bip-0458: Add vendored secp256k1lab library

Add a vendored copy of the secp256k1lab library (master branch, commit a265da139aea27386085a2a8760f8698e1bda64e) that the half-aggregation reference implementation and test vector scripts depend on.
2026-11-02 19:41:29 +00:00 · 2026-10-20 17:53:54 +02:00
1 parent 130b8e0fa7
commit 1eb496599c
@@ -0,0 +1,34 @@
+name: Tests
+on: [push, pull_request]
+jobs:
+  ruff:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - name: Install the latest version of uv
+        uses: astral-sh/setup-uv@v5
+      - run: uvx ruff check .
+  mypy:
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        python-version: ["3.11", "3.12", "3.13", "3.14"]
+    steps:
+      - uses: actions/checkout@v4
+      - name: Install the latest version of uv, setup Python ${{ matrix.python-version }}
+        uses: astral-sh/setup-uv@v5
+        with:
+          python-version: ${{ matrix.python-version }}
+      - run: uvx mypy .
+  unittest:
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        python-version: ["3.11", "3.12", "3.13", "3.14"]
+    steps:
+      - uses: actions/checkout@v4
+      - name: Setup Python ${{ matrix.python-version }}
+        uses: actions/setup-python@v5
+        with:
+          python-version: ${{ matrix.python-version }}
+      - run: python3 -m unittest
@@ -0,0 +1,10 @@
+# Python-generated files
+__pycache__/
+*.py[oc]
+build/
+dist/
+wheels/
+*.egg-info
+
+# Virtual environments
+.venv
@@ -0,0 +1 @@
+3.11
@@ -0,0 +1,25 @@
+# Changelog
+
+All notable changes to this project will be documented in this file.
+
+The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
+and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
+
+## [Unreleased]
+
+#### Added
+ - Added new methods `Scalar.from_int_nonzero_checked` and `Scalar.from_bytes_nonzero_checked`
+   that ensure a constructed scalar is in the range `0 < s < N` (i.e. is non-zero and within the
+   group order) and throw a `ValueError` otherwise. This is e.g. useful for ensuring that newly
+   generated secret keys or nonces are valid without having to do the non-zero check manually.
+   The already existing methods `Scalar.from_int_checked` and `Scalar.from_bytes_checked` error
+   on overflow, but not on zero, i.e. they only ensure `0 <= s < N`.
+
+ - Added a new method `GE.from_bytes_compressed_with_infinity` to parse a compressed
+   public key (33 bytes) to a group element, where the all-zeros bytestring maps to the
+   point at infinity. This is the counterpart to the already existing serialization
+   method `GE.to_bytes_compressed_with_infinity`.
+
+## [1.0.0] - 2025-03-31
+
+Initial release.
@@ -0,0 +1,23 @@
+The MIT License (MIT)
+
+Copyright (c) 2009-2024 The Bitcoin Core developers
+Copyright (c) 2009-2024 Bitcoin Developers
+Copyright (c) 2025- The secp256k1lab Developers
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.
@@ -0,0 +1,13 @@
+secp256k1lab
+============
+
+![Dependencies: None](https://img.shields.io/badge/dependencies-none-success)
+
+An INSECURE implementation of the secp256k1 elliptic curve and related cryptographic schemes written in Python, intended for prototyping, experimentation and education.
+
+Features:
+* Low-level secp256k1 field and group arithmetic.
+* Schnorr signing/verification and key generation according to [BIP-340](https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki).
+* ECDH key exchange.
+
+WARNING: The code in this library is slow and trivially vulnerable to side channel attacks.
@@ -0,0 +1,34 @@
+[project]
+name = "secp256k1lab"
+version = "1.0.0"
+description = "An INSECURE implementation of the secp256k1 elliptic curve and related cryptographic schemes, intended for prototyping, experimentation and education"
+readme = "README.md"
+authors = [
+    { name = "Pieter Wuille", email = "pieter@wuille.net" },
+    { name = "Tim Ruffing", email = "me@real-or-random.org" },
+    { name = "Jonas Nick", email = "jonasd.nick@gmail.com" },
+    { name = "Sebastian Falbesoner", email = "sebastian.falbesoner@gmail.com" }
+]
+maintainers = [
+    { name = "Tim Ruffing", email = "me@real-or-random.org" },
+    { name = "Jonas Nick", email = "jonasd.nick@gmail.com" },
+    { name = "Sebastian Falbesoner", email = "sebastian.falbesoner@gmail.com" }
+]
+requires-python = ">=3.11"
+license = "MIT"
+license-files = ["COPYING"]
+keywords = ["secp256k1", "elliptic curves", "cryptography", "Bitcoin"]
+classifiers = [
+  "Development Status :: 5 - Production/Stable",
+  "Intended Audience :: Developers",
+  "Intended Audience :: Education",
+  "Intended Audience :: Science/Research",
+  "License :: OSI Approved :: MIT License",
+  "Programming Language :: Python",
+  "Topic :: Security :: Cryptography",
+]
+dependencies = []
+
+[build-system]
+requires = ["hatchling"]
+build-backend = "hatchling.build"
@@ -0,0 +1,73 @@
+# The following functions are based on the BIP 340 reference implementation:
+# https://github.com/bitcoin/bips/blob/master/bip-0340/reference.py
+
+from .secp256k1 import FE, GE, G
+from .util import int_from_bytes, bytes_from_int, xor_bytes, tagged_hash
+
+
+def pubkey_gen(seckey: bytes) -> bytes:
+    d0 = int_from_bytes(seckey)
+    if not (1 <= d0 <= GE.ORDER - 1):
+        raise ValueError("The secret key must be an integer in the range 1..n-1.")
