Jung Hee Cheon

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.

The Cheon-Kim-Kim-Song (CKKS) homomorphic encryption scheme is widely adopted for securely evaluating circuits over real numbers, such as those arising in privacy-preserving machine learning (PPML), because it efficiently supports approximate floating-point arithmetic of messages. A CKKS ciphertext has a finite level, which corresponds to the budget for how many multiplicative operations can be applied. Once these levels are consumed, the ciphertext must be refreshed through a bootstrapping procedure to restore its capacity for further computation. The CKKS bootstrapping procedure consists of four main steps: 1) ModRaise, which raises the ciphertext coefficient modulus; 2) C2S, which homomorphically evaluates the inverse-DFT (iDFT) to enable further operations on the ciphertext coefficients; 3) EvalMod, which homomorphically removes the unintended coefficients introduced by ModRaise and shifted to the message side by C2S; and 4) S2C, which homomorphically evaluates the DFT to map the ciphertext back from the iDFT domain. However, these bootstrapping procedures also consume a significant number of levels, leaving fewer levels after each bootstrapping. In this work, we introduce three techniques—OverModRaise1, OverModRaise2, and Tuple-C2S/S2C—that target reductions in the modulus consumption of C2S/S2C among the CKKS bootstrapping procedures, without introducing substantial overhead or compromising security. By combining these techniques, our implementation demonstrates at most 41% throughput improvement compared to the state-of-the-art bootstrapping.