同态加密

同态加密：在“不看”中计算的魔法

在数字化浪潮席卷全球的今天，我们的个人数据、财务信息乃至健康记录无时无刻不在网络中流转。云计算、人工智能等技术的飞速发展，极大便利了我们的生活，但也随之带来了前所未有的隐私挑战：如何既能享受便捷的在线服务，又能确保敏感数据不被泄露？“同态加密”（Homomorphic Encryption, HE）技术，正是解决这一难题的“魔法钥匙”，它允许我们在不对数据解密的情况下进行计算，实现数据的“可算不可见”。

什么是同态加密？—— 想象一个神奇的盒子

为了更好地理解同态加密，我们可以想象这样一个场景：你有一件非常珍贵的物品（数据），需要送到一个珠宝匠那里进行加工（计算）。但你不信任珠宝匠，不希望他看到你的物品。怎么办呢？

同态加密就像一个神奇的、带孔的手套箱。你可以把珍贵物品放进去，然后锁上箱子。箱子是完全不透明的，珠宝匠看不到里面的物品。但是，箱壁上的手套孔允许珠宝匠伸进手去，在不打开箱子、不看到物品的情况下，对里面的物品进行加工。加工完成后，你取回的仍然是上锁的箱子，只有你用自己的钥匙才能打开，看到加工后的物品。
更形象的比喻是，你可以把数据想象成面团。常规的加密方式是把面团装进一个不透明的保险箱里，需要计算时必须打开箱子、取出面团，在明文状态下（没有加密的面团）加工成面包，再把面包装回保险箱。而同态加密则像一个特殊的保险箱，你把面团放进去并锁上，一个机器手可以在保险箱内部对面团进行揉捏、发酵、烘烤等操作，最终生产出面包。整个过程中，面团（数据）始终在保险箱（加密状态）里，没有人能看到面团的原始样子，直到你用钥匙打开箱子，取出已经变成面包的最终结果。

同态加密的核心思想是，一个加密函数E如果满足以下条件，就称之为同态加密：
E(数据1) ☆ E(数据2) = E(数据1 ★ 数据2)
这里的”☆”和”★”代表两种可能不同的运算。简单来说，在加密数据上进行某种运算，其结果在解密后，与直接在原始数据上进行相同的运算所得结果是一致的。这意味着，服务提供方不需要知道数据的真实内容，就能对数据执行操作并返回加密的结果，极大地保护了用户的隐私。

同态加密的分类：从部分到完全

同态加密根据其支持的运算类型和次数，可以分为几类：

  1. 部分同态加密 (Partial Homomorphic Encryption, PHE)：这类加密方案只支持一种类型的同态运算，比如只支持加法同态（如Paillier加密算法）或只支持乘法同态（如RSA算法的乘法同态性）。它的优点是原理简单、易于实现，但功能有限。
  2. 层次同态加密 (Leveled Homomorphic Encryption, LHE / Somewhat Homomorphic Encryption, SWHE)：这类方案支持有限次数的加法和乘法运算。在进行一定次数的运算后，密文中的“噪声”会累积，导致无法继续计算或解密失败。因此，它只能处理“深度”有限的计算。
  3. 全同态加密 (Fully Homomorphic Encryption, FHE)：这是同态加密的“圣杯”。FHE 允许对加密数据进行任意多次的加法和乘法运算，从而支持任意复杂的计算，而无需解密。这意味着理论上，任何在明文上能完成的计算，都可以在加密数据上完成。2009年，美国IBM公司研究员Craig Gentry首次提出了第一个构建FHE的方案，为该领域的研究奠定了基础。

为什么同态加密如此重要？

同态加密的出现，为大数据时代的数据隐私保护带来了曙光。它解决了传统加密方式的痛点：数据在存储和传输时可以加密，但一旦需要计算，就必须解密成明文，这使得数据在计算过程中处于“裸奔”状态，极易被窃取或滥用。

有了同态加密，以下场景将成为可能：

  • 云安全：用户可以将加密数据上传到云端，云服务商在不解密的情况下进行数据分析和处理，用户隐私得到极致保护。例如，医院可以将敏感的患者记录进行加密，放到云计算平台上进行人工智能数据分析，而无需担心数据泄露。
  • 联邦学习与隐私AI：在人工智能领域，特别是联邦学习中，不同机构的数据在不共享原始数据的前提下，共同训练一个AI模型，同态加密可以在模型训练过程中保护各方的数据隐私。研究表明，同态加密在深度学习中的应用正不断发展，包括卷积神经网络和Transformer模型等。
  • 金融与保险：银行可以在加密状态下分析客户的财务数据，进行风险评估或欺诈检测，确保敏感交易数据的安全。
  • 区块链与Web3：在去中心化的Web3世界中，FHE可以为链上交易、智能合约提供更强的隐私保护，实现数据的“可算不可见”，被认为是下一代隐私保护技术。