+    P = d0 * G
+    assert not P.infinity
+    return P.to_bytes_xonly()
+
+
+def schnorr_sign(
+    msg: bytes, seckey: bytes, aux_rand: bytes, tag_prefix: str = "BIP0340"
+) -> bytes:
+    d0 = int_from_bytes(seckey)
+    if not (1 <= d0 <= GE.ORDER - 1):
+        raise ValueError("The secret key must be an integer in the range 1..n-1.")
+    if len(aux_rand) != 32:
+        raise ValueError("aux_rand must be 32 bytes instead of %i." % len(aux_rand))
+    P = d0 * G
+    assert not P.infinity
+    d = d0 if P.has_even_y() else GE.ORDER - d0
+    t = xor_bytes(bytes_from_int(d), tagged_hash(tag_prefix + "/aux", aux_rand))
+    k0 = (
+        int_from_bytes(tagged_hash(tag_prefix + "/nonce", t + P.to_bytes_xonly() + msg))
+        % GE.ORDER
+    )
+    if k0 == 0:
+        raise RuntimeError("Failure. This happens only with negligible probability.")
+    R = k0 * G
+    assert not R.infinity
+    k = k0 if R.has_even_y() else GE.ORDER - k0
+    e = (
+        int_from_bytes(
+            tagged_hash(
+                tag_prefix + "/challenge", R.to_bytes_xonly() + P.to_bytes_xonly() + msg
+            )
+        )
+        % GE.ORDER
+    )
+    sig = R.to_bytes_xonly() + bytes_from_int((k + e * d) % GE.ORDER)
+    assert schnorr_verify(msg, P.to_bytes_xonly(), sig, tag_prefix=tag_prefix)
+    return sig
+
+
+def schnorr_verify(
+    msg: bytes, pubkey: bytes, sig: bytes, tag_prefix: str = "BIP0340"
+) -> bool:
+    if len(pubkey) != 32:
+        raise ValueError("The public key must be a 32-byte array.")
+    if len(sig) != 64:
+        raise ValueError("The signature must be a 64-byte array.")
+    try:
+        P = GE.from_bytes_xonly(pubkey)
+    except ValueError:
+        return False
+    r = int_from_bytes(sig[0:32])
+    s = int_from_bytes(sig[32:64])
+    if (r >= FE.SIZE) or (s >= GE.ORDER):
+        return False
+    e = (
+        int_from_bytes(tagged_hash(tag_prefix + "/challenge", sig[0:32] + pubkey + msg))
+        % GE.ORDER
+    )
+    R = s * G - e * P
+    if R.infinity or (not R.has_even_y()) or (R.x != r):
+        return False
+    return True
@@ -0,0 +1,16 @@
+import hashlib
+
+from .secp256k1 import GE, Scalar
+
+
+def ecdh_compressed_in_raw_out(seckey: bytes, pubkey: bytes) -> GE:
+    """TODO"""
+    shared_secret = Scalar.from_bytes_checked(seckey) * GE.from_bytes_compressed(pubkey)
+    assert not shared_secret.infinity  # prime-order group
+    return shared_secret
+
+
+def ecdh_libsecp256k1(seckey: bytes, pubkey: bytes) -> bytes:
+    """TODO"""
+    shared_secret = ecdh_compressed_in_raw_out(seckey, pubkey)
+    return hashlib.sha256(shared_secret.to_bytes_compressed()).digest()
@@ -0,0 +1,15 @@
+from .secp256k1 import GE, G
+from .util import int_from_bytes
+
+# The following function is based on the BIP 327 reference implementation
+# https://github.com/bitcoin/bips/blob/master/bip-0327/reference.py
+
+
+# Return the plain public key corresponding to a given secret key
+def pubkey_gen_plain(seckey: bytes) -> bytes:
+    d0 = int_from_bytes(seckey)
+    if not (1 <= d0 <= GE.ORDER - 1):
+        raise ValueError("The secret key must be an integer in the range 1..n-1.")
