Elliptic Curve Cryptography for Developers

ECC achieves the same security as RSA with much smaller key sizes, reducing memory, processing time, and system cost. [1]

ECC is used in credit card transactions, web authentication, blockchain for aggregate signatures, and privacy-preserving proofs. [1]

Key exchange protocols like Diffie-Hellman use elliptic curve mathematics to securely generate shared secrets between parties. [1] [2]

A good curve has a large prime cardinality and a small cofactor, making it resistant to known attacks and suitable for secure cryptography. [1] [2]

Digital signatures like Schnorr and ECDSA use elliptic curve operations for signing and verification, providing strong security with efficient computation. [1] [2]

Finite field arithmetic and polynomial operations form the mathematical foundation for all elliptic curve cryptographic algorithms. [1] [2] [3] [4] [5] [6] [7]

Pairings like Weil and Tate allow for constructions such as identity-based encryption and aggregate signatures by mapping points to field extension values. [1] [2]

BLS multi-signatures aggregate multiple signatures into one, enabling efficient verification and scalability in blockchain and distributed systems. [1] [2]

Zero-knowledge proofs, including zk-SNARKs, allow one to prove knowledge of a secret without revealing it, using elliptic curve pairings for succinct, noninteractive proofs. [1]

Algorithms using complex multiplication and Hilbert class polynomials search for curves with optimal security and efficiency for pairing-based protocols. [1] [2]