Without the requirement of trusted third parties (TTPs), Blockchain builds an environment where mutual trust among valid members is established. Nevertheless, the associated transparency property caused a hazard to real-world applications because every on-chain information is exposed to the public. That implies those applications involving sensitive data or personal information, which require security and privacy protection, are not suitable to be implemented in Blockchain, directly. Fully homomorphic encryption (FHE) schemes have been treated as one of the end-to-end solutions to data security and privacy protection problems. In this article, we examine the possibility (or cost) of embedding the ideal lattice-based FHE into the Ethereum Blockchain for building up a new trustworthy framework with security and privacy protection capability. Due to the limitations of current Blockchain, the execution of FHE is conducted off-chain; at the same time, on-chain members can call FHE-based functions to directly compute the ciphertext domain operations after their Smart Contracts have been deployed to the Blockchain. To illustrate and benchmark the examining results of our framework, an FHE and Blockchain-based Vickrey auction system is also developed, in which the online bidding prices are kept in secret. Simultaneously, the determination of the winner and the transferring of payments are conducted autonomously by Smart Contracts.

中文翻译：

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基于理想格的全同态加密方案在以太坊区块链中的适用性研究

无需可信第三方（TTP），区块链构建了一个有效成员之间建立相互信任的环境。然而，相关的透明度属性对现实世界的应用程序造成了危害，因为每个链上信息都向公众公开。这意味着那些需要安全和隐私保护的涉及敏感数据或个人信息的应用程序不适合直接在区块链中实现。全同态加密（FHE）方案已被视为解决数据安全和隐私保护问题的端到端解决方案之一。在本文中，我们研究了将理想的基于格的 FHE 嵌入到以太坊区块链中的可能性（或成本），以构建具有安全和隐私保护能力的新可信赖框架。由于当前区块链的限制，FHE的执行是在链下进行的；同时，链上成员在其智能合约部署到区块链后，可以调用基于 FHE 的函数直接计算密文域操作。为了说明和衡量我们框架的检查结果，还开发了一个基于 FHE 和区块链的 Vickrey 拍卖系统，其中在线投标价格是保密的。同时，获胜者的确定和付款的转移由智能合约自主进行。为了说明和衡量我们框架的检查结果，还开发了一个基于 FHE 和区块链的 Vickrey 拍卖系统，其中在线投标价格是保密的。同时，获胜者的确定和付款的转移由智能合约自主进行。为了说明和衡量我们框架的检查结果，还开发了一个基于 FHE 和区块链的 Vickrey 拍卖系统，其中在线投标价格是保密的。同时，获胜者的确定和付款的转移由智能合约自主进行。