What Is Homomorphic Encryption?

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Homomorphic Encryption

Homomorphism is an algebraic term that gives rise to the word homomorphic.

“A homomorphism is a structure-preserving map between two identical algebraic structures, such as two groups, two rings, or two vector spaces.” (Wiki source)

Homomorphic encryption is a kind of encryption that enables users to carry out binary operations on encrypted data without ever the necessity of decoding the data.

This type of encryption enables data encryption and outsourcing to cloud services/environments for processing without allowing access to the raw data.

Introduction to Homomorphic Encryption

There are three different states that data might be in: at rest, in transit, and in use. The first two of them are the topics that most encryption addresses. Data at rest or in transit is not actively altering, which causes this. When it is decrypted, it retains the same value as when it was encrypted.

In contrast, the data that is currently being used lack this characteristic. 

Nearly all computations performed on ciphertexts would alter the value of the matching plaintext. The “right way” to modify the plaintext must be ensured.

The purpose of encryption algorithms is to break any connections between the plaintext and the associated ciphertext. An effective encryption technique generates ciphertext that is identical to random data. Using the right key to decrypt is the only method to determine which plaintext belongs to a given ciphertext.

Plaintexts and ciphertexts must be related to executing mathematical operations on encrypted data. The outcome of performing the same operation on the two plaintexts and then encrypting them must be the same when adding or multiplying two ciphertexts.

At the same time, this connection must be carried out to conceal it from others. The encryption is compromised if observing mathematical operations on ciphertexts discloses information about the related plaintexts.

Achieving these interrelated aims of solid encryption and accurate mathematical computations on ciphertexts is challenging. The algorithms that have succeeded in doing this are homomorphic encryption methods.

What are the Benefits of Homomorphic Encryption?

We must first decrypt the data to execute computations, such as mathematical operations, in the modern world. After our calculations, we must re-encrypt the data before sending it back.

What happens, though, when the data is susceptible, and we don’t want other services to have access to it? Homomorphic encryption serves a purpose in this situation.

A more realistic example is a system or service that analyses medical data to determine if a patient has a problem.

We would likely provide private details about the patient’s medical history in our shared data. Therefore, we want to be sure that nobody else can access this.

With the assistance of homomorphic encryption, the system/service may carry out the necessary calculations on the encrypted data and deliver the diagnostic’ outcome without being aware of the information being processed.

Sharing private information on several networks breaches our freedom of privacy. On the other hand, the privacy of the data is ensured by the ability to alter and conduct operations on it while it is encrypted.


Homomorphic Encryption protects sensitive data against unauthorized access by keeping the data encrypted. It guarantees the data’s absolute secrecy, privacy, and integrity.


Homomorphic encryption allows for data processing without changing the encryption format. It enables the data to undergo several calculations and transformations without ever needing to be decrypted.

Easy Access:

Homomorphic Encryption provides secure access to encrypted data by permitted users without affecting the encryption or putting the security of the data at risk.

Ease Data Management: 

Homomorphic encryption makes it possible to process data without decrypting it, eliminating the need to maintain significant volumes of decrypted data.


Homomorphic Encryption makes it possible for cloud computing to scale up quickly to handle big data. It permits data processing while upholding total privacy and security, preventing any violations of the data confidentiality regulations.

What are Various Types of Homomorphic Encryption?

Homomorphic encryption aims to provide an encryption method that allows for several data additions or multiplications. The procedure output should be the ciphertext generated if the identical procedures were carried out on the matching plaintexts and the result was encrypted.

It’s challenging to create such an encryption technique. Consequently, a few distinct “types” of homomorphic encryption categorize how close a method is to that desired outcome.

The following are the most common kinds of homomorphic encryption:

  • Partially Homomorphic Encryption (PHE)
  • Somewhat Homomorphic Encryption (SHE)
  • Fully Homomorphic Encryption (FHE)

Partially Homomorphic Encryption (PHE)

Algorithms for partially homomorphic encryption enable indefinite repetitions of a particular operation. For instance, an algorithm could be additively homomorphic, which means that combining two ciphertexts yields the same result as encrypting the total of the two plaintexts.

Algorithms for partially homomorphic encryption are simple to create. Specific widely used encryption algorithms are partially homomorphic.

The RSA algorithm is multiplicatively homomorphic, for instance. It is due to the exponentiation-based encryption used by RSA: C = (m^x) (mod n), where x is a secret key and m is the message.

The regulations of exponents say that (a^n)(b^n)=(ab)^n. The product of the plaintexts is raised to the power of the secret key when multiplying two ciphertexts encrypted with the same key. RSA is, therefore, multiplicatively homomorphic.

