Demonstrably Secure Signature Scheme Resistant to <inline-formula> <tex-math notation="LaTeX">${k}$ </tex-math></inline-formula>-Traitor Collusion Attack

Abstract

This paper presents the proposal of a new implicit and explicit certificate-based signature scheme (IE-CBS-kCAA scheme) using Sakai-Kasahara's type keys. The scheme security depends on the computational difficulty of solving the modified collusion attack algorithm with k traitors (k-mCAA problem), reducible in particular cases to the known k-CAA problem. The originality of the scheme consists not only in the formulation and application of a new difficult computational problem but also in its design to meet the paradigm of public key cryptography based on implicit and explicit certificates. Due to such an approach, the proposed signature scheme can be used in the traditional public key infrastructure with the revocation of explicit certificates and in non-standard infrastructures without the revocation of implicit certificates. In this paper, the security model is formulated and it is shown that the IE-CBS-kCAA signature scheme is existentially unforgeable against adaptively chosen messages in the random oracle model. Moreover, it results from the comparison of the IE-CBS-kCAA scheme with other signature schemes based on implicit and/or explicit certificates that its computational efficiency is at a similar level. Computational tests have also shown that the scheme can be used in practice.

Keywords

• Signature scheme
• implicit and explicit certificates-based public key cryptography
• bilinear pairing
• security analysis
• k-CAA problem