NTRU型多密钥全同态加密方案的优化

现有的NTRU型多密钥全同态加密方案多是基于2的幂次分圆多项式环构造的,全同态计算过程使用了复杂的密钥交换操作,这类方案容易遭受子域攻击,且同态运算效率较低,对此本文提出了一个安全性更好、效率更高的NTRU型多密钥全同态加密方案。首先,将现有方案底层的分圆多项式环扩展应用到素数次分圆多项式环上,给出了基于素数次分圆多项式环的NTRU型多密钥全同态加密的基础方案模型（文中B-MKFHE方案）,该方案模型可以抵御更多的子域攻击。其次,在B-MKFHE方案模型的基础上,通过扩展密文多项式维度,优化了NTRU多密钥同态运算结构,使得同态运算过程不再需要复杂耗时的密钥交换操作。最后,根据优化的多密钥同态运算结构,结合模交换技术,构造了无需密钥交换的层级型NTRU多密钥全同态加密方案（文中M-MKFHE方案）。通过与现有方案对比分析,本文提出的M-MKFHE方案改进了底层的分圆多项式环,提高了安全性;优化的同态运算结构具有较小的存储开销和计算开销,运算效率较高,并且方案在同态运算过程中产生的噪声值较小,支持更深层次的同态运算。     

基于NTRU的多密钥同态加密方案解密结构

为了进一步提升NTRU型多密钥全同态加密（MKFHE）方案的安全性和效率,基于素数幂次分圆多项式环,研究了NTRU型多密钥同态加密的原始解密结构特点,并提出了两种多密钥同态解密结构改进优化方法。首先通过降低多项式系数,设计了“Regev-Style”多密钥解密结构;其次通过扩展密文维度,设计了“Ciphertext-Expansion”多密钥解密结构。通过与NTRU型多密钥同态加密方案的原始解密结构进行对比分析,结果表明“Regev-Style”多密钥解密结构降低了产生噪声的量级,用于NTRU型多密钥全同态加密方案设计时能减少密钥交换次数和模交换次数;“Ciphertext-Expansion”多密钥解密结构消除了密钥交换过程,降低了产生噪声的量级,且能更有效地处理重复用户的密文乘积。改进优化的多密钥解密结构的安全性均基于素数幂次分圆多项式环上的误差学习（LWE）问题和判定小多项式比（DSPR）假设,这些结构能较好地抵御子域攻击。通过选取合适的参数,它们可用于设计更加安全高效的NTRU型多密钥全同态加密方案。     

Round efficient privacy-preserving federated learning based on MKFHE

Federated learning (FL) was created with the intention of enabling collaborative training of models without the need for direct data exchange. However, data leakage remains an issue in FL. Multi-Key Fully Homomorphic Encryption (MKFHE) is a promising technique that allows computations on ciphertexts encrypted by different parties. MKFHE’s aptitude to handle multi-party data makes it an ideal tool for implementing privacy-preserving federated learning.We present a multi-hop MKFHE with compact ciphertext. MKFHE allows computations on data encrypted by different parties. In MKFHE, the compact ciphertext means that the size of the ciphertext is independent of the number of parties. The multi-hop property means that parties can dynamically join the homomorphic computation at any time. Prior MKFHE schemes were limited by their inability to combine these desirable properties. To address this limitation, we propose a multi-hop MKFHE scheme with compact ciphertext based on the random sample common reference string(CRS). We construct our scheme based on the residue number system (RNS) variant CKKS17 scheme, which enables efficient homomorphic computation over complex numbers due to the RNS representations of numbers.We construct a round efficient privacy-preserving federated learning based on our multi-hop MKFHE. In FL, there is always the possibility that some clients may drop out during the computation. Previous HE-based FL methods did not address this issue. However, our approach takes advantage of multi-hop MKFHE that users can join dynamically and constructs an efficient federated learning scheme that reduces interactions between parties. Compared to other HE-based methods, our approach reduces the number of interactions during a round from 3 to 2. Furthermore, in situations where some users fail, we are able to reduce the number of interactions from 3 to just 1.