At Remiza, we are developing encryption algorithms that can withstand quantum attacks, known as quantum-resistant encryption algorithms. With the threat of quantum computing looming, traditional encryption methods may become vulnerable, making it essential to develop new algorithms that can resist quantum attacks. Our project utilizes advanced mathematical and cryptographic techniques to develop algorithms that can offer better security for sensitive data. Our project is a prime example of how advanced mathematics and cryptography can help create innovative and useful applications.
Lattice-based cryptography employs the use of lattices, which are discrete groups of points arranged in a regular pattern. The encryption key is based on a lattice basis and is kept secret, while the public key is derived from the basis and made available to anyone. The decryption process involves solving a lattice problem that can only be solved with the private key. The hardness of the problem is based on the closest vector problem (CVP) or the shortest vector problem (SVP) in a lattice, which are known to be hard problems. Mathematically, the CVP can be defined as finding the closest vector to a given target vector in a lattice, while the SVP can be defined as finding the shortest non-zero vector in a lattice.
Hash-based cryptography uses a one-way function to encrypt data. A one-way function is a function that is easy to compute in one direction but hard to reverse. The function generates a fixed-length output, known as a hash, that represents the original data. The hash is used as the encryption key, and the original data is discarded. Decryption involves verifying that the hash matches the original data. Hash-based cryptography is based on the difficulty of inverting the one-way function. Mathematically, the function can be defined as H(x) = y, where x is the original data, y is the hash value, and H is the one-way function.
Code-based cryptography is based on the difficulty of decoding linear codes. A linear code is a set of vectors that can be added together and multiplied by a scalar. The encryption key is a set of vectors that are kept secret, while the public key is a set of vectors derived from the secret key. Decryption involves solving a linear code equation that can only be solved with the secret key. The hardness of the problem is based on the minimum distance problem in a linear code, which is known to be an NP-hard problem. Mathematically, the problem can be defined as finding the minimum distance between any two distinct codewords in a linear code.
These techniques are designed to be resistant to attacks by quantum computers, which are based on the principles of quantum mechanics and can solve certain mathematical problems much faster than classical computers. By using advanced mathematical techniques, Quantum-Resistant Encryption Algorithms can ensure secure encryption of sensitive data even in the face of quantum computing-based attacks