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Accelerating CKKS on GPUs with Cheddar and Theodosian
TL;DR: Modern GPUs provide enormous parallel computation capability, making them an attractive platform for accelerating CKKS. However, achieving high performance requires redesigning both the cryptographic algorithms and the GPU implementation together rather than simply porting CPU code. In this post, I introduce Cheddar, a GPU-native CKKS library based on a 32-bit RNS construction that achieves state-of-the-art performance, and Theodosian, which shows that modern GPU implementations are no longer compute-bound but instead limited by on-chip L2 cache bandwidth. Together, these works illustrate both how far GPU acceleration has come and where the next performance barriers lie.
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FHE for SIMD Arithmetic Logic Units with Amortized O(1) Bootstrapping per Ciphertext
TL;DR: We propose a new CKKS-compatible encoding framework that supports both arithmetic and Boolean operations for a vector of, for example, 64-bit integers. The key idea is using multiple complex slots to represent one integer, with a special ring isomorphism to maintain the desired integer arithmetic. For arithmetic-only workloads, each refreshing requires only two bootstrapping operations for one ciphertext. For Boolean operations, the arithmetic-to-Boolean conversion can batch $O(n)$ ciphertexts, resulting in amortized $O(1)$ bootstrapping per ciphertext. The prototype is available at
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Faster Bootstrapping for CKKS with Less Modulus Consumption
TL;DR: To improve efficiency and reduce the modulus consumption in standard CKKS bootstrapping, we propose two novel core techniques: level-conserving rescaling (LCR) and aggregated key-switching (AKS), which act on the matrix-vector multiplications in linear transformations and can be further combined into the lossless LCR+AKS. The contributions enable bootstrapping that consumes one fewer modulus level, improves throughput by 20%–35%, and reduces CtS rotation key size by 11.9%–15.2%, while preserving identical precision and failure probability.
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On the (In)security of Approximate Computation Protocols from CKKS
TL;DR: Recent advances in approximate HE, particularly CKKS, have significantly advanced the practicality of secure computation involving approximate arithmetic. However, the inherent errors introduced by CKKS pose substantial challenges in the security analysis and protocol design. We investigate the correctness and security of existing CKKS-based protocols relying on the noise smudging technique, in which each party independently samples exponentially large noise. We show that these constructions fail to achieve standard simulation-based security. To address this issue, we propose a collaborative sampling approach in which parties jointly generate additive shares of the smudging noise. We present concrete constructions for both asymmetric two-party and symmetric multiparty settings, together with formal ideal functionalities. Furthermore, we provide concrete implementations of round-efficient collaborative sampling protocols. As an alternative perspective, we show that existing protocols satisfy a weaker security notion called liberal security.
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Modern Construction of Moduli Chain in HEaaN2
TL;DR: Every CKKS computation is built upon a sequence of moduli that predetermines the rescaling amount after each multiplication. A new CKKS library, HEaaN2, generalizes the construction of this parameter with a carefully designed scheme and API set. In this article, we break down the traditional construction of the moduli chain to derive the new one.