当前的挑战与最新进展

尽管FHE被誉为“密码学的圣杯”，但其实现和大规模应用仍面临一些挑战：

  • 计算效率：同态加密的计算开销远高于明文计算，密文操作的速度可能比明文操作慢数万到数百万倍，这严重影响了实际应用中的效率。例如，Zama TFHE的256位加减法耗时约200毫秒，而明文计算仅需几十到几百纳秒。
  • 密文膨胀：加密后的数据量会显著增加，导致存储和传输成本的增加。
  • 复杂性：算法的复杂性使得部署和集成较为困难。

然而，全球的科研机构和科技公司都在不懈努力，推动同态加密技术的发展和成熟。

  • 性能优化：研究人员正通过算法创新、工程优化、硬件加速等多种手段来提升效率。例如，可以通过并行计算、数据分块处理等方式优化计算效率。
  • 标准化与算法库：FHE方案从Gentry首次提出至今已发展到第四代，效率更高，安全性更强，目前常用的同态加密库主要支持第三代和第四代算法。
  • 商业化落地：一些公司和项目正在积极探索FHE的商业化应用，例如专注于开源FHE工具构建的Zama，以及将FHE引入区块链的Fhenix等。2024年4月，CryptoLab与基因数据分析公司Macrogen签订协议，将FHE技术融入个性化基因组分析服务，以增强客户数据隐私。
  • 与AI的结合：同态加密在深度学习中的应用综述已成为研究热点，探讨如何在加密环境中有效应用深度学习模型，解决其非线性运算的近似、计算复杂度和效率等挑战。
  • 区块链领域的潜力：以太坊联合创始人Vitalik Buterin在2025年指出，零知识证明（ZK）与同态加密（FHE）等新型密码学技术正快速成熟，未来将重塑区块链，并提升去中心化程度。

结语

同态加密正在重塑我们对数据安全和隐私保护的认知。它为我们描绘了一个充满可能性的未来：在这个未来里，数据价值可以被充分挖掘，而个人隐私依然能得到严密守护。尽管当前仍有挑战，但随着技术的不断发展和突破，同态加密有望在不久的将来，真正实现其“可算不可见”的强大愿景，彻底改变我们与数据交互的方式。

Homomorphic Encryption: The Magic of Computing Without “Seeing”

In the digital wave sweeping across the globe today, our personal data, financial information, and even health records are constantly circulating through networks. The rapid development of technologies like cloud computing and artificial intelligence has greatly facilitated our lives, but it has also brought unprecedented privacy challenges: how can we enjoy convenient online services while ensuring that sensitive data is not leaked? “Homomorphic Encryption” (HE) is the “magic key” to solving this problem, allowing us to perform calculations on data without decrypting it, achieving the goal of making data “computable but invisible.”

What is Homomorphic Encryption? — Imagine a Magic Box

To better understand Homomorphic Encryption, let’s imagine a scenario: you have a very precious item (data) that needs to be processed by a jeweler (computation). However, you do not trust the jeweler and do not want them to see your item. What can you do?

Homomorphic Encryption is like a magical glovebox. You can put the precious item inside and lock the box. The box is completely opaque, so the jeweler cannot see the item inside. However, the glove holes on the side of the box allow the jeweler to put their hands in and process the item inside without opening the box or seeing the item. After the processing is complete, what you retrieve is still the locked box. Only you can open it with your own key to see the processed item.

A more vivid metaphor is to imagine data as dough. Conventional encryption is like putting dough into an opaque safe. When calculation is needed, you must open the safe, take out the dough, process it into bread in a plaintext state (unencrypted dough), and then put the bread back into the safe. Homomorphic Encryption, on the other hand, is like a special safe. You put the dough in and lock it, and a robotic arm can knead, ferment, and bake the dough inside the safe. Finally, bread is produced. Throughout the process, the dough (data) remains in the safe (encrypted state), and no one can see the original appearance of the dough until you unlock the box with the key and take out the final result, which has become bread.

The core idea of Homomorphic Encryption is that an encryption function E if it satisfies the following condition, it is called homomorphic encryption:
E(Data1) ☆ E(Data2) = E(Data1 ★ Data2)
Here “☆” and “★” represent two possibly different operations. Simply put, performing a certain operation on encrypted data results in a value which, when decrypted, matches the result of performing the same operation directly on the raw data. This means that service providers do not need to know the true content of the data to perform operations on it and return encrypted results, greatly protecting user privacy.

