Homomorphic encryption is a cryptographic technique that allows computations to be performed on encrypted data without decrypting it first. It allows a recipient who holds the private key to perform operations on encrypted data and obtain an encrypted result that matches the result of performing the same operations on the plaintext. The key types include partially homomorphic (supports addition or multiplication but not both), somewhat homomorphic (supports a limited number of addition or multiplication operations), and fully homomorphic (supports unlimited addition and multiplication operations). Homomorphic encryption has applications in secure cloud computing, privacy-preserving data analytics, and machine learning. It provides confidentiality during data processing while traditional encryption requires decryption before computations.

1. HOMOMORPHIC
ENCRYPTION
1

2. WHAT IS DATA ?
Definition of Data:
• Data refers to raw, unprocessed information,
often in the form of numbers, text, images, or
other formats. It represents facts,
observations, or values that can be stored and
manipulated by a computer.
Digital Information:
• In the context of the internet, data refers to
digital information exchanged between
devices, servers, and users. This can include
text, images, videos, audio, and various other
digital formats
Structured and Unstructured Data:
• .Structured data may include organized
information like databases and tables, while
unstructured data encompasses content like
emails, tweets, and forum discussions that lack
a predefined format.

3. SCALE OF DATA
• The scale of data generation is staggering, with a
daily output of 2.5 quintillion bytes.
Every Minute
• People send about 42 million WhatsApp messages.
• 2,704 individuals make TikTok installations.
• YouTubers upload 500 hours of video to YouTube.
• Twitter accounts get 319 new Twitter followers.
• Insta users make almost 348,000 posts on Instagram.
• People share more than 147,000 photographs on
Facebook.

4. GROWTH OF
DATA
Recent surveys around the globe suggests that the yearly data
usage will reach approximately 175 ZB (Zetta Bytes) by 2025
1 ZB = Approx 1 Trillion GB

5. WHY DATA NEEDS
PROTECTION ?
Ubiquity of Cyber Threats:
The internet is rife with cyber threats, exposing
data to potential breaches and unauthorized
access.
Evolving Cyber Threat Landscape:
Cyber-attacks continually advance in
sophistication, necessitating robust protection to
counter emerging threats.
Data's Intrinsic Value:
As a valuable asset, data is a prime target for
cybercriminals, demanding stringent safeguards
against compromise.
Risks of Data Breaches:
Data breaches pose significant risks, leading to
financial losses, reputational damage, and legal
consequences.

6. CRYPTOGRAPHY

7. Cryptography is the science of secure communication and
data protection. It involves encoding information in a way that
only authorized parties can access it, ensuring confidentiality,
integrity, and authentication of the data.
Encryption:
• Encryption is a process where data (plaintext) is
transformed into an unreadable format (cipher text) using
an algorithm and a key. This transformation ensures that
even if unauthorized parties intercept the data, they
cannot interpret it without the corresponding decryption
key.
Decryption:
• Decryption is the reverse process of encryption. It involves
transforming the cipher text back into its original, readable
form (plaintext) using the decryption key. This process ensures
that only authorized parties can access and interpret the
information.
Cipher Text:
• Cipher text is the result of applying an encryption algorithm
to plaintext using a specific key. It is the encrypted form of the
original data and appears as random and unreadable
characters. Only those with the proper decryption key can
revert it to its original form.
FUNDAMENTALS OF CRYPTOGRAPHY

8. SYMMETRIC ENCRYPTION ASYMMETRIC ENCRYPTION
Requires secure key management, as
compromise of the key jeopardizes
the security of the data.
Efficient for bulk data encryption,
commonly used in secure
communications and file storage.
Requires secure key management, as
compromise of the key jeopardizes the
security of the data.
Ideal for secure key exchange, digital
signatures, and scenarios where secure
communication channels may not be
available
Uses a single key for both
encryption and decryption.
Uses a pair of keys – a public key for encryption
and a private key for decryption.
Requires secure key distribution since the
same key is used for both parties.
Public keys can be openly
shared, eliminating the need for secure
key distribution..
Generally faster and computationally less
complex for large amounts of data.
Slower due to the complexity of mathematical
operations, especially for larger datasets.

