## What is Quantum proof Encryption

Quantum proof encryption refers to cryptographic methods that are resistant to attacks by quantum computers. These methods use mathematical problems that are believed to be hard for a quantum computer to solve, such as the learning with errors (LWE) problem, in order to secure communications. While current computers would take many years to crack these codes, a quantum computer would be able to do it in a matter of seconds. The most notable of these is the Post-Quantum Cryptography (PQC) standard.

## Post-Quantum Cryptography (PQC) standard.

Post-Quantum Cryptography (PQC) is a type of encryption that is resistant to attacks by quantum computers. The goal of PQC is to provide a secure means of communication that will remain secure even if and when large-scale quantum computers are built. PQC is based on mathematical problems that are believed to be hard for quantum computers to solve, such as the learning with errors (LWE) problem and the lattice-based problems. PQC standards are being developed by organizations such as the National Institute of Standards and Technology (NIST) to ensure that they are secure and efficient.

## learning with errors (LWE) problem

The learning with errors (LWE) problem is a mathematical problem that is used in post-quantum cryptography as the basis for encryption schemes. It is believed to be hard for a quantum computer to solve, making it a suitable candidate for use in quantum-resistant encryption.

In the LWE problem, a secret vector is chosen at random, and a set of noisy linear equations are generated based on the secret vector and a publicly known matrix. The goal is to recover the secret vector from the noisy linear equations. It is widely believed that solving the LWE problem is computationally infeasible for a quantum computer, making it a suitable candidate for use in post-quantum cryptography.

Many cryptographic schemes such as the Ring-LWE, the RLWE-based key exchange, the LWE-based encryption are based on LWE problem which are believed to be secure against quantum computers.

## Ring-LWE

Ring-LWE (Learning with Errors over Rings) is a variation of the LWE problem that uses polynomials over a finite ring, rather than vectors over a field. It is used as a basis for various cryptographic schemes, such as key exchange, digital signature and encryption.

In the Ring-LWE problem, a secret polynomial is chosen at random, and a set of noisy polynomial equations are generated based on the secret polynomial and a publicly known matrix. The goal is to recover the secret polynomial from the noisy equations. Ring-LWE is considered to be a hard problem for a quantum computer to solve, making it a suitable candidate for use in post-quantum cryptography.

Some of the notable implementation of Ring-LWE are the NewHope, the Kyber and the Frodo, which are considered to be secure and efficient.

## Examples where Quantum proof Encryption is being used

Quantum proof encryption is not yet widely used in practice, as large-scale quantum computers capable of breaking current encryption methods do not yet exist. However, organizations and governments are beginning to prepare for the eventual arrival of quantum computers by researching and developing quantum-resistant encryption methods.

One example of where quantum proof encryption is being used is in the development of new cryptographic standards by organizations such as the National Institute of Standards and Technology (NIST). NIST is currently running a competition to select new post-quantum cryptographic algorithms that can be used to protect sensitive information.

Another example is the use of quantum proof encryption in communication networks like 5G networks. The 5G standard includes support for quantum-safe key exchange to ensure the security of 5G communications even against the potential threats of a quantum computer.

In the future, it is likely that quantum-resistant encryption will be used in a wide range of applications, including secure communication, digital signatures, and secure storage of sensitive data.