ecc

Elliptic curve arithmetic, and the signature, key-agreement and commitment schemes built on it, in typed Python.

It is fully annotated and ships py.typed.

What is here

• modular arithmetic: inverse, blinded and variable-time, Legendre symbol, square root (number_theory)
• the elliptic curve class, over any curve in short Weierstrass form
  • Jacobian coordinates, and the secp256k1 endomorphism
  • double and multi scalar multiplication (Straus's algorithm and Bos-Coster's)
  • SEC 1 octet encodings of points and scalars
  • the SEC 2 v1 and v2, NIST and Brainpool curves, and low cardinality test curves
• ECDSA, with DER encoding, public key recovery, low-R grinding and RFC 6979 deterministic nonces
• BIP340 Schnorr signatures, and their batch verification
• the anti-exfil protocol, and the sign-to-contract commitment it rests on, for both signature schemes
• MuSig2 multi-signatures and FROST (draft BIP445) threshold signatures, one primitive per round of each protocol
• Diffie-Hellman, and the BIP324 ElligatorSwift encoding of a public key
• ECDSA adaptor signatures of the DLC specification
• DLC oracle signatures, BIP340 with a nonce committed in advance, and their signature points
• single-signer BIP340 adaptor signatures, after the module BlockstreamResearch/secp256k1-zkp#299 proposes
• BIP374 discrete logarithm equality proofs
• ECIES in the BIE1 layout, the block cipher supplied by the caller
• Pedersen commitments, Borromean ring signatures and the range proofs of libsecp256k1-zkp
• the ANSI X9.63 key derivation function and HKDF (kdf), and the BIP340 tagged hash (hashes)

For secp256k1 the arithmetic is delegated to btclib-secp256k1, bindings to Bitcoin Core's libsecp256k1, wherever a call's own guard admits them. They are the secp256k1 extra below. Without them, or with the delegation turned off, every call still answers, on the Python arithmetic, which is slower and not constant-time; that Python arithmetic serves every other curve anyway, and the suite validates it against the bindings. SECURITY.md's "Limitations, not vulnerabilities" states which calls delegate and what the Python path does and does not hide.

The suite answers to vectors their authors publish -- the BIPs' own, Wycheproof's and libsecp256k1-zkp's -- and tests/_data/README.md pins each vendored file to the upstream commit it was copied from.

Installing

python -m pip install --upgrade "ecc[secp256k1]"

The secp256k1 extra installs the libsecp256k1 bindings. The quotes are for zsh, which reads the brackets as a glob.

The gmpy2 extra installs gmpy2, and the Jacobian group law of the Python arithmetic then runs on GMP's integers. It changes nothing where the bindings serve. On PyPy the extra installs nothing, and the package ignores a gmpy2 installed by other means:

python -m pip install --upgrade "ecc[secp256k1,gmpy2]"

First use

An ECDSA signature, verified from the DER octets a peer would send, and a BIP340 Schnorr signature:

from ecc.curves import sec_point
from ecc.ecc import dsa, ssa

prv_key = 0xB7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF

_, pub_key = dsa.gen_keys(prv_key)
assert sec_point.bytes_from_point(pub_key).hex() == (
    "02dff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659"
)
sig = dsa.sign(b"hello", prv_key)
assert dsa.verify(b"hello", pub_key, sig.serialize())
assert not dsa.verify(b"HELLO", pub_key, sig.serialize())

msg = bytes.fromhex("243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89")
_, x_pub_key = ssa.gen_keys(prv_key)
assert x_pub_key == int(
    "DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659", 16
)
assert ssa.verify_(msg, x_pub_key, ssa.sign_(msg, prv_key))

The private key and the message are test vector 1 of BIP340, and tests/readme_test.py runs every Python block of this file.

Security

SECURITY.md says how to report a vulnerability, which versions are supported, and how a published file is traced back to the run that built it. ASSURANCE_CASE.md argues why the security it states holds: the threat model, the trust boundaries, the design principles and the weaknesses countered.

Contributing

CONTRIBUTING.md has the commands each CI job runs, verbatim. uv sync creates the environment; uv is the only tool that has to be installed. REVIEWING.md is what a pull request is answered against.

How the organization decides, and who holds which role, is its GOVERNANCE.md; what it intends to do, and what it deliberately does not, is its ROADMAP.md.

Links

• Documentation: https://btclib-ecc.readthedocs.io/
• Source: https://github.com/btclib-org/ecc
• Releases: https://github.com/btclib-org/ecc/releases
• CHANGELOG.md, and RELEASE_NOTES.md for what a release asks a user to act on

The btclib organization and its projects are actively supported by DGI and CheckSig.