Homomorphic Encryption (HE) enables computation on encrypted data while preserving privacy. We explore its application in the multi-party setting, where data is stored in the cloud under several distinct keys. For n parties, Multi-Key HE (MKHE) supports such scenarios but incurs O ( n ) space and computational overhead, making it impractical for large-scale use. Conversely, Multi-Party HE (MPHE) achieves constant O ( 1 ) overhead but is typically limited by a static group structure: ciphertexts are traditionally tied to a fixed set of parties, which poses challenges for dynamically joining new members or reusing existing ciphertexts for different party sets. To address these limitations, we first construct a Dynamic MPHE (dMPHE) scheme that allows new parties to join, while the original parties are not required to remain online. Our construction bridges the gap between existing MPHE and MKHE frameworks while achieving superior efficiency compared to prior dynamic MPHE attempts. Building on this, we introduce Reusable Dynamic MPHE (rdMPHE), a new primitive that simultaneously supports dynamicity and ciphertext reusability. We implement both schemes based on the RLWE assumption. Our analyzes and experiments demonstrate that rdMPHE maintains O ( 1 ) efficiency while overcoming the scalability and static constraints of previous MKHE and MPHE. To support open research, our code has been made publicly available.
Cheon et al. (2026) studied this question.