This paper presents a hybrid blockchain-edge architecture for managing Electronic Health Records (EHRs) with attribute-based cryptographic mechanisms. The architecture introduces a novel attribute-based signature aggregation (ABSA) scheme and multi-authority attribute-based encryption (MA-ABE) integrated with Paillier homomorphic encryption (HE) to protect patients' anonymity and safeguard their EHRs. All the EHR activities and access control events are recorded permanently as blockchain transactions. We develop the ABSA module on Hyperledger Ursa cryptography library, MA-ABE module on OpenABE toolset, and blockchain network on Hyperledger Fabric. We measure the execution time of ABSA's signing and verification functions, MA-ABE with different access policies and homomorphic encryption schemes, and compare the results with other existing blockchain-based EHR systems. We validate the access activities and authentication events recorded in blockchain transactions and evaluate the transaction throughput and latency using Hyperledger Caliper. The results show that the performance meets real-world scenarios' requirements while safeguarding EHR and is robust against unauthorized retrievals.