However, there are various types of cryptography techniques that are used nowadays. One of them is lattice-based cryptography, which relies on the concepts of mathematical lattices, often in the cipher’s construction or its proof.

So, let’s discuss what lattice-based cryptography is, its importance, and its main benefits.

What Is Lattice-Based Cryptography?

Lattice-based cryptography has become increasingly popular as the world braces for the advent of quantum computing. Post-quantum cryptography is picking up steam, especially as there have been several breakthroughs in the quantum computing space.

Lattice-based cryptography is a type of cryptographic system based on the mathematical concept of a lattice. In a lattice, lines connect points to form a geometric structure. In lattice-based cryptography, this geometric structure encodes and decodes messages.

Because of the nature of a lattice, it is difficult to break into a lattice-based cryptographic system, as some patterns extend infinitely. This makes lattice-based cryptography an attractive alternative to common encryption types like RSA, which has been shown to be vulnerable to attack.

Lattice-based cryptography allows for encoding messages in such a way that they can only be decoded by someone who knows the correct key. For example, imagine you have two lattices, one with 10 points and one with 100 points.

If you were to pick two points randomly from each lattice, it would be complicated to determine which point on the 10-point lattice corresponds to which point on the 100-point lattice. However, if you knew the correct key, you could easily match up the points and decode the message.

Interestingly, lattice-based ciphers like Dilithium and Kyber have shown great potential to resist attacks from quantum computing sources and are widely considered examples of quantum-proof encryption.

Lattice-based cryptographic algorithms can be classified into two broad categories: keyed and unkeyed algorithms. Keyed algorithms, such as the NTRUEncrypt algorithm, require using a secret key to encrypt and decrypt messages. Unkeyed algorithms, such as the Dual EC_DRBG algorithm, do not require a private key.

Understanding Lattices

In order to properly understand the construction of a lattice-based cipher, it’s vitally important to know lattices and the mathematical problems surrounding them.

Lattices have been studied extensively by mathematicians and have a number of interesting properties. For example, every two-dimensional lattice has a basis, a set of vectors defining the lattice. The number of vectors in a basis is called the rank of the lattice.

A basis for such a lattice would be the vectors (2, 0) and (0, 2). The rank of this lattice would be 2. Another interesting property of lattices is that they can be classified into one of three categories: periodic, aperiodic, or chaotic.

A periodic lattice is one where the pattern repeats over and over again with no gaps or overlaps. An aperiodic lattice is one where the pattern does not repeat exactly, but there are no gaps or overlaps. A chaotic lattice is one with gaps or overlaps in the pattern, introducing randomness in the equation.

The security of lattice-based algorithms often depends on how certain mathematical plans can be solved on lattices. Two common problems, for instance, include the closest vector problem (CVP) and the shortest vector problem (SVP). The former is a mathematical problem in which one must find the shortest “nonzero” vector in a given lattice.

The closest vector problem is a problem in which one must find the vector in a given lattice that is closest to a given vector. Both the SVP and CVP are believed to be computationally complex problems. As a result, algorithms that are based on these problems are resistant to attacks by classical computers.

Four Benefits of Using Lattice-Based Cryptography

Lattice-based cryptography offers a variety of benefits over conventional ciphers. Some of them are as follows:

1. Improved Security

One of the biggest benefits of lattice-based cryptography is that it offers improved security. This is because lattices are more difficult to break than other mathematical structures commonly used for cryptography, such as elliptic curves.

2. Faster Computation Times

Another benefit of lattice-based cryptography is that it can be computed much faster than other cryptographic algorithms. This is important because faster computation times can improve performance, especially in applications requiring real-time responses, such as streaming media or online gaming.

3. Lower Energy Consumption

In addition to being faster, lattice-based cryptographic algorithms also consume less energy than other types of cryptographic algorithms. This is because they can be implemented in hardware that requires less power.

For example, certain types of processors designed for cryptocurrency mining are up to many times more energy-efficient than traditional processors when running lattice-based cryptographic algorithms.

4. Flexible and Easy to Implement

Another advantage of using lattice-based cryptography is that it is relatively easy to implement. Other methods, such as elliptic curve cryptography, can be pretty complex and require a large amount of computer resources.

Lattice-based cryptography can be implemented on off-the-shelf hardware, which makes it more accessible and less expensive. Additionally, there are no special requirements for implementing lattice-based cryptography.

More importantly, lattice-based ciphers can be used for a number of different applications. For example, it can be used for digital signatures, password-based encryption, and key exchange. Additionally, there are several different ways to construct a lattice, which means that there is a lot of flexibility in how it can be used.

New Cryptographic Standards Are Expected to Rise in Popularity

As global security experts look at quantum-resistant cryptographic standards, we can expect other standards, like lattice-based cryptography, to rise in popularity. Since quantum computers can quickly solve problems in seconds that regular computers will take over 100,000 years to complete, its power could easily overcome the encryption protocols we use today.

Quantum computers pose a grave threat to many encryption standards that have been able to withstand the test of time so far. Still, you can expect cryptography to change and evolve, especially as quantum machines, which have the potential to outperform supercomputers, eventually become mainstream.