Mobile technologies are capable of offering individual level health care services to users. Mobile Healthcare (m-Healthcare) frameworks, which feature smartphone (SP) utilizations of ubiquitous computing made possible by applying wireless Body Sensor Networks (BSNs), have been introduced recently to provide SP clients with health condition monitoring and access to medical attention when necessary. However, in a vulnerable m-Healthcare framework, clients' personal info and sensitive data can easily be poached by intruders or any malicious party, causing serious security problems and confidentiality issues. In 2013, Lu et al. proposed a mobile-Healthcare emergency framework based on privacy-preserving opportunistic computing (SPOC), claiming that their splendid SPOC construction can opportunistically gather SP resources such as computing power and energy to handle computing-intensive Personal Health Information (PHI) with minimal privacy disclosure during an emergency. To balance between the risk of personal health information exposure and the essential PHI processing and transmission, Lu et al. presented a patient-centric privacy ingress control framework based on an attribute-based ingress control mechanism and a Privacy-Preserving Scalar Product Computation (PPSPC) technique. In spite of the ingenious design, however, Lu et al.'s framework still has some security flaws in such aspects as client anonymity and mutual authentication. In this article, we shall offer an improved version of Lu et al.'s framework with the security weaknesses mended and the computation efficiency further boosted. In addition, we shall also present an enhanced mobile-Healthcare emergency framework using Partial Discrete Logarithm (PDL) which does not only achieve flawless mutual authentication as well as client anonymity but also reduce the computation cost.