9. VULNERABILITIES OF
CONVENTIONAL
ENCRYPTION AND
DECRYPTION
• The need to decrypt data for processing introduces
a vulnerability, exposing sensitive information at that
stage.
• When computations are outsourced to external
services, decrypted data is exposed, raising privacy
concerns.
• In cloud computing, multiple stages of encryption
and decryption increase the risk of data exposure and
potential security breaches.
• Decrypting data for processing creates an expanded
attack surface. Adversaries could exploit
vulnerabilities during the decryption phase to gain
unauthorized access to sensitive information.
• Traditional methods often restrict the ability to
perform computations directly on encrypted data. This
limitation hinders the efficiency and security of data
processing operations.

10. HOMOMORPHIC ENCRYPTION
(Actual Introduction)

11. Homomorphic encryption is an advanced cryptographic technique that
allows computations to be performed directly on encrypted data
without the need for decryption.
It is a public key encryption:
Encryption Process:
Sender encrypts data using recipient's public key.
Computation Phase:
Recipient, holding the private key, performs computations directly on the encrypted data.
Data Confidentiality:
Sensitive information remains encrypted throughout the computation phase.
Decryption After Computation:
Only after computations are complete, recipient uses
the private key to decrypt the final result.
Protection of Sensitive Data:
Ensures that sensitive data is never exposed during processing, maintaining privacy

14. APPLICATIONS OF
HOMOMORPHIC
ENCRYPTION
Secure Cloud Computing:
Homomorphic encryption allows for secure processing of
sensitive data in the cloud without revealing the actual content.
Data can be encrypted before outsourcing to the cloud, and
computations can be performed directly on the encrypted data.
Privacy-Preserving Data Analytics:
Organizations can perform data analytics on encrypted datasets
without exposing the raw information. This is valuable for
collaborative research, sharing insights without revealing the
underlying data.
Secure Outsourcing of Computations:
Homomorphic encryption enables the secure outsourcing of
computational tasks to external services. The service provider
can perform operations on the encrypted data without accessing
the original content.
Privacy-Enhanced Machine Learning:
Homomorphic encryption contributes to privacy-preserving
machine learning. Models can be trained on encrypted data, and
predictions can be made on encrypted inputs without revealing
sensitive information.
Secure Electronic Voting Systems:
Homomorphic encryption ensures the privacy and integrity of
votes in electronic voting systems. Votes can be encrypted, and
computations can be performed on the encrypted votes without
compromising anonymity.

15. APPLICATIONS OF
HOMOMORPHIC
ENCRYPTION
Privacy in Healthcare Data:
Healthcare data, including patient records, can be stored and
processed in an encrypted form. Medical computations can be
performed directly on the encrypted data, preserving patient
privacy.
Confidential Search Queries:
Homomorphic encryption allows for secure search queries
without revealing the actual search terms. This is relevant in
privacy-focused search engines or applications.
Secure IoT Data Processing:
Homomorphic encryption can be applied in the Internet of
Things (IoT) domain. Data generated by IoT devices can be
encrypted, and computations can be performed on the
encrypted data while protecting the privacy of device-generated
information.
Confidential Financial Transactions:
Homomorphic encryption is applicable in the financial sector to
perform computations on encrypted financial data. This ensures
the confidentiality of transactions and prevents exposure of
sensitive financial information

16. TYPES OF OPERATIONS
Addition Operation:
• Description: Homomorphic encryption allows secure addition
operations on encrypted data.
• Example: If A and B are encrypted values, homomorphic addition
produces an encrypted result equivalent to the sum of A and B.
• Application: Useful for scenarios requiring aggregated or
cumulative information while maintaining data privacy.

