What is Homomorphic Encryption?

Homomorphic Encryption

Definition and basic concept

Homomorphic encryption is a revolutionary advancement in cryptography that allows computations to be performed directly on encrypted data . Unlike traditional methods where data must be decrypted to be used, homomorphic encryption ensures that information remains protected at all stages of processing.

This process offers complete confidentiality: only those with the decryption keys can access the results. This makes it particularly valuable for sensitive sectors, such as healthcare , financial services , and cloud computing , where data protection is paramount.

In short, this technology combines advanced security with convenience , eliminating the need to compromise between privacy and functionality.

History and evolution

The concept of homomorphic encryption first appeared in 1978 thanks to visionary researchers such as Ronald Rivest, Leonard Adleman , and Michael Dertouzos . However, it wasn’t until 2009 that Craig Gentry proposed the first working implementation with a scheme based on cryptographic lattices .

Since then, significant progress has been made:

• Cryptographic noise reduction , which improved the accuracy of calculations.
• Optimization of algorithms , making processing faster.
• Development of open source libraries such as HElib (IBM) and SEAL (Microsoft), promoting wider adoption.

Comparison with other cryptographic approaches

Homomorphic encryption is distinguished from other cryptographic methods, such as symmetric algorithms or Zero-Knowledge (ZK) proofs , by its unique ability to preserve the confidentiality of data during processing .

Unlike symmetric encryption , FHE ( Fully Homomorphic Encryption ) guarantees protection even during processing. Although it shares with ZK a confidentiality objective, homomorphic encryption does not require a centralized prover .

Principles and algorithms of homomorphic encryption

General operation

Homomorphic encryption is revolutionizing the way sensitive data is used. Unlike traditional methods that require decrypting data to perform processing, FHE ( Fully Homomorphic Encryption ) allows direct calculations on encrypted data , without ever revealing their contents.

Basic principle : The results of calculations on encrypted data are identical to those obtained on clear data, but remain protected by permanent encryption .

Example : A company may encrypt its data internally before transmitting it to an external service provider, such as a cloud provider. The latter performs the necessary calculations without ever accessing the unencrypted data. The results, still encrypted, are then returned to the company, where they are decrypted locally.

Conditions for effective encryption

To be fully functional, a homomorphic encryption system must meet several conditions:

• Correction : The results of encrypted operations, once decrypted, must be faithful to those obtained with unencrypted data.
• Error handling : Calculations on encrypted data often generate cryptographic noise . This noise must be limited to ensure the accuracy and reliability of the results.

Types of homomorphic encryption

1. Partially homomorphic encryption (PHE)
   Allows a single operation (addition or multiplication) to be performed on encrypted data. This type of encryption is lightweight and fast, ideal for simple use cases .
   
   
• Example : A bank can add up its customers’ encrypted deposits to calculate the total without ever decrypting each deposit .
2. Fully homomorphic encryption (FHE)
   offers complete flexibility , supporting an unlimited sequence of arithmetic operations . However, this method is more complex and resource-intensive.
   
   
• Example : Secure machine learning , where models can be trained on encrypted data without compromising their confidentiality.

Mathematical properties

Homomorphic encryption is based on solid foundations in linear algebra and number theory . Key features include:

• Homomorphic addition : Ability to add two encrypted data without decryption.
• Homomorphic multiplication : Ability to multiply encrypted data.
• Combining operations : Performing complex calculations by combining several types of operations.

To ensure robust security , even in the face of threats from quantum computers , the FHE uses tools such as cryptographic lattices (mathematical networks).

Examples of popular algorithms

• Gentry’s FHE : The first fully homomorphic algorithm, proposed in 2009.
• BGV : A scheme optimized for complex calculations, reducing processing times.
• CKKS : Designed for approximate calculations, often used in applications like machine learning .

Practical applications of homomorphic encryption

Privacy in blockchain

Homomorphic encryption brings a new dimension of privacy to the traditionally transparent and public blockchain . With encrypted blockchains, even smart contracts can remain confidential, accessible only to authorized users. Validators , on the other hand, do not have access to sensitive data, ensuring a high level of protection.

Securing cloud computing

In cloud computing , homomorphic encryption transforms computing spaces into truly secure environments . It allows complex computations to be performed without the data ever being decrypted.

Example : A company can analyze a fully encrypted customer database through a cloud service. The provider then has no access to sensitive information, thus complying with regulations such as GDPR in Europe.

Protection of medical data

Homomorphic encryption meets the critical needs of the medical sector by ensuring the confidentiality of sensitive data while facilitating its exploitation. It complies with strict regulations such as GDPR ( European Union) and HIPAA (United States).

Example : Researchers can analyze encrypted medical records without compromising patient privacy. This technology promotes secure collaboration between medical institutions while reducing the risk of sensitive data breaches.

Secure financial transactions

Banks and financial institutions are adopting homomorphic encryption to protect sensitive data such as revenue or transaction history. This technology allows for analysis without decryption, ensuring complete confidentiality .

Example : A bank can assess a customer’s creditworthiness or calculate financial risks while maintaining the confidentiality of the information. This also helps meet regulatory data standards.

Secure Search and Privacy

Homomorphic encryption facilitates secure searches by protecting both queries and database contents. It is particularly important in sensitive areas such as national defense or advanced technologies .

Example : Machine learning models can be trained directly on encrypted data, ensuring complete confidentiality, even in shared or collaborative environments.

Towards a quantified daily life

In the future, homomorphic encryption could become as common a technology as HTTPS connections on the Internet.

