Quantum Proofs of Deletion for Learning with Errors
Quantum Proofs of Deletion for Learning with Errors
复制标题
用于错误学习的删除量子证明
DOI：
10.48550/arxiv.2203.01610
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Alexander Poremba
中科院分区：
文献类型：
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作者：
Alexander Poremba
量子信息具有这样的性质，即测量是一个固有的破坏性过程。这一特征在互补性原则中最为明显，该原则规定，互不相容的可观测对象不能同时被测量。布罗德本特和伊斯拉姆最近的工作(TCC 2020)建立在量子力学的这一方面，以实现一种称为认证删除的密码概念。虽然这一非凡的概念使经典验证者能够确信(私钥)量子密文已被不可信方删除，但它没有提供额外的功能层。在这项工作中，我们使用完全同态加密(FHE)来增强删除证明范例。我们构造了第一个具有认证删除的全同态加密方案--一个交互协议，它使不可信的量子服务器能够对加密数据进行计算，并且如果请求，可以同时向客户端证明数据删除。我们的方案具有理想的特性，即删除证书的验证是公开的；这意味着任何人都可以验证已经发生了删除。我们的主要技术组成部分是一个交互协议，通过该协议，量子证明者可以说服经典验证者，以量子态的形式从有错误学习(LWE)分布中删除了样本。作为协议的一个应用，我们构造了一个具有证明删除的双Regev公钥加密方案，并将其扩展到同一类型的(分级)FHE方案。我们引入了高斯折叠哈希函数的概念--Unruh(Eurocrypt 2016)定义的折叠哈希函数的一个特例--并且在假设Ajtai哈希函数在存在泄漏的情况下满足一定的强高斯折叠性质的情况下证明了我们的方案的安全性。
Quantum information has the property that measurement is an inherently destructive process. This feature is most apparent in the principle of complementarity, which states that mutually incompatible observables cannot be measured at the same time. Recent work by Broadbent and Islam (TCC 2020) builds on this aspect of quantum mechanics to realize a cryptographic notion called certified deletion. While this remarkable notion enables a classical verifier to be convinced that a (private-key) quantum ciphertext has been deleted by an untrusted party, it offers no additional layer of functionality. In this work, we augment the proof-of-deletion paradigm with fully homomorphic encryption (FHE). We construct the first fully homomorphic encryption scheme with certified deletion -- an interactive protocol which enables an untrusted quantum server to compute on encrypted data and, if requested, to simultaneously prove data deletion to a client. Our scheme has the desirable property that verification of a deletion certificate is public; meaning anyone can verify that deletion has taken place. Our main technical ingredient is an interactive protocol by which a quantum prover can convince a classical verifier that a sample from the Learning with Errors (LWE) distribution in the form of a quantum state was deleted. As an application of our protocol, we construct a Dual-Regev public-key encryption scheme with certified deletion, which we then extend towards a (leveled) FHE scheme of the same type. We introduce the notion of Gaussian-collapsing hash functions -- a special case of collapsing hash functions defined by Unruh (Eurocrypt 2016) -- and we prove the security of our schemes under the assumption that the Ajtai hash function satisfies a certain strong Gaussian-collapsing property in the presence of leakage.
DOI：
10.1007/978-3-030-77886-6_17
发表时间：
2020-05
期刊：
--
影响因子：
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作者：
P. Ananth;R. L. Placa
通讯作者：
P. Ananth;R. L. Placa
关于量子选择密文攻击和错误学习
DOI：
--
发表时间：
2019
期刊：
and Cryptography 2019
影响因子：
--
作者：
Alagic, Gorjan;Jeffery, Stacey;Ozols, Maris;Poremba, Alexander
通讯作者：
Poremba, Alexander
具有认证删除功能的密码学
DOI：
--
发表时间：
2023
期刊：
CRYPTO 2023
影响因子：
--
作者：
Bartusek, James;Khurana, Dakshita
通讯作者：
Khurana, Dakshita