Digital signature schemes (DSS) are ubiquitously used for public authentication in the infrastructure of the internet, in addition to their use as a cryptographic tool to construct even more sophisticated schemes such as those that are identity-based. The security of DSS is analyzed through the existential unforgeability under chosen message attack (EUF-CMA) experiment which promises unforgeability of signatures on new messages even when the attacker has access to an arbitrary set of messages and their corresponding signatures. However, the EUF-CMA model does not account for attacks such as an attacker forging a different signature on an existing message, even though the attack could be devastating in the real world and constitutes a severe breach of the security system. Nonetheless, most of the DSS are not analyzed in this security model, which possibly makes them vulnerable to such an attack. In contrast, a better security notion known as strong EUF-CMA (sEUF-CMA) is designed to be resistant to such attacks. This review aims to identify DSS in the literature that are secure in the sEUF-CMA model. In addition, the article discusses the challenges and future directions of DSS. In our review, we consider the security of existing DSS that fit our criterion in the sEUF-CMA model; our criterion is simple as we only require the DSS to be at least secure against the minimum of existential forgery. Our findings are categorized into two classes: the direct and indirect classes of sEUF-CMA. The former is inherently sEUF-CMA without any modification while the latter requires some transformation. Our comprehensive review contributes to the security and cryptographic research community by discussing the efficiency and security of DSS that are sEUF-CMA, which aids in selecting robust DSS in future design considerations.

Identification schemes are used by machines to securely authenticate the identity of other machines or their users over computer networks. As conventional public key schemes require a trusted third party (TTP) or a public file to ensure the corresponding public key matches with the identity, identitybased cryptosystems emerged as a form of certificate-free system. The entity’s identity is the public key itself, therefore eliminating the need for a TTP. The identity-based identification (IBI) scheme introduced by Kurosawa and Heng using their transform in 2004 remains as the only IBI derived from the Boneh-Lynn- Shacham (BLS) short signature scheme which has the advantage of shorter keys. We show tight security reduction against active and concurrent attackers (imp-aa/ca) on our scheme that is obtained from the same transform. As the transform will only produce schemes that are only secure against passive attackers (imppa), security against imp-aa/ca scheme relies on a strong One-More interactive assumption and therefore resulted in weak security. While the OR-proof method allows schemes secure against imp-pa to be secure against imp-aa/ca, the resulting security against imp-aa/ca will suffer from loose bounds in addition to the user secret keys being doubled in size. Our work avoids both OR-proof and strong interactive assumptions by showing an ad-hoc proof for our construction which utilizes the weaker well-studied co-computational Diffie-Hellman assumption and yet still has tight security against imp-aa/ca. We demonstrate the tight security of our scheme which allows usage of even shorter key sizes.