Example : A concept similar to ” httpz ” could emerge, ensuring end-to-end encryption not only for data transmission, but also for data processing and storage. This would provide comprehensive protection against cyber threats in diverse sectors, ranging from healthcare to finance, blockchain, and online gaming.

Recent advances in homomorphic encryption

Technological evolution and advances

Since the 1970s, homomorphic encryption has come a long way, evolving from a purely theoretical concept to a practical technology . This evolution was made possible by the development of open source tools such as HElib (IBM) and SEAL (Microsoft). These tools have enabled its adoption in strategic sectors such as cloud computing , healthcare and finance .

Significant progress:

• Cryptographic noise reduction : Modern schemes such as BGV and CKKS have limited the accumulation of noise generated by successive calculations. This has significantly improved the speed and reliability of operations.
• Algorithmic optimizations : Processing times have been reduced while increasing the accuracy of calculations , making the technology more efficient.
• Dedicated hardware support : Cryptography-specific processors accelerate computations, making homomorphic encryption more accessible to resource-intensive applications .

However, challenges remain , particularly for environments requiring low latency, such as the Internet of Things (IoT) .

Recent technological innovations

• Homomorphic machine learning : This innovation enables predictive models to be trained on encrypted data, guaranteeing total confidentiality. It revolutionizes the secure analysis of sensitive data , particularly in health and finance.
• Secure Multi-Party Computation : By combining homomorphic encryption with other cryptographic techniques, this approach facilitates collaboration between companies while protecting the information exchanged.
• Post-quantum resilience : Current research is moving towards schemes that are resistant to attacks on quantum computers , thus ensuring the sustainability of this technology in the future.

Tools and Libraries for Adoption

These advancements enable wider adoption, particularly in demanding environments such as cloud, machine learning and interconnected systems.

Advantages of homomorphic encryption

Homomorphic encryption (FHE) is a leading innovation in the protection of sensitive data , providing unprecedented guarantees of security and confidentiality . This technology is essential for companies and institutions handling large amounts of critical information , particularly in the fields of healthcare , finance and cloud computing .

Enhanced confidentiality

FHE ensures that data remains encrypted throughout processing , eliminating the risk of accidental or malicious exposure. Sensitive data is always protected, even from systems or third parties performing the calculations. Service providers and other stakeholders never have access to the information in plain text, which enhances confidentiality.

Secure outsourcing

Homomorphic encryption allows complex processing to be outsourced to cloud service providers or other third parties without compromising data confidentiality. Service providers can perform the necessary operations without ever seeing the data content. This mechanism is particularly useful for business collaborations, where data protection is crucial.

Regulatory compliance

The FHE helps businesses comply with strict data protection regulations, such as the GDPR in Europe and the CCPA in the United States. Businesses reduce the risk of legal sanctions by ensuring the security of personal information. Users and partners are reassured by rigorous and transparent data management.

Versatility and flexibility

Homomorphic encryption offers unparalleled flexibility compared to other encryption methods, allowing complex computations to be performed directly on encrypted data .

Balanced traceability

FHE offers an ideal combination of anonymity and traceability , making it suitable for sensitive scenarios such as blind auctions (participants remain anonymous while ensuring the integrity of the process.) or OTC market transactions (sensitive data is protected while meeting compliance requirements .)

Disadvantages of homomorphic encryption

Despite its many advantages, full homomorphic encryption (FHE) has significant limitations that hinder its widespread adoption. In areas such as IoT or real -time computing platforms , speed and power limitations reduce the effectiveness of this technology.

High computational complexity

Computations performed on encrypted data require significantly more computing resources than those performed on plaintext data. The direct consequence is increased slowness, which is particularly problematic for applications requiring low latency or real-time processing , such as cloud services or IoT devices.

Size of encrypted files

Data encrypted with homomorphic algorithms is much larger than its plaintext counterparts. This increase in size complicates its use in environments where storage space is limited or expensive. As a result , infrastructures must be sized to accommodate these volumes, increasing operating costs.

Complex implementation

Implementing homomorphic encryption requires advanced technical expertise , making its deployment complex for many organizations. Therefore, developers must redesign their algorithms to work without access to cleartext data , which represents a major programming challenge. The tools needed for large-scale deployment require significant investment , thus limiting access to FHE to large companies and institutions with sufficient resources.

Table of advantages and disadvantages of homomorphic encryption

Conclusion: A promising technology facing many challenges

Homomorphic encryption (FHE) is emerging as a critical solution to address the growing cyber threats and the need to protect sensitive data. By enabling direct computation on encrypted data , it ensures complete confidentiality while meeting compliance requirements, such as GDPR and CCPA .

However, this technology is hampered by major challenges: computational complexity, high costs, and implementation difficulties. These limitations restrict its adoption to large enterprises and raise questions about its accessibility.

To democratize FHE, initiatives such as the development of open source tools and the establishment of audit standards are necessary. At the same time, it opens up promising prospects, particularly in confidential auctions , secure transactions and blockchain applications .

By combining security , flexibility and confidentiality , homomorphic encryption positions itself as a pillar of data protection in an increasingly digital world.

Recommendations

To effectively integrate homomorphic encryption , it is essential to adopt a structured approach:

• Needs Assessment : Identify priority use cases, such as secure processing of medical or financial data.
• Tool selection : Select libraries that match the requirements, such as Microsoft SEAL or HElib .
• Resource planning : Consider costs related to implementation, infrastructure, and team training.
• Phased Adoption : Deploy FHE in stages to anticipate and resolve technical or operational challenges.