**secp256k1**, one of the most important and widely used elliptic curves in cryptography. It is a Koblitz Curve used for Elliptic Curve Cryptography (ECC), defined over a **256-bit prime field**. It is best known as the **curve used by Bitcoin** and other cryptocurrencies for digital signatures and **public/private key generation**.
# Technical Specs - **Full name**: *Standards for Efficient Cryptography Prime 256k1* - **Defined in**: SEC 2 (by SECG – Standards for Efficient Cryptography Group) - **No "a" or "b" coefficients** except $b = 7$, which simplifies computations. - **Base point (G)** and **order (n)** are defined to ensure good cryptographic properties.
# Why it's special * **Koblitz Curve**: It's part of a special family of curves that allow for faster arithmetic due to certain optimizations. * **Efficiency**: `secp256k1` is faster than many other NIST curves, especially when using optimized libraries like [libsecp256k1](https://github.com/bitcoin-core/secp256k1). * **Deterministic signatures**: Most implementations use RFC 6979 to ensure nonces are generated deterministically, avoiding catastrophic leaks.
# Use in Bitcoin Bitcoin uses `secp256k1` to: * Generate public keys from private keys * Create and verify digital signatures on transactions * Derive addresses (via hashing the public key)
# Controversy (NIST Curves vs. secp256k1) * Unlike NIST curves (like `P-256`), `secp256k1` was **not generated with a random seed**, which avoids some suspicion of NSA backdoors. * Some cryptographers prefer `secp256k1` precisely because its parameters are simple and fully explained — no "magic constants."
# Libraries that support it * **libsecp256k1** (Bitcoin Core’s high-speed library, in C) * **OpenSSL** (has support, but not enabled by default in all builds) * **Python (`ecdsa`, `coincurve`)** * **JavaScript (`elliptic` in Node.js, used by ethers.js/web3.js)** * **Go, Rust, Java** – widely supported
# Summary `secp256k1` is: * **Efficient**, **well-vetted**, and **widely used** * Particularly important for **blockchain**, **cryptocurrency**, and **zero-knowledge proof systems**
# See - Command line for secp256k1