+    P = d0 * G
+    assert not P.infinity
+    return P.to_bytes_compressed()
@@ -0,0 +1,483 @@
+# Copyright (c) 2022-2023 The Bitcoin Core developers
+# Distributed under the MIT software license, see the accompanying
+# file COPYING or http://www.opensource.org/licenses/mit-license.php.
+
+"""Test-only implementation of low-level secp256k1 field and group arithmetic
+
+It is designed for ease of understanding, not performance.
+
+WARNING: This code is slow and trivially vulnerable to side channel attacks. Do not use for
+anything but tests.
+
+Exports:
+* FE: class for secp256k1 field elements
+* GE: class for secp256k1 group elements
+* G: the secp256k1 generator point
+"""
+
+from __future__ import annotations
+from typing import Self
+
+# TODO Docstrings of methods still say "field element"
+class APrimeFE:
+    """Objects of this class represent elements of a prime field.
+
+    They are represented internally in numerator / denominator form, in order to delay inversions.
+    """
+
+    # The size of the field (also its modulus and characteristic).
+    SIZE: int
+
+    def __init__(self, a: int | Self = 0, b: int | Self = 1) -> None:
+        """Initialize a field element a/b; both a and b can be ints or field elements."""
+        if isinstance(a, type(self)):
+            num = a._num
+            den = a._den
+        else:
+            assert isinstance(a, int)
+            num = a % self.SIZE
+            den = 1
+        if isinstance(b, type(self)):
+            den = (den * b._num) % self.SIZE
+            num = (num * b._den) % self.SIZE
+        else:
+            assert isinstance(b, int)
+            den = (den * b) % self.SIZE
+        assert den != 0
+        if num == 0:
+            den = 1
+        self._num: int = num
+        self._den: int = den
+
+    def __add__(self, a: int | Self) -> Self:
+        """Compute the sum of two field elements (second may be int)."""
+        if isinstance(a, type(self)):
+            return type(self)(self._num * a._den + self._den * a._num, self._den * a._den)
+        if isinstance(a, int):
+            return type(self)(self._num + self._den * a, self._den)
+        return NotImplemented
+
+    def __radd__(self, a: int) -> Self:
+        """Compute the sum of an integer and a field element."""
+        return type(self)(a) + self
+
+    @classmethod
+    def sum(cls, *es: Self) -> Self:
+        """Compute the sum of field elements.
+
+        sum(a, b, c, ...) is identical to (0 + a + b + c + ...)."""
+        return sum(es, start=cls(0))
+
+    def __sub__(self, a: int | Self) -> Self:
+        """Compute the difference of two field elements (second may be int)."""
+        if isinstance(a, type(self)):
+            return type(self)(self._num * a._den - self._den * a._num, self._den * a._den)
+        if isinstance(a, int):
+            return type(self)(self._num - self._den * a, self._den)
+        return NotImplemented
+
+    def __rsub__(self, a: int) -> Self:
+        """Compute the difference of an integer and a field element."""
+        return type(self)(a) - self
+
+    def __mul__(self, a: int | Self) -> Self:
+        """Compute the product of two field elements (second may be int)."""
+        if isinstance(a, type(self)):
+            return type(self)(self._num * a._num, self._den * a._den)
+        if isinstance(a, int):
+            return type(self)(self._num * a, self._den)
+        return NotImplemented
+
+    def __rmul__(self, a: int) -> Self:
+        """Compute the product of an integer with a field element."""
+        return type(self)(a) * self
+
+    def __truediv__(self, a: int | Self) -> Self:
+        """Compute the ratio of two field elements (second may be int)."""
+        if isinstance(a, type(self)) or isinstance(a, int):
+            return type(self)(self, a)
+        return NotImplemented
+
+    def __pow__(self, a: int) -> Self:
+        """Raise a field element to an integer power."""
+        return type(self)(pow(self._num, a, self.SIZE), pow(self._den, a, self.SIZE))
+
+    def __neg__(self) -> Self:
+        """Negate a field element."""
+        return type(self)(-self._num, self._den)
+
+    def __int__(self) -> int:
+        """Convert a field element to an integer in range 0..SIZE-1. The result is cached."""
+        if self._den != 1:
+            self._num = (self._num * pow(self._den, -1, self.SIZE)) % self.SIZE
+            self._den = 1
+        return self._num
+
+    def sqrt(self) -> Self | None:
+        """Compute the square root of a field element if it exists (None otherwise)."""