Classification of Homomorphic Encryption: From Partial to Fully

Homomorphic Encryption can be divided into several categories based on the types and frequency of operations it supports:

  1. Partial Homomorphic Encryption (PHE): This type of encryption scheme only supports one type of homomorphic operation, such as only additive homomorphism (like the Paillier encryption algorithm) or only multiplicative homomorphism (like the RSA algorithm). Its advantage is that the principle is simple and easy to implement, but its functions are limited.
  2. Leveled Homomorphic Encryption (LHE) / Somewhat Homomorphic Encryption (SWHE): These schemes support a limited number of addition and multiplication operations. After a certain number of operations, the “noise” in the ciphertext accumulates, leading to an inability to continue calculations or decryption failure. Therefore, it can only handle calculations of limited “depth.”
  3. Fully Homomorphic Encryption (FHE): This is the “Holy Grail” of Homomorphic Encryption. FHE allows for an arbitrary number of addition and multiplication operations on encrypted data, thereby supporting arbitrarily complex calculations without decryption. This means that theoretically, any calculation that can be done on plaintext can be done on encrypted data. In 2009, Craig Gentry, a researcher at IBM in the United States, first proposed the first scheme to construct FHE, laying the foundation for research in this field.

Why is Homomorphic Encryption So Important?

The emergence of Homomorphic Encryption has brought dawn to data privacy protection in the era of big data. It solves the pain point of traditional encryption methods: data can be encrypted during storage and transmission, but once calculation is required, it must be decrypted into plaintext. This leaves data in a “naked” state during the calculation process, making it extremely vulnerable to theft or misuse.

With Homomorphic Encryption, the following scenarios become possible:

  • Cloud Security: Users can upload encrypted data to the cloud, and cloud service providers can analyze and process data without decrypting it, providing ultimate protection for user privacy. For example, hospitals can encrypt sensitive patient records and place them on a cloud computing platform for AI data analysis without worrying about data leakage.
  • Federated Learning and Privacy AI: In the field of artificial intelligence, especially in Federated Learning, data from different institutions can be used to jointly train an AI model without sharing the raw data. Homomorphic encryption can protect the data privacy of all parties during the model training process. Research shows that applications of homomorphic encryption in deep learning are constantly developing, including Convolutional Neural Networks and Transformer models.
  • Finance and Insurance: Banks can analyze customers’ financial data in an encrypted state, perform risk assessment or fraud detection, and ensure the security of sensitive transaction data.
  • Blockchain and Web3: In the decentralized Web3 world, FHE can provide stronger privacy protection for on-chain transactions and smart contracts, realizing “computable but invisible” data, and is considered the next generation of privacy protection technology.

Current Challenges and Latest Progress

Although FHE is hailed as the “Holy Grail of Cryptography,” its implementation and large-scale application still face some challenges:

  • Computational Efficiency: The computational overhead of Homomorphic Encryption is much higher than that of plaintext computation. The speed of ciphertext operations may be tens of thousands to millions of times slower than plaintext operations, which seriously affects efficiency in practical applications. For example, Zama TFHE’s 256-bit addition and subtraction takes about 200 milliseconds, while plaintext computation takes only tens to hundreds of nanoseconds.
  • Ciphertext Expansion: The volume of data after encryption increases significantly, leading to increased storage and transmission costs.
  • Complexity: The complexity of the algorithms makes deployment and integration relatively difficult.

However, research institutions and technology companies around the world are working tirelessly to promote the development and maturity of Homomorphic Encryption technology.

  • Performance Optimization: Researchers are improving efficiency through various means such as algorithmic innovation, engineering optimization, and hardware acceleration. For example, computational efficiency can be optimized through parallel computing and data block processing.
  • Standardization and Algorithm Libraries: Since Gentry first proposed it, FHE schemes have developed to the fourth generation, with higher efficiency and stronger security. Currently commonly used Homomorphic Encryption libraries mainly support third and fourth-generation algorithms.
  • Commercial Implementation: Some companies and projects are actively exploring commercial applications of FHE, such as Zama, which focuses on building open-source FHE tools, and Fhenix, which brings FHE to the blockchain. In April 2024, CryptoLab signed an agreement with genetic data analysis company Macrogen to integrate FHE technology into personalized genome analysis services to enhance customer data privacy.
  • Combination with AI: Reviews on the application of Homomorphic Encryption in deep learning have become a research hotspot, exploring how to effectively apply deep learning models in encrypted environments and solving challenges such as the approximation of non-linear operations, computational complexity, and efficiency.
  • Potential in Blockchain: Ethereum co-founder Vitalik Buterin pointed out in 2025 that new cryptographic technologies such as Zero-Knowledge Proofs (ZK) and Homomorphic Encryption (FHE) are maturing rapidly and will reshape blockchain and improve decentralization in the future.

Conclusion

Homomorphic Encryption is reshaping our understanding of data security and privacy protection. It paints a future full of possibilities for us: a future where the value of data can be fully mined while personal privacy remains strictly guarded. Although challenges remain, with the continuous development and breakthrough of technology, Homomorphic Encryption is expected to truly realize its powerful vision of “computable but invisible” in the near future, completely changing the way we interact with data.