Research And Design Of Provably Secure Signature Schemes

Security evaluation plays a crucial role in designing and analyzing cryptographic schemes and protocols. Provable security based on computational complexity theory provides an efficient way for providing the convincing evidence of security. Our contributions can be summarized as follows: proof of security for ID-based signature schemes, design of ID-based signature schemes, and exploration of universally composable security for forward-secure signatures.Firstly, through analyzing the existing ID-based signature schemes and extending the notion of generic signature schemes, a notion of generic ID-based signature schemes (GIBSS) is proposed. Moreover the Forking Lemma for GIBSS is also proved. The theoretical result can be viewed as an extension of the Forking Lemma due to Pointcheval and Stern for ID-based signature schemes, and can help to understand and simplify the security proofs of previous work such as Hess's scheme, BLMQ's scheme, and so on.Secondly, a new ID-based signature scheme derived from the extract algorithm due to Sakai and Kasahara is proposed. The security of the new scheme can be proved based on the assumption of the k-CAA (collusion attack algorithm with k traitors), in the random oracle model.At last, universally composable security of forward-secure signatures is explored. More specifically, an ideal functionality for forward-secure signatures is proposed, and the assertion is also proved that universally composable definition of security is equivalent to the definition of security which is existential unforgeability under adaptively chosen-message attacks.