Cryptography research

Mathematics of cryptography

Mathematical cryptography is the foundation of modern secure communication, relying on complex mathematical structures and problems to create systems that protect data from unauthorized access. At its core, cryptography transforms data using mathematical algorithms, making it incomprehensible to anyone who does not possess the correct key for decryption. Key areas of mathematical cryptography include number theory, algebra, and geometry, which underpin critical systems like RSA, elliptic curve cryptography (ECC), and lattice-based cryptography and other areas of private and public-key cryptography

Post-quantum cryptography

Post-quantum cryptography (PQC) refers to cryptographic algorithms designed to secure information against the potential threat posed by quantum computers. Unlike classical computers, which process information in binary, quantum computers use quantum bits (qubits) to perform complex calculations exponentially faster. This capability threatens to break widely-used cryptographic protocols like RSA and ECC, which rely on the
difficulty of factoring large numbers or solving discrete logarithm problems—tasks that
quantum algorithms like Shor’s algorithm can handle efficiently. PQC aims to develop
new cryptographic systems, such as lattice-based, hash-based, code-based, and multivariate polynomial schemes, that remain secure even in the presence of powerful quantum adversaries. These new algorithms are critical for ensuring long-term data security in the post-quantum era, particularly as advancements in quantum computing continue to accelerate.

Elliptic-curve cryptography

Cryptographic protocols

Cryptography for blockchain