+        raise NotImplementedError
+
+    def is_square(self) -> bool:
+        """Determine if this field element has a square root."""
+        # A more efficient algorithm is possible here (Jacobi symbol).
+        return self.sqrt() is not None
+
+    def is_even(self) -> bool:
+        """Determine whether this field element, represented as integer in 0..SIZE-1, is even."""
+        return int(self) & 1 == 0
+
+    def __eq__(self, a: object) -> bool:
+        """Check whether two field elements are equal (second may be an int)."""
+        if isinstance(a, type(self)):
+            return (self._num * a._den - self._den * a._num) % self.SIZE == 0
+        elif isinstance(a, int):
+            return (self._num - self._den * a) % self.SIZE == 0
+        return False # for other types
+
+    def to_bytes(self) -> bytes:
+        """Convert a field element to a 32-byte array (BE byte order)."""
+        return int(self).to_bytes(32, 'big')
+
+    @classmethod
+    def from_int_checked(cls, v: int) -> Self:
+        """Convert an integer to a field element (no overflow allowed)."""
+        if v >= cls.SIZE:
+            raise ValueError
+        return cls(v)
+
+    @classmethod
+    def from_int_wrapping(cls, v: int) -> Self:
+        """Convert an integer to a field element (reduced modulo SIZE)."""
+        return cls(v % cls.SIZE)
+
+    @classmethod
+    def from_bytes_checked(cls, b: bytes) -> Self:
+        """Convert a 32-byte array to a field element (BE byte order, no overflow allowed)."""
+        v = int.from_bytes(b, 'big')
+        return cls.from_int_checked(v)
+
+    @classmethod
+    def from_bytes_wrapping(cls, b: bytes) -> Self:
+        """Convert a 32-byte array to a field element (BE byte order, reduced modulo SIZE)."""
+        v = int.from_bytes(b, 'big')
+        return cls.from_int_wrapping(v)
+
+    def __str__(self) -> str:
+        """Convert this field element to a 64 character hex string."""
+        return f"{int(self):064x}"
+
+    def __repr__(self) -> str:
+        """Get a string representation of this field element."""
+        return f"{type(self).__qualname__}(0x{int(self):x})"
+
+
+class FE(APrimeFE):
+    SIZE = 2**256 - 2**32 - 977
+
+    def sqrt(self) -> Self | None:
+        # Due to the fact that our modulus p is of the form (p % 4) == 3, the Tonelli-Shanks
+        # algorithm (https://en.wikipedia.org/wiki/Tonelli-Shanks_algorithm) is simply
+        # raising the argument to the power (p + 1) / 4.
+
+        # To see why: (p-1) % 2 = 0, so 2 divides the order of the multiplicative group,
+        # and thus only half of the non-zero field elements are squares. An element a is
+        # a (nonzero) square when Euler's criterion, a^((p-1)/2) = 1 (mod p), holds. We're
+        # looking for x such that x^2 = a (mod p). Given a^((p-1)/2) = 1, that is equivalent
+        # to x^2 = a^(1 + (p-1)/2) mod p. As (1 + (p-1)/2) is even, this is equivalent to
+        # x = a^((1 + (p-1)/2)/2) mod p, or x = a^((p+1)/4) mod p.
+        v = int(self)
+        s = pow(v, (self.SIZE + 1) // 4, self.SIZE)
+        if s**2 % self.SIZE == v:
+            return type(self)(s)
+        return None
+
+
+class Scalar(APrimeFE):
+    """TODO Docstring"""
+    SIZE = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
+
+    @classmethod
+    def from_int_nonzero_checked(cls, v: int) -> Self:
+        """Convert an integer to a scalar (no zero or overflow allowed)."""
+        if not (0 < v < cls.SIZE):
+            raise ValueError
+        return cls(v)
+
+    @classmethod
+    def from_bytes_nonzero_checked(cls, b: bytes) -> Self:
+        """Convert a 32-byte array to a scalar (BE byte order, no zero or overflow allowed)."""
+        v = int.from_bytes(b, 'big')
+        return cls.from_int_nonzero_checked(v)
+
+
+class GE:
+    """Objects of this class represent secp256k1 group elements (curve points or infinity)
+
+    GE objects are immutable.
+
+    Normal points on the curve have fields:
+    * x: the x coordinate (a field element)
+    * y: the y coordinate (a field element, satisfying y^2 = x^3 + 7)
+    * infinity: False
+
+    The point at infinity has field:
+    * infinity: True
+    """
+
+    # TODO The following two class attributes should probably be just getters as
+    # classmethods to enforce immutability. Unfortunately Python makes it hard
+    # to create "classproperties". `G` could then also be just a classmethod.
