"The Invisible Cloak in the Big Data Era: Unveiling the Magic of Homomorphic Encryption Recommender System"

Introduction: The Homomorphic Encryption technology is like an invisible cloak in the digital world, quietly appearing. It promises a seemingly impossible future: performing complex data analysis and calculations without revealing the original data. This article will take you deep into the application of Homomorphic Encryption in recommendation systems, revealing how this technology safeguards our privacy in the era of big data.

1. The Privacy Dilemma of Recommender Systems a) Review and Impact of User Data Breach Incidents In history, many major personal information leakage incidents have been discovered. According to Bleeping Computer, in early 2023, Pepsi Bottling Ventures LLC suffered a cyber attack. The attackers installed malware to steal a large amount of sensitive data from the company's IT system. What is even more concerning is that this attack was not discovered until nearly a month after it occurred, fully exposing the vulnerability of the enterprise in terms of cybersecurity.

Not only enterprises, but even government agencies are not immune. In February 2023, a server hosting 3TB of internal military emails was exposed online for two weeks at the U.S. Department of Defense. The server was hosted on Microsoft's Azure Government Cloud, which was supposed to be a secure environment physically isolated from other commercial customers. The leaked data included sensitive information related to the U.S. Special Operations Command, which is responsible for carrying out special military operations in the United States.

Image source: Blockworks

In the digital age, even large enterprises and government agencies find it difficult to fully guarantee data security. As data plays an increasingly important role in modern society, the potential risks posed by such security vulnerabilities are becoming more serious.

b) The contradiction between privacy protection and personalized recommendations Personalized recommendation systems have become a core component of user experience, with a difficult-to-reconcile contradiction between this convenience and user privacy. On the one hand, users desire precise and personalized recommendations that align with their individual preferences, which requires the system to have a deep understanding of the user. On the other hand, in order to obtain this personalized service, users have to provide a large amount of personal information to the system, undoubtedly increasing the risk of privacy breaches. Ultimately, a new balance may need to be struck between users, businesses, and regulatory agencies.

2. Unveiling Homomorphic Encryption: The Invisible Clothes of Data In this context, Homomorphic Encryption technology provides us with a new perspective. The Decentralization feature of blockchain, combined with advanced cryptographic technologies such as Homomorphic Encryption, has the potential to completely change the way personal data is collected, stored, and used.

For example, a recommendation system based on the Block chain may operate as follows: user's personal data is stored on-chain in encryption Blocks, and only the user owns the decryption Secret Key. The recommendation Algorithm runs on the encrypted data to generate encrypted recommendation results. These results can only be decrypted and used with the user's authorization. This method ensures both the accuracy of the recommendations and maximizes user privacy protection. Furthermore, Smart Contracts can be used to automatically enforce rules and restrictions on data usage, ensuring that enterprises can only use data within the scope explicitly agreed upon by users. This not only increases transparency but also gives users more control over their own data.

Image source: zama.ai

a) What is Homomorphic Encryption? Layman's Explanation Homomorphic Encryption (HE) is a technique that allows data to be processed without decryption. It can be used to create private Smart Contracts on-chain in a public, permissionless Block, where only specific users can see transaction data and contract states. While Fully Homomorphic Encryption (FHE) has been impractical in the past due to slow speeds, recent breakthroughs are expected to achieve this goal in the coming years.

Let's take an example to illustrate. Suppose there are two good frens, Peter and Julie, who both like to collect rare stamps. One day, Peter wants to know which stamps are common in his and Julie's stamp collections, but he doesn't want to completely expose his own collection.

Traditional way: Peter showed his stamp catalog to Julie. Julie looked through Peter's catalog while comparing it to her own collection. Whenever they found stamps that they both had, they would list them on a new inventory. In the end, Julie gave this list of matching stamps to Peter. This way, Peter knew which stamps they both owned, but at the same time, Julie also saw Peter's entire collection catalog.

Privacy Protection Method: Now imagine a magical machine. Peter and Julie each enter their own stamp catalog into the machine. The machine magically compares the two catalogs and only shows Peter the common stamps. During this process, Julie cannot see Peter's catalog, and Peter cannot see Julie's catalog. Julie doesn't even know what the final result is unless Peter tells her.

This is the application of Homomorphic Encryption in the blockchain world. It enables us to conduct private transactions and operations on a public platform, protecting privacy while maintaining the transparency and security of the blockchain. Although this technology was previously difficult to apply in practice due to speed issues, with recent technological breakthroughs, it is expected to become a reality in the next few years, bringing more privacy protection and innovation possibilities to our digital lives.

b) The Magic of Homomorphic Encryption: Performing calculations in the encryption state The core principle of Homomorphic Encryption is that the operation on encrypted data is equivalent to the operation on the original data followed by encryption of the result. This means that we can perform meaningful calculations and analysis on encrypted data without knowing the content of the original data.