17. TYPES OF
OPERATIONS
Multiplication Operation:
•Description: Homomorphic
encryption supports secure
multiplication operations on
encrypted values
•Example: If A and B are encrypted
values, homomorphic multiplication
produces an encrypted result
equivalent to the product of A and B
•Application: Enables privacy-
preserving computations involving
multiplication, extending the range of
possible operations.

18. TYPES OF
OPERATIONS
Other Arithmetic Operations:
• Description: Homomorphic encryption
schemes may extend to other arithmetic
operations like subtraction and division.
• Example: Secure subtraction of encrypted
values produces a result equivalent to the
subtraction of the plaintext values.
• Application: Provides a broader set of
arithmetic operations for diverse
computations while preserving data
privacy.
Based on these operations, Homomorphic
Encryption is classifies into three types.

19. TYPES OF
HOMOMORPHIC
ENCRYPTION
Partially Homomorphic Encryption (PHE):
• Supports only one type of operation, either addition or
multiplication, on encrypted data.
• Can be performed an unlimited number of times on the
ciphertext.
Somewhat Homomorphic Encryption (SHE):
• Supports a specific operation (addition or multiplication) up to a
particular complexity level.
• These operations can only be carried out a fixed number of
times before the noise in the ciphertext becomes too large for
accurate computation.
Fully Homomorphic Encryption (FHE):
• The most powerful type, allowing any mathematical operation
to be performed on encrypted data an unlimited number of
times.
• However, FHE schemes are typically much slower and more
computationally expensive than PHE or SHE schemes.

20. PARTIALLY
HOMOMORPHIC
ENCRYPTION (PHE)
Introduction to Partial Homomorphic Encryption:
Partial Homomorphic Encryption (PHE) is a type of
homomorphic encryption that supports only one
type of mathematical operation on encrypted
data. It is a less complex variant compared to fully
homomorphic encryption (FHE) but still offers
valuable privacy-preserving capabilities.
Single Homomorphic Operation:
PHE allows either addition or multiplication
operations to be performed on encrypted data,
but not both simultaneously. This means that
computations on encrypted values can be limited
to a specific mathematical operation.
Example: Paillier Cryptosystem (Additive
Homomorphism):
The Paillier cryptosystem is an example of a
partially homomorphic encryption scheme that
supports additive homomorphism. Encrypted
values can be added together, and the decryption
of the sum is equivalent to the sum of the original
plaintext values.

21. PARTIALLY
HOMOMORPHIC
ENCRYPTION (PHE)
Example: ElGamal Cryptosystem
(Multiplicative Homomorphism):
The ElGamal cryptosystem is another example of
a partially homomorphic encryption scheme,
but it supports multiplicative homomorphism.
Encrypted values can be multiplied together, and
the decryption of the product is equivalent to
the product of the original plaintext values.
Applications of PHE:
PHE finds applications in scenarios where only
one type of operation is needed. For example,
secure aggregation of data, voting systems, or
scenarios where either addition or multiplication
operations are sufficient.
Efficiency Advantages:
PHE is often more computationally efficient than
fully homomorphic encryption because it
supports a limited set of operations. This makes
it practical for certain applications where the full
flexibility of FHE is not necessary.

22. SOMEWHAT
HOMOMORPHIC
ENCRYPTION (SHE)
Somewhat Homomorphic Encryption (SHE) :
It is an intermediate form of homomorphic encryption that
allows for the repeated application of a single type of
mathematical operation on encrypted data. Unlike PHE, SHE
supports a broader range of computations.
Repetitive Application of On Operation:
SHE enables the repeated application of either addition or
multiplication operations on encrypted data. While it doesn't
support both operations simultaneously, it provides more
flexibility compared to PHE.
Example: Learning with Errors (LWE) Schemes
(Multiplicative Homomorphism):
Learning with Errors-based schemes, a class of cryptographic
primitives, is an example of somewhat homomorphic
encryption that supports multiplicative homomorphism.
Encrypted values can be multiplied together, and the
decryption of the product is equivalent to the product of the
original plaintext values.