+
+    # Order of the group (number of points on the curve, plus 1 for infinity)
+    ORDER = Scalar.SIZE
+
+    # Number of valid distinct x coordinates on the curve.
+    ORDER_HALF = ORDER // 2
+
+    @property
+    def infinity(self) -> bool:
+        """Whether the group element is the point at infinity."""
+        return self._infinity
+
+    @property
+    def x(self) -> FE:
+        """The x coordinate (a field element) of a non-infinite group element."""
+        assert not self.infinity
+        return self._x
+
+    @property
+    def y(self) -> FE:
+        """The y coordinate (a field element) of a non-infinite group element."""
+        assert not self.infinity
+        return self._y
+
+    def __init__(self, x: int | FE | None = None, y: int | FE | None = None) -> None:
+        """Initialize a group element with specified x and y coordinates, or infinity."""
+        if x is None:
+            # Initialize as infinity.
+            assert y is None
+            self._infinity = True
+        else:
+            # Initialize as point on the curve (and check that it is).
+            assert x is not None
+            assert y is not None
+            fx = FE(x)
+            fy = FE(y)
+            assert fy**2 == fx**3 + 7
+            self._infinity = False
+            self._x = fx
+            self._y = fy
+
+    def __add__(self, a: GE) -> GE:
+        """Add two group elements together."""
+        # Deal with infinity: a + infinity == infinity + a == a.
+        if self.infinity:
+            return a
+        if a.infinity:
+            return self
+        if self.x == a.x:
+            if self.y != a.y:
+                # A point added to its own negation is infinity.
+                assert self.y + a.y == 0
+                return GE()
+            else:
+                # For identical inputs, use the tangent (doubling formula).
+                lam = (3 * self.x**2) / (2 * self.y)
+        else:
+            # For distinct inputs, use the line through both points (adding formula).
+            lam = (self.y - a.y) / (self.x - a.x)
+        # Determine point opposite to the intersection of that line with the curve.
+        x = lam**2 - (self.x + a.x)
+        y = lam * (self.x - x) - self.y
+        return GE(x, y)
+
+    @staticmethod
+    def sum(*ps: GE) -> GE:
+        """Compute the sum of group elements.
+
+        GE.sum(a, b, c, ...) is identical to (GE() + a + b + c + ...)."""
+        return sum(ps, start=GE())
+
+    @staticmethod
+    def batch_mul(*aps: tuple[Scalar, GE]) -> GE:
+        """Compute a (batch) scalar group element multiplication.
+
+        GE.batch_mul((a1, p1), (a2, p2), (a3, p3)) is identical to a1*p1 + a2*p2 + a3*p3,
+        but more efficient."""
+        # Reduce all the scalars modulo order first (so we can deal with negatives etc).
+        naps = [(int(a), p) for a, p in aps]
+        # Start with point at infinity.
+        r = GE()
+        # Iterate over all bit positions, from high to low.
+        for i in range(255, -1, -1):
+            # Double what we have so far.
+            r = r + r
+            # Add then add the points for which the corresponding scalar bit is set.
+            for (a, p) in naps:
+                if (a >> i) & 1:
+                    r += p
+        return r
+
+    def __rmul__(self, a: int | Scalar) -> GE:
+        """Multiply an integer or scalar with a group element."""
+        if self == G:
+            return FAST_G.mul(Scalar(a))
+        return GE.batch_mul((Scalar(a), self))
+
+    def __neg__(self) -> GE:
+        """Compute the negation of a group element."""
+        if self.infinity:
+            return self
+        return GE(self.x, -self.y)
+
+    def __sub__(self, a: GE) -> GE:
+        """Subtract a group element from another."""
+        return self + (-a)
+
+    def __eq__(self, a: object) -> bool:
+        """Check if two group elements are equal."""
+        if not isinstance(a, type(self)):
+            return False
+        return (self - a).infinity
+
+    def has_even_y(self) -> bool:
+        """Determine whether a non-infinity group element has an even y coordinate."""
+        assert not self.infinity
+        return self.y.is_even()
+
+    def to_bytes_compressed(self) -> bytes:
+        """Convert a non-infinite group element to 33-byte compressed encoding."""
+        assert not self.infinity
+        return bytes([3 - self.y.is_even()]) + self.x.to_bytes()
+
+    def to_bytes_compressed_with_infinity(self) -> bytes:
+        """Convert a group element to 33-byte compressed encoding, mapping infinity to zeros."""
+        if self.infinity:
+            return 33 * b"\x00"
+        return self.to_bytes_compressed()
+
+    def to_bytes_uncompressed(self) -> bytes:
+        """Convert a non-infinite group element to 65-byte uncompressed encoding."""