The main types of Homomorphic Encryption include:  部分Homomorphic Encryption(Partially Homomorphic Encryption, PHE): Only one operation is supported, such as addition or multiplication. For example, RSA encryption supports multiplicative homomorphism, and Paillier encryption supports additive homomorphism.  Some Homomorphic Encryption(Somewhat Homomorphic Encryption, SHE): Support addition and multiplication operations with limited number of times. For example: the early Gentry scheme.  Fully Homomorphic Encryption (FHE): Supports addition and multiplication operations any number of times, theoretically can perform any calculation. For example: the improved Gentry scheme, IBM's HElib library.  Leveled Homomorphic Encryption: — Between SHE and FHE, supports circuit computation with pre-defined Depth.

Technical implementation:  Lattice-based Cryptography: Many modern FHE schemes are based on lattice cryptography, such as Gentry's original scheme and subsequent improvements. These schemes are typically based on the Ring-LWE (Learning With Errors on the Ring) problem.  Integer base scheme: Some schemes work directly on integers, such as the scheme proposed by van Dijk et al.  Approximate Math: The CKKS scheme allows homomorphic computation on approximate numbers, suitable for machine learning and other applications.  Learning-based: Some solutions combine machine learning techniques, such as neural network-based Homomorphic Encryption.

Of course, there are practical use cases as well, such as secure multi-party computation where multiple parties can jointly compute a function without revealing their respective inputs. Another example is privacy-preserving machine learning, which trains and runs machine learning models on encrypted data to protect data privacy.

Although Homomorphic Encryption technology is very powerful, it also faces some challenges, primarily in terms of computational efficiency. The computational overhead of fully Homomorphic Encryption is still significant, which limits its use in certain real-time applications. However, with ongoing research and advancements in hardware, these limitations are gradually being overcome.

Image source: tvdn

c)与传统encryption方法的对比 Homomorphic Encryption(HE) and Zero-Knowledge Proof(ZKP) are both privacy protection technologies that are highly followed in the field of cryptography, but they have significant differences in application and characteristics, with several key distinctions:

1. Homomorphic Encryption allows direct computation on encrypted data, while Zero-Knowledge Proof can prove the correctness of a statement without revealing specific information. In terms of data availability, Homomorphic Encryption usually stores the encrypted data on-chain in a Block, which enables constant access and processing of the data. In contrast, Zero-Knowledge Proof may keep the original data off-chain and only provide verification results on-chain.
2. One notable advantage of Homomorphic Encryption is its excellent composability: once the data is encrypted and placed on-chain, it can be easily integrated into other applications for further computation and processing due to its homomorphic properties. This feature is particularly important in building complex privacy-preserving applications. On the other hand, the flexibility of Zero-Knowledge Proof in this aspect is relatively low, making it difficult to directly use the result of one proof in another proof process. However, these two technologies are not mutually exclusive. On the contrary, they are often combined to leverage their respective advantages.

With the continuous development of blockchain and privacy computing technology, we can foresee that Homomorphic Encryption and Zero-Knowledge Proof will play an increasingly important role in future privacy protection applications. The combination of these technologies will provide powerful technical support for building more secure and private Decentralization systems.

Conclusion In this data-driven era, we are standing at a critical crossroads. The Homomorphic Encryption technology is like an invisible cloak in the digital world, providing us with strong privacy protection while enjoying the convenience brought by big data. It allows us to perform calculations in the fog of encryption, protecting personal privacy without compromising the accuracy and value of data analysis.

However, the balance between accuracy and privacy is a delicate art. The magic of Homomorphic Encryption in recommendation systems lies not only in its technological innovation, but also in its attempt to find a subtle balance between personalized services and privacy protection. But we must also recognize that such a balance is not easy to achieve. There is no free lunch, and technological advances always come with challenges and trade-offs. While Homomorphic Encryption is powerful, its computational cost is still high, which may affect the system's response speed and efficiency. In addition, how to ensure the security of encrypted data and how to prevent potential attacks are issues that we need to continue to follow and address.

Looking ahead, we look forward to seeing more innovative technologies emerge, which will continue to drive the balance between privacy protection and data utilization. Perhaps one day, we will be able to build a true digital utopia, where everyone can freely share and use data without worrying about their privacy being violated.