The Core Issue: libsecp256k1, Bitcoin’s Cryptographic Heart
Bitcoin Magazine The Core Issue: libsecp256k1, Bitcoin’s Cryptographic Heart Common phrases heard among Bitcoiners include “don’t trust, verify” or “not your keys, not your coins”, sometimes even claiming that it’s “backed by math”. But what do these proverbs ultimately boil down to, and how exactly is this involved math put into practice? Most readers are surely aware that a fundamental ingredient in the design of Bitcoin is public-key cryptography and more specifically digital signatures, which are essential to prove ownership without needing a central entity. Probably less well-known is what piece of software is under the hood to make that elliptic curve math work and what efforts are involved to ensure that this happens in the most secure and performant way, with continuous improvements. Let’s dive into the exciting history and evolution of “libsecp256k1”, a library that started out as a small hobby project and over the years evolved into an essential part of consensus rules protecting a multi-trillion dollar asset. The Genesis For reasons we don’t know for sure, Satoshi picked an elliptic curve named “secp256k1” for creating and verifying digital signatures in Bitcoin. The initial version of the Bitcoin client was shipped using the widespread OpenSSL library for signing and verifying transactions. Relying on a third-party library sounds like a reasonable approach from a software engineering perspective (even more so if it is something as domain-specific and complex as elliptic-curve cryptography), but this choice turned out to be problematic later due to inconsistencies in the signature parsing code. In the worst case, this could even lead to unintended chain splits. One lesson from that time period was that OpenSSL is not a suitable library for a consensus-critical system like Bitcoin. The issue was later fixed by BIP66, which ensured a strict encoding of ECDSA signatures. After that, the OpenSSL dependency was replaced with libsecp256k1 in Bitcoin Core v0.12, released in early 2016.1 But taking a step back, the initial motivation behind starting the libsecp256k1 project was mostly curiosity about a potential speed-up. Sometime in the year 2012, Bitcoin Core developer Pieter Wuille a.k.a. “sipa” stumbled upon a bitcointalk thread by Hal Finney (footnote: known for being the recipient of the very first Bitcoin transaction in 2009 from Satoshi). Under the subject “Speeding up signature verification”, the post discussed an optimization that would make use of a so-called “endomorphism” (footnote: more specifically using the so-called GLV-method, Gallant-Lambert-Vanstone), something that only certain elliptic curves allow, secp256k1 conveniently being one of them. Hal Finney himself implemented it using OpenSSL primitives, it was later even submitted as a PR to Bitcoin Core.2 Even though it showed a solid ~20% speedup, it was never merged in the end due to concerns about increasing code complexity and missing assurance that the involved cryptography is sound. Pieter Wuille went ahead and decided to start a new library from scratch, with the initial commit of the “secp256k1” repository dating back to March 5th 2013. After only one week the library was able to verify the full blockchain (block height ~225000 at that time), within another week the signing functionality was implemented. It took some more time and testing until the library was ready to be used in Bitcoin Core as a replacement for OpenSSL, first for signing in the wallet (release v0.10, 2015), and finally for ECDSA signature verification in consensus (release v0.12, 2016). The efforts were absolutely worth it: according to the PR description in Core, using libsecp256k1 for signature verification was “anywhere between 2.5 and 5.5 times faster”. Ironically, this didn’t yet include the earlier mentioned endomorphism optimization, since it wasn’t turned on by default due to worries about patent violation. It was only activated in the year 2020, after the patent expired (enabled in release v0.20), leading to another solid speed-up of around 16%. Over time, the project attracted several other contributors. This naturally involved people that were closely working with Pieter from the start at Blockstream, namely then-CTO Gregory Maxwell and researcher Andrew Poelstra. In 2015, Jonas Nick and a few years later Tim Ruffing joined, both employed by Blockstream as researchers and now holding the role of maintainers of libsecp256k1 for several years. As they are responsible for both specifying new cryptographic protocols (including detailed security proofs) and putting them into practice by implementing and reviewing them, it is very appropriate to call them “full-stack cryptographers”, as Tim Ruffing likes to describe himself. Occasionally even cryptographers from outside the Bitcoin space have contributed to libsecp256k1. One notable example of that is Peter Dettman, known for being one of the maintainers of the C#/Java cryptography library BouncyCastle, who up to this day shows up every now and then with various performance improvement suggestions. One of his major contributions was implementing modular inversion using the “safegcd” algorithm in 2021 to safely improve , following a paper by Daniel J. Bernstein and Bo-Yin Yang. Why Reinvent The Wheel? The goal of libsecp256k1 is to provide the highest quality library for cryptographic operations on the secp256k1 curve, with the primary intent of being useful in the broader Bitcoin ecosystem–Bitcoin Core is simply the main client using it. The API of libsecp256k1 is designed to be robust and hard to misuse, in order to prevent users from performing insecure operations (e.g. by rolling their own cryptographic schemes) that could lead to a loss of funds in the worst case. By focussing only on one elliptic curve and by limiting its functionality to operations relevant to Bitcoin (that is, primarily signing and verifying transactions), the code can be both faster and simpler to review, leading to a lower maintenance burden and higher overall quality in comparison to other implementations. libsecp256k1 is written in C and doesn’t have any dependency on other libraries, so it only uses internal code written specifically for the project. As such it is designed to also run on constrained devices like micro-controllers, which are commonly used in hardware wallets. Measure Twice, Cut Once From very early on, libsecp256k1 had a strong focus
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