+        assert not self.infinity
+        return b'\x04' + self.x.to_bytes() + self.y.to_bytes()
+
+    def to_bytes_xonly(self) -> bytes:
+        """Convert (the x coordinate of) a non-infinite group element to 32-byte xonly encoding."""
+        assert not self.infinity
+        return self.x.to_bytes()
+
+    @staticmethod
+    def lift_x(x: int | FE) -> GE:
+        """Return group element with specified field element as x coordinate (and even y)."""
+        y = (FE(x)**3 + 7).sqrt()
+        if y is None:
+            raise ValueError
+        if not y.is_even():
+            y = -y
+        return GE(x, y)
+
+    @staticmethod
+    def from_bytes_compressed(b: bytes) -> GE:
+        """Convert a compressed to a group element."""
+        assert len(b) == 33
+        if b[0] != 2 and b[0] != 3:
+            raise ValueError
+        x = FE.from_bytes_checked(b[1:])
+        r = GE.lift_x(x)
+        if b[0] == 3:
+            r = -r
+        return r
+
+    @staticmethod
+    def from_bytes_compressed_with_infinity(b: bytes) -> GE:
+        """Convert a compressed to a group element, mapping zeros to infinity."""
+        if b == 33 * b"\x00":
+            return GE()
+        else:
+            return GE.from_bytes_compressed(b)
+
+    @staticmethod
+    def from_bytes_uncompressed(b: bytes) -> GE:
+        """Convert an uncompressed to a group element."""
+        assert len(b) == 65
+        if b[0] != 4:
+            raise ValueError
+        x = FE.from_bytes_checked(b[1:33])
+        y = FE.from_bytes_checked(b[33:])
+        if y**2 != x**3 + 7:
+            raise ValueError
+        return GE(x, y)
+
+    @staticmethod
+    def from_bytes(b: bytes) -> GE:
+        """Convert a compressed or uncompressed encoding to a group element."""
+        assert len(b) in (33, 65)
+        if len(b) == 33:
+            return GE.from_bytes_compressed(b)
+        else:
+            return GE.from_bytes_uncompressed(b)
+
+    @staticmethod
+    def from_bytes_xonly(b: bytes) -> GE:
+        """Convert a point given in xonly encoding to a group element."""
+        assert len(b) == 32
+        x = FE.from_bytes_checked(b)
+        r = GE.lift_x(x)
+        return r
+
+    @staticmethod
+    def is_valid_x(x: int | FE) -> bool:
+        """Determine whether the provided field element is a valid X coordinate."""
+        return (FE(x)**3 + 7).is_square()
+
+    def __str__(self) -> str:
+        """Convert this group element to a string."""
+        if self.infinity:
+            return "(inf)"
+        return f"({self.x},{self.y})"
+
+    def __repr__(self) -> str:
+        """Get a string representation for this group element."""
+        if self.infinity:
+            return "GE()"
+        return f"GE(0x{int(self.x):x},0x{int(self.y):x})"
+
+    def __hash__(self) -> int:
+        """Compute a non-cryptographic hash of the group element."""
+        if self.infinity:
+            return 0  # 0 is not a valid x coordinate
+        return int(self.x)
+
+
+# The secp256k1 generator point
+G = GE.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)
+
+
+class FastGEMul:
+    """Table for fast multiplication with a constant group element.
+
+    Speed up scalar multiplication with a fixed point P by using a precomputed lookup table with
+    its powers of 2:
+
+        table = [P, 2*P, 4*P, (2^3)*P, (2^4)*P, ..., (2^255)*P]
+
+    During multiplication, the points corresponding to each bit set in the scalar are added up,
+    i.e. on average ~128 point additions take place.
+    """
+
+    def __init__(self, p: GE) -> None:
+        self.table: list[GE] = [p]  # table[i] = (2^i) * p
+        for _ in range(255):
+            p = p + p
+            self.table.append(p)
+
+    def mul(self, a: Scalar | int) -> GE:
+        result = GE()
+        a_ = int(a)
+        for bit in range(a_.bit_length()):
+            if a_ & (1 << bit):
+                result += self.table[bit]
+        return result
+
+# Precomputed table with multiples of G for fast multiplication
+FAST_G = FastGEMul(G)
@@ -0,0 +1,24 @@
+import hashlib
+
+
+# This implementation can be sped up by storing the midstate after hashing
+# tag_hash instead of rehashing it all the time.