23. SOMEWHAT
HOMOMORPHIC
ENCRYPTION (SHE)
Multiple Homomorphic Operations in Sequence:
SHE allows for multiple homomorphic operations to be
performed in sequence. While each operation is limited to
either addition or multiplication, the repetitive application of
these operations provides a level of flexibility suitable for
more complex computations.
Applications of SHE:
SHE finds applications in scenarios where a sequence of
either addition or multiplication operations is required. Use
cases include secure data aggregation, privacy-preserving
analytics, and computations in constrained environments.
Balancing Flexibility and Computational Complexity:
SHE strikes a balance between flexibility and computational
complexity. While not as powerful as Fully Homomorphic
Encryption (FHE), it offers a reasonable level of flexibility for
applications that do not require the full generality of FHE.

24. FULLY
HOMOMORPHIC
ENCRYPTION (FHE)
Introduction to Fully Homomorphic Encryption (FHE):
Fully Homomorphic Encryption (FHE) is the most advanced
form of homomorphic encryption, allowing for arbitrary
computations to be performed on encrypted data. It
supports both addition and multiplication operations on
encrypted values.
Arbitrary Computations on Encrypted Data:
FHE allows for the execution of any computation on
encrypted data without the need for decryption. This
includes complex operations such as addition, multiplication,
and more, making it a powerful tool for privacy-preserving
computations.
Example: Gentry's Scheme:
The introduction of FHE is often credited to Craig Gentry,
who proposed the first fully homomorphic encryption
scheme. His scheme allows for both addition and
multiplication operations on encrypted data, paving the way
for practical applications of FHE.

25. FULLY
HOMOMORPHIC
ENCRYPTION (FHE)
Encrypted Cloud Computing:
FHE is particularly useful in scenarios where data is stored in
the cloud, and computations need to be performed without
revealing the sensitive information. With FHE, the cloud
server can execute operations on encrypted data directly
Complexity and Performance Challenges:
FHE is computationally intensive, and performing operations
directly on encrypted data can be slower compared to
traditional computations on plaintext data. Efforts are
ongoing to improve the efficiency of FHE schemes.
Applications in Sensitive Domains:
FHE finds applications in sensitive domains such as
healthcare, finance, and secure data analytics, where
maintaining privacy during data processing is critical. It
allows for computations on encrypted medical records,
financial transactions, and more.

26. DRAWBACKS OF
HOMOMORPHIC
ENCRYPTION
Performing computations on encrypted data is computationally
intensive, often requiring significantly more time and resources
compared to traditional, unencrypted computations.
Implementing homomorphic encryption correctly requires
expertise in cryptography, and integrating it into existing systems
can be complex.
Managing the keys in homomorphic encryption systems, especially
in large-scale applications, can be challenging. Key management
becomes critical for security.
Partial homomorphic encryption schemes, such as PHE and SHE,
support only specific types of mathematical operations (addition or
multiplication), limiting the range of computations.
While homomorphic encryption libraries exist, the availability of
well-established and optimized libraries for certain programming
languages or platforms may be limited.

27. FUTURE OF
HOMOMORPHIC
ENCRYPTION
•
Homomorphic encryption is at the forefront of cryptographic advancements, offering unparalleled potential for reshaping how data
privacy is maintained in an increasingly interconnected world. As we look ahead, several key trends and developments are poised to
define the future landscape of homomorphic encryption.
• One pivotal area of focus is the ongoing quest for efficiency improvements. Recognizing that homomorphic encryption introduces
computational overhead, researchers are tirelessly working to streamline its operations.
• Standardization initiatives are concurrently underway to establish a unified framework for homomorphic encryption. The
establishment of industry-wide standards is crucial for ensuring interoperability
• In conclusion, the future of homomorphic encryption is characterized by a dynamic interplay of technological advancements,
standardization efforts, and an evolving understanding of its applications. The trajectory suggests a future where privacy-preserving
computations become integral to diverse sectors, forging a path towards a more secure and interconnected digital landscape

28. ANY QUESTIONS ?

29. THANK YOU !!!