Somewhat Homomorphic Encryption (SHE)

This specific homomorphic encryption is the next level from partially homomorphic encryption. Instead of allowing unlimited operations, a relatively homomorphic encryption method enables a finite number of any operation.

For instance, any combination of up to five additions or multiplications may be supported by a moderately homomorphic encryption method. 

Nevertheless, a sixth operation of any kind would provide an invalid outcome.

An essential step towards completely homomorphic encryption is using somewhat homomorphic encryption techniques. Making an algorithm that enables the addition and multiplication of ciphertexts is more challenging than making one that supports limitless addition or multiplication of ciphertexts (even for a limited number of operations).

Fully Homomorphic Encryption (FHE)

Homomorphic encryption’s desired goal is fully homomorphic encryption. A fully homomorphic encryption technique permits endless ciphertext additions or multiplications without compromising the integrity of the final product.

Today, fully homomorphic encryption techniques are available. Craig Gentry first developed the fully homomorphic encryption technique in 2009.

Since then, several algorithms that enhance the original method have been developed.                                                              

What are the Applications of Homomorphic Encryption?

Supply Chain Security

The potential risks of unsecured supply chains have been highlighted by recent incidents, demonstrating how hackers would go for the weakest link in the chain to accomplish their goals. This scenario implies that giving a partner access to sensitive data might expose a company to a costly and harmful data breach.

An organization can help protect itself against these supply chain threats using homomorphic encryption. 

A data breach does not harm the organization if all data given to reputable third parties for processing is encrypted. It reduces the risk associated with outsourcing necessary data processing for an organization.

Cloud Computing

Users can outsource their data to cloud providers using homomorphic encryption without worrying about their data’s privacy being compromised. Because homomorphic encryption allows for the processing of data while it is still encrypted, a cloud provider can run computations on encrypted data without having access to it in plaintext.

Financial Services

When sensitive data like credit card numbers, transaction data, and personal details must be computed securely, such as in the financial services industry, homomorphic encryption is beneficial.

The possibility of data breaches is decreased with homomorphic encryption, which enables financial organizations to perform calculations on encrypted data.


Since the healthcare sector values patient privacy, homomorphic encryption can be employed. Thanks to homomorphic encryption, patient data is protected during processing or transmission to outside service providers.

Intelligent Transportation Systems

Intelligent transportation systems, such as traffic monitoring, driver behavior analysis, and surveillance systems, can use homomorphic encryption.

By enabling secure computation on the encrypted data, homomorphic encryption enables consumers to use transportation services while maintaining their privacy.

Detecting Fraud

 When sensitive data, such as credit card information, social security numbers, and account numbers, must be secured, fraud detection systems can benefit from homomorphic encryption. By enabling secure computation on encrypted

Wrap up!

Homomorphic encryption can address several significant business challenges. Since it exists, everyone ought to be utilizing it.

When it comes to the security and privacy of data, homomorphic encryption (HE) seems like a fantasy. But despite this, its poor performance and high price limit it from being used in commercial or industrial applications.

But lately, there have been a lot of performance improvements. It will be adopted globally over the coming years at the current rate.


Example of Fully Homomorphic Encryption

The hospital uses a fully homomorphic encryption technique to protect its private information while enabling computation.

How It Operates: The hospital delivers patient records to the doctor’s cloud computing environment after encrypting them homomorphically.

What are Some Uses for Homomorphic Encryption?

Homomorphic encryption is an encryption method that may be used to process data without decryption. Data privacy and security can be increased by using a homomorphic encryption system (PDF, 3 MB) to ensure that only parts of different data sets are shared with those authorized to access them.

What is an Example of Homomorphic Encryption?

When a data owner wants to transmit data to the cloud for processing but does not trust a service provider with their data, homomorphic encryption is most frequently used in this situation. The data owner encrypts their data and delivers it to the server using homomorphic encryption.

What are the Types of Homomorphic Encryption?

The following are the most common kinds of homomorphic encryption:

  • Partially Homomorphic Encryption (PHE)
  • Somewhat Homomorphic Encryption (SHE)
  • Fully Homomorphic Encryption (FHE)

Does Google use homomorphic encryption?

Google’s Fully Homomorphic Encryption Compiler — A Primer

Janki Mehta

Janki Mehta

Janki Mehta is a passionate Cyber-Security Enthusiast who keenly monitors the latest developments in the Web/Cyber Security industry. She puts her knowledge into practice and helps web users by arming them with the necessary security measures to stay safe in the digital world.