+def tagged_hash(tag: str, msg: bytes) -> bytes:
+    tag_hash = hashlib.sha256(tag.encode()).digest()
+    return hashlib.sha256(tag_hash + tag_hash + msg).digest()
+
+
+def bytes_from_int(x: int) -> bytes:
+    return x.to_bytes(32, byteorder="big")
+
+
+def xor_bytes(b0: bytes, b1: bytes) -> bytes:
+    return bytes(x ^ y for (x, y) in zip(b0, b1))
+
+
+def int_from_bytes(b: bytes) -> int:
+    return int.from_bytes(b, byteorder="big")
+
+
+def hash_sha256(b: bytes) -> bytes:
+    return hashlib.sha256(b).digest()
@@ -0,0 +1,5 @@
+from pathlib import Path
+import sys
+
+# Ensure secp256k1lab is found and can be imported directly
+sys.path.insert(0, str(Path(__file__).parent / "../src/"))
@@ -0,0 +1,51 @@
+import csv
+from pathlib import Path
+from random import randbytes
+import unittest
+
+from secp256k1lab.bip340 import pubkey_gen, schnorr_sign, schnorr_verify
+
+
+class BIP340Tests(unittest.TestCase):
+    """Test schnorr signatures (BIP 340)."""
+
+    def test_correctness(self):
+        seckey = randbytes(32)
+        pubkey_xonly = pubkey_gen(seckey)
+        aux_rand = randbytes(32)
+        message = b'this is some arbitrary message'
+        signature = schnorr_sign(message, seckey, aux_rand)
+        success = schnorr_verify(message, pubkey_xonly, signature)
+        self.assertTrue(success)
+
+    def test_vectors(self):
+        # Test against vectors from the BIPs repository
+        # [https://github.com/bitcoin/bips/blob/master/bip-0340/test-vectors.csv]
+        vectors_file = Path(__file__).parent / "vectors" / "bip340.csv"
+        with open(vectors_file, encoding='utf8') as csvfile:
+            reader = csv.DictReader(csvfile)
+            for row in reader:
+                with self.subTest(i=int(row['index'])):
+                    self.subtest_vectors_case(row)
+
+    def subtest_vectors_case(self, row):
+        seckey = bytes.fromhex(row['secret key'])
+        pubkey_xonly = bytes.fromhex(row['public key'])
+        aux_rand = bytes.fromhex(row['aux_rand'])
+        msg = bytes.fromhex(row['message'])
+        sig = bytes.fromhex(row['signature'])
+        result_str = row['verification result']
+        comment = row['comment']
+
+        result = result_str == 'TRUE'
+        assert result or result_str == 'FALSE'
+        if seckey != b'':
+            pubkey_xonly_actual = pubkey_gen(seckey)
+            self.assertEqual(pubkey_xonly.hex(), pubkey_xonly_actual.hex(), f"BIP340 test vector ({comment}): pubkey mismatch")
+            sig_actual = schnorr_sign(msg, seckey, aux_rand)
+            self.assertEqual(sig.hex(), sig_actual.hex(), f"BIP340 test vector ({comment}): sig mismatch")
+        result_actual = schnorr_verify(msg, pubkey_xonly, sig)
+        if result:
+            self.assertEqual(result, result_actual, f"BIP340 test vector ({comment}): verification failed unexpectedly")
+        else:
+            self.assertEqual(result, result_actual, f"BIP340 test vector ({comment}): verification succeeded unexpectedly")
@@ -0,0 +1,18 @@
+from random import randbytes
+import unittest
+
+from secp256k1lab.ecdh import ecdh_libsecp256k1
+from secp256k1lab.keys import pubkey_gen_plain
+
+
+class ECDHTests(unittest.TestCase):
+    """Test ECDH module."""
+
+    def test_correctness(self):
+        seckey_alice = randbytes(32)
+        pubkey_alice = pubkey_gen_plain(seckey_alice)
+        seckey_bob = randbytes(32)
+        pubkey_bob = pubkey_gen_plain(seckey_bob)
+        shared_secret1 = ecdh_libsecp256k1(seckey_alice, pubkey_bob)
+        shared_secret2 = ecdh_libsecp256k1(seckey_bob, pubkey_alice)
+        self.assertEqual(shared_secret1, shared_secret2)
@@ -0,0 +1,180 @@
+"""Test low-level secp256k1 field and group arithmetic classes."""
