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 Elliptic-curve cryptography (ECC) is a powerful approach to public-key cryptography that leverages the mathematical properties of elliptic curves over finite fields. Its primary appeal lies in providing equivalent levels of security as traditional systems, such as RSA, but with much smaller key sizes, which results in faster computations and reduced storage requirements. ECC works by utilizing the algebraic structure of elliptic curves to define cryptographic algorithms, making it suitable for resource-constrained environments like mobile devices and embedded systems. It supports a variety of cryptographic tasks, including secure key exchange, digital signatures, and encryption, with popular protocols like ECDSA and ECDH built on its principles. ECC's efficiency and security have made it a standard choice in modern cryptographic applications, including securing internet communications and blockchain technologies.
Cryptographic protocols A cryptographic protocol is a structured sequence of operations that ensures secure communication or data processing between parties, leveraging principles of cryptography. These protocols often include mechanisms like zero-knowledge proofs (ZKPs) and signature schemes to ensure confidentiality, authenticity, and integrity. ZKPs are innovative methods by which one party (the prover) can convince another party (the verifier) of a statement's truth without revealing any additional information beyond its validity. For example, in blockchain systems, ZKPs enable privacy-preserving transactions by proving ownership or knowledge without exposing sensitive data. Signature schemes, on the other hand, provide a way to authenticate the origin of messages or documents through digital signatures, ensuring that data has not been tampered with. Together, these components are foundational in building systems like blockchain, secure voting, and encrypted messaging, balancing transparency with privacy and security.
	Cryptography for blockchain Cryptography is a cornerstone of blockchain technology, ensuring security, privacy, and trust in decentralized systems. It underpins key features such as secure transaction processing, data integrity, and user authentication. Public-key cryptography allows users to sign transactions with private keys, proving ownership without revealing sensitive information, while cryptographic hash functions ensure the immutability of blockchain data by linking blocks in a secure chain. Advanced techniques like zero-knowledge proofs enhance privacy by enabling parties to validate transactions without exposing details. By leveraging cryptography, blockchain achieves a balance between transparency and confidentiality, enabling robust applications like cryptocurrencies, smart contracts, and decentralized finance.