Latticebased cryptography technique is an excellent method of securing information using a series of mathematical formulae.
Cryptography comes in multiple flavors. In general, it uses a series of codes to encrypt your data.
For the longest time, cryptographic tools like encryption schemes followed adhoc designs. Security was completely based on heuristics and intuition.
Also, codes are easier to break; hence, securing data is a question for those who are using codebased security designs.
Another problem is that existing standards of cryptography are not that reliable. The development of quantum computers can further break the standards, resulting in an increased feat among users.
Therefore, encrypting personal information is essential for everyone. Subsequently, there was a requirement for a new idea or technique that no one could break. We needed improved standards that can secure data even after using quantum computers.
After a lot of brainstorming, a new method has evolved, i.e., Latticebased Cryptography.
In this article, I’ll discuss latticebased cryptography, its importance, how it works, and more.
Here we go!
What Is Cryptography?
Cryptography is a technique of securing communications and information using a wide range of codes so that the information can be read and processed by those for whom they are intended. This will prevent unauthorized access to the data.
The term “cryptography” is created by combining two words – crypt and writing.
Here, “crypt” means “hidden” and “graphy” means “writing”.
The methods used to protect your information are obtained from different mathematical concepts and some rulebased calculations, i.e., algorithms to turn messages into a hardcore problem that seems to be difficult to decode.
There are three types of Cryptography:
 Symmetric Key Cryptography: It is a type of encryption system that allows the sender of a message and its receiver to use a single key to code and decode messages. This method is simpler and faster.
 Hash Functions: In this algorithm, you don’t need any key. A hash value is calculated as plain text, which is difficult for contents to be recovered. Various OS use this method to encrypt passwords.
 Asymmetric Key Cryptography: Under this technique, a pair of keys has been used to code and decode information – one key for encryption and another key for decryption. The first key is public, but the second key is a private key that only the receiver knows.
What’s LatticeBased Cryptography?
Latticebased cryptography is a simple term used for the building of cryptographic algorithms that involve lattices. It is used for postquantum cryptography to secure information. Unlike knownpublic schemes, latticebased schemes are more resilient and can withstand attacks from quantum computers.
Now, if you are wondering what a lattice is in the context of latticebased cryptography, let me make that clear for you.
A lattice resembles a grid as in graph paper that uses a set of points located in a crisscross way. This is not finite; instead, a lattice defines a pattern that keeps continuing infinitely. A set of points is known as a vector where you can add numbers in any integer multiples. The hard part is finding the points from this infinite grid that are close to some point, let’s say 0.
Additionally, latticebased cryptography uses complex mathematical problems to encrypt the data, making it difficult for attackers to solve these kinds of problems and steal data.
Talking about its history, latticebased cryptography was first introduced by Miklos Ajtai in the year 1996, whose security was based on lattice problems.
In 1998, Joseph H. Silverman, Jill Pipher, and Jeffrey Hoofstein introduced a latticebased public key encryption scheme. However, the encryption scheme is not that hard to solve. Finally, in 2005, Oded Regev introduced the first public key encryption scheme that is proven to withstand even in the worstcase scenario.
Since then, the followup work has continued to improve the efficiency of the original encryption scheme. In 2009, Craig Gentry came up with the first homomorphic encryption scheme based on complex lattice problems.
Examples: CRYSTALSDilithium (digital signature algorithm) and CRYSTALSKYBER (public key encryption and key establishment algorithm).
How Does LatticeBased Cryptography Work?
To understand the working principle of latticebased, let’s dive into some important terms:
 Lattices: Lattices are basically thought of as a regularspaced grid of a set of points that are infinite in number.
 Vector: A vector is the name of a point, and the numbers on it are called coordinates. For example, (2,3) is a vector having two coordinates – 2 and 3. A lattice is a collection of these vectors in an infinite series.
 Basis: Lattices have large objects, but computers have a finite amount of memory. So, mathematicians and cryptographers thought of a succinct way to use lattices. So, they use the “basis” of a lattice. It is a collection of vectors used to present any point in the lattice grid that forms a lattice.
Now, let’s take a 2D lattice as an example to understand the concept easily. Here, you will find a grid of points on a flat surface like a piece of paper. Let’s choose two or more points that are not a single line going through the origin.
For example, you choose (3,0) and (0,3). To generate the third point using these points, you need to choose two whole numbers, like 2 and 1. Multiple the coordinates of (3,0) by 2 to get (6,0) and (0,3) by 1 to get (0, 3). Add the result points to get (6,3).
With this method, you can generate the entire grid of points, evenly spaced from each other vertically and horizontally. You can name the coordinates as (x,y), where you see x and y are even numbers, including 0.
Lattices are classified into three categories:
 Aperiodic: An aperiodic lattice is a pattern that doesn’t repeat exactly, but there are no overlaps and gaps.
 Chaotic: A chaotic lattice is a pattern with overlaps and gaps, introducing randomness in your equation.
 Periodic: A periodic lattice is a pattern that repeats again and again with no overlaps and gaps.
Every lattice works as a pattern where the one with the known vector can only decrypt the message. Since it has many patterns, the attacker finds it difficult to find the origin point and key to decrypt it. Whether you have lattices with 10 points or 100 points, the one with the correct key can only decrypt the information.
If an attacker is asked to pick two random points, it will be difficult to determine which point on 10point lattice patterns leads to the 100point lattice. Thus, if you know the key, you can easily decode the message.
Benefits of LatticeBased Cryptography
Latticebased cryptography offers a lot of benefits for individuals and businesses.
Lower Energy Consumption
Energy consumption increases with the increase in the usage of any system. Despite being faster, latticebased cryptography consumes less energy as compared to other encryption schemes. This is because latticebased cryptography is implemented in hardware, resulting in less power consumption.
For example, processors designed for cryptocurrency mining are more energy efficient than traditional processors when using latticebased cryptography.
HighSpeed Computation
Unlike other cryptography algorithms, the encryption scheme of lattices is computed much faster. Faster computation times result in increased performance, giving better responses in realtime, such as online gaming or streaming media.
Easy to Implement and Flexible
Nowadays, businesses are looking for flexible options and saving time. Latticebased cryptography is easy to implement as it requires less amount of resources and is highly accessible. You can also implement it on offtheshelf hardware easily.
Additionally, latticebased cryptography is used in multiple applications, such as digital signatures, key exchange, and passwordbased encryption. Do not limit yourself to one design; instead, you can construct lattices in different ways you can. Thus, it offers a lot of flexibility.
Reasonable Key Sizes
Latticebased cryptography key sizes are small but not as small as classical cryptographic algorithms or quantumsafe isogenybased schemes. Thus, you can use these keys in standard protocols.
Diverse Usage
Lattices let users solve a variety of security challenges, including practical constructions like signatures and key agreement schemes. In addition, you can get to construct security channels across your organization to secure everyone’s data, such as fully homomorphic encryption and identitybased encryption.
Mathematical Foundation
Since the algorithm is completely based on mathematical problems, it is hard to get a real solution to it unless you know the key. This gives assurance to individuals and professionals about their information security.
Understandability
The algorithms used in latticebased cryptography are based on simple linear algebra that requires a less mathematical background to understand the concept of its working. Thus, you can implement this in no time, giving you fast security and efficiency.
Learning Resources
If you want to learn more about technology, here are some books and courses you can refer to. These are available online and can help you to become a pro in this security method. Let’s dive into these books and courses.
#1. Latticebased Cryptosystems: A Design Perspective
Preview  Product  Rating  Price  