+from random import randint
+import unittest
+
+from secp256k1lab.secp256k1 import FE, G, GE, Scalar
+
+
+class PrimeFieldTests(unittest.TestCase):
+    def test_fe_constructors(self):
+        P = FE.SIZE
+        random_fe_valid = randint(0, P-1)
+        random_fe_overflowing = randint(P, 2**256-1)
+
+        # wrapping constructors
+        for init_value in [0, P-1, P, P+1, random_fe_valid, random_fe_overflowing]:
+            fe1 = FE(init_value)
+            fe2 = FE.from_int_wrapping(init_value)
+            fe3 = FE.from_bytes_wrapping(init_value.to_bytes(32, 'big'))
+            reduced_value = init_value % P
+            self.assertEqual(int(fe1), reduced_value)
+            self.assertEqual(int(fe1), int(fe2))
+            self.assertEqual(int(fe2), int(fe3))
+
+        # checking constructors (should throw on overflow)
+        for valid_value in [0, P-1, random_fe_valid]:
+            fe1 = FE.from_int_checked(valid_value)
+            fe2 = FE.from_bytes_checked(valid_value.to_bytes(32, 'big'))
+            self.assertEqual(int(fe1), valid_value)
+            self.assertEqual(int(fe1), int(fe2))
+
+        for overflow_value in [P, P+1, random_fe_overflowing]:
+            with self.assertRaises(ValueError):
+                _ = FE.from_int_checked(overflow_value)
+            with self.assertRaises(ValueError):
+                _ = FE.from_bytes_checked(overflow_value.to_bytes(32, 'big'))
+
+    def test_scalar_constructors(self):
+        N = Scalar.SIZE
+        random_scalar_valid = randint(0, N-1)
+        random_scalar_overflowing = randint(N, 2**256-1)
+
+        # wrapping constructors
+        for init_value in [0, N-1, N, N+1, random_scalar_valid, random_scalar_overflowing]:
+            s1 = Scalar(init_value)
+            s2 = Scalar.from_int_wrapping(init_value)
+            s3 = Scalar.from_bytes_wrapping(init_value.to_bytes(32, 'big'))
+            reduced_value = init_value % N
+            self.assertEqual(int(s1), reduced_value)
+            self.assertEqual(int(s1), int(s2))
+            self.assertEqual(int(s2), int(s3))
+
+        # checking constructors (should throw on overflow)
+        for valid_value in [0, N-1, random_scalar_valid]:
+            s1 = Scalar.from_int_checked(valid_value)
+            s2 = Scalar.from_bytes_checked(valid_value.to_bytes(32, 'big'))
+            self.assertEqual(int(s1), valid_value)
+            self.assertEqual(int(s1), int(s2))
+
+        for overflow_value in [N, N+1, random_scalar_overflowing]:
+            with self.assertRaises(ValueError):
+                _ = Scalar.from_int_checked(overflow_value)
+            with self.assertRaises(ValueError):
+                _ = Scalar.from_bytes_checked(overflow_value.to_bytes(32, 'big'))
+
+        # non-zero checking constructors (should throw on zero or overflow, only for Scalar)
+        random_nonzero_scalar_valid = randint(1, N-1)
+        for valid_value in [1, N-1, random_nonzero_scalar_valid]:
+            s1 = Scalar.from_int_nonzero_checked(valid_value)
+            s2 = Scalar.from_bytes_nonzero_checked(valid_value.to_bytes(32, 'big'))
+            self.assertEqual(int(s1), valid_value)
+            self.assertEqual(int(s1), int(s2))
+
+        for invalid_value in [0, N, random_scalar_overflowing]:
+            with self.assertRaises(ValueError):
+                _ = Scalar.from_int_nonzero_checked(invalid_value)
+            with self.assertRaises(ValueError):
+                _ = Scalar.from_bytes_nonzero_checked(invalid_value.to_bytes(32, 'big'))
+
+
+class GeSerializationTests(unittest.TestCase):
+    @classmethod
+    def setUpClass(cls):
+        cls.point_at_infinity = GE()
+        cls.group_elements_on_curve = [
+            # generator point
+            G,
+            # Bitcoin genesis block public key
+            GE(0x678afdb0fe5548271967f1a67130b7105cd6a828e03909a67962e0ea1f61deb6,
+               0x49f6bc3f4cef38c4f35504e51ec112de5c384df7ba0b8d578a4c702b6bf11d5f),
+        ]
+        # generate a few random points, to likely cover both even/odd y polarity
+        cls.group_elements_on_curve.extend([randint(1, Scalar.SIZE-1) * G for _ in range(8)])
+        # generate x coordinates that don't have a valid point on the curve
+        # (note that ~50% of all x coordinates are valid, so finding one needs two loop iterations on average)
+        cls.x_coords_not_on_curve = []
+        while len(cls.x_coords_not_on_curve) < 8:
+            x = randint(0, FE.SIZE-1)
+            if not GE.is_valid_x(x):
+                cls.x_coords_not_on_curve.append(x)
+
+        cls.group_elements = [cls.point_at_infinity] + cls.group_elements_on_curve
+
+    def test_infinity_raises(self):
+        with self.assertRaises(AssertionError):
+