Digital signature schemes with strong existential unforgeability

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.