Paper 2023/699
Latticebased, more general antileakage model and its application in decentralization
Abstract
In the case of standard \LWE samples $(\mathbf{A},\mathbf{b = sA + e})$, $\mathbf{A}$ is typically uniformly over $\mathbb{Z}_q^{n \times m}$, and under the \LWE assumption, the conditional distribution of $\mathbf{s}$ given $\mathbf{b}$ and $\mathbf{s}$ should be consistent. However, if an adversary chooses $\mathbf{A}$ adaptively, the gap between the two may be larger. In this work, we are mainly interested in quantifying $\tilde{H}_\infty(\mathbf{s}\mathbf{sA + e})$, while $\mathbf{A}$ an adversary chooses. Brakerski and D\"{o}ttling answered the question in one case: they proved that when $\mathbf{s}$ is uniformly chosen from $\mathbb{Z}_q^n$, it holds that $\tilde{H}_\infty(\mathbf{s}\mathbf{sA + e}) \varpropto \rho_\sigma(\Lambda_q(\mathbf{A}))$. We prove that for any $d \leq q$, $\mathbf{s}$ is uniformly chosen from $\mathbb{Z}_d^n$ or is sampled from a discrete Gaussian, the above result still holds. In addition, as an independent result, we have also proved the regularity of the hash function mapped to the primeorder group and its Cartesian product. As an application of the above results, we improved the multikey fully homomorphic encryption\cite{TCC:BraHalPol17} and answered the question raised at the end of their work positively: we have GSWtype ciphertext rather than DualGSW, and the improved scheme has shorter keys and ciphertexts
Metadata
 Available format(s)
 Category
 Cryptographic protocols
 Publication info
 Preprint.
 Keywords
 Leftover hash lemmaLeakage resilient cryptographyMultikey FHE
 Contact author(s)

daixiaokang @ cigit ac cn
chenjingwei @ cigit ac cn
wuwenyuan @ cigit ac cn
yongfeng @ cigit ac cn  History
 20230727: last of 10 revisions
 20230516: received
 See all versions
 Short URL
 https://ia.cr/2023/699
 License

CC BY
BibTeX
@misc{cryptoeprint:2023/699, author = {Xiaokang Dai and Jingwei Chen and Wenyuan Wu and Yong Feng}, title = {Latticebased, more general antileakage model and its application in decentralization}, howpublished = {Cryptology ePrint Archive, Paper 2023/699}, year = {2023}, note = {\url{https://eprint.iacr.org/2023/699}}, url = {https://eprint.iacr.org/2023/699} }