Healthcare blockchains provide an innovative way to store healthcare information, execute healthcare transactions, and build trust for healthcare data sharing and data integration in a decentralized open healthcare network environment. Although the healthcare blockchain technology has attracted broad interests and attention in industry, government and academia, the security and privacy concerns remain the focus of debate when deploying blockchains for information sharing in the healthcare sector from business operation to research collaboration. This paper focuses on the security and privacy requirements for medical data sharing using blockchain, and provides a comprehensive analysis of the security and privacy risks and requirements, accompanied by technical solution techniques and strategies. First, we discuss the security and privacy requirements and attributes required for electronic medical data sharing by deploying the healthcare blockchain. Second, we categorize existing efforts into three reference blockchain usage scenarios for electronic medical data sharing, and discuss the technologies for implementing these security and privacy properties in the three categories of usage scenarios for healthcare blockchain, such as anonymous signatures, attribute-based encryption, zero-knowledge proofs, verification techniques for smart contract security. Finally, we discuss other potential blockchain application scenarios in healthcare sector. We conjecture that this survey will help healthcare professionals, decision makers, and healthcare service developers to gain technical and intuitive insights into the security and privacy of healthcare blockchains in terms of concepts, risks, requirements, development and deployment technologies and systems.