LatticeBased Cryptosystems: A Design Perspective  $134.90  Buy on Amazon 
The authors of the book, Jiang Zhang and Zhenfeng Zhang, focus on the latticebased cryptosystems that are widely considered to be the most promising postquantum crypto schemes. This book provides fundamental insights into the proper construction of the security layer from hard lattice problems.
The primary concept is to inform you about the tool that can be used to choose the choice of lattice for designing cryptosystems. This includes designing attributebased encryption, digital signatures, key change, identitybased encryption, and publickey encryption.
#2. Latticebased PublicKey Cryptography in Hardware
Preview  Product  Rating  Price  

LatticeBased PublicKey Cryptography in Hardware (Computer Architecture and Design Methodologies)  $47.07  Buy on Amazon 
The book is written by Sujoy Sinha Roy and Ingrid Verbauwhede. They describe how efficient the implementation of publickey cryptography is, which addresses critical security challenges of large amounts of data generated by the network of connected devices. The devices can be tiny Radio Frequency Identification tags, desktops, and more.
The authors also investigate the implementation of postquantum homomorphic encryption and publickey cryptography schemes.
#3. Lattices and Their Application in Cryptography:
Preview  Product  Rating  Price  

Lattices and their application in Cryptography  $42.90  Buy on Amazon 
This thesis was written by Merve Cakir in the year 2014. The aim of this thesis is to identify the features of latticebased cryptosystems and how the use of signature and encryption schemes is becoming insecure with the coming of a quantum computer.
In the thesis, the author proposed alternative cryptography based on the worst scenario of lattice problems. The hardness and security of computational problems are analyzed by offering collaboration between complexity theory, publickey cryptography, and linear algebra.
#4. Basic to Advance Level Cryptography
This course is introduced by Udemy that gives you a clear idea of cryptography and some related terminologies. In this course, you will learn about cryptography, hashing, hacking and breaking code, cryptanalysis, and encryption decryption.
You will find 5 sections, including 17 lectures, and the total duration of the course i.e., 2h 7m. To enroll yourself in this course, you just need to have a basic knowledge of computers and high school mathematics.
Conclusion
Cryptography is a simple yet powerful tool to protect the information saved in your systems. It works with the help of complex mathematical problems and different algorithms for securing data, which is everyone’s primary goal these days.
Latticebased cryptography is one of the most secure security mechanisms that use simple linear algebra to encrypt the data. It includes lattices, vectors, and basis that are used to construct a tough pattern. The decryption method depends on the patterns, and for that, you need to know the origin point. If you have the key, you can easily decrypt data.
Thus, latticebased cryptography is a proven technique to secure the data of individuals and businesses operating in multiple industries, from IT and security service firms to finance and many more.
You may also read Cloud Cryptography.

Amrita is a freelance copywriter and content writer. She helps brands enhance their online presence by creating awesome content that connects and converts. She has completed her Bachelor of Technology (B.Tech) in Aeronautical Engineering…. read more