Design of DL-based certificateless digital signatures

Public-key cryptosystems without requiring digital certificates are very attractive in wireless communications due to limitations imposed by communication bandwidth and computational resource of the mobile wireless communication devices. To eliminate public-key digital certificate, Shamir introduced the concept of the identity-based (ID-based) cryptosystem. The main advantage of the ID-based cryptosystem is that instead of using a random integer as each user’s public key as in the traditional public-key systems, the user’s real identity, such as user’s name or email address, becomes the user’s public key. However, all identity-based signature (IBS) schemes have the inherent key escrow problem, that is private key generator (PKG) knows the private key of each user. As a result, the PKG is able to sign any message on the users’ behalf. This nature violates the “non-repudiation” requirement of digital signatures. To solve the key escrow problem of the IBS while still taking advantage of the benefits of the IBS, certificateless digital signature (CDS) was introduced. In this paper, we propose a generalized approach to construct CDS schemes. In our proposed CDS scheme, the user’s private key is known only to the user himself, therefore, it can eliminate the key escrow problem from the PKG. The proposed construction can be applied to all Discrete Logarithm (DL)-based signature schemes to convert a digital signature scheme into a CDS scheme. The proposed CDS scheme is secure against adaptive chosen-message attack in the random oracle model. In addition, it is also efficient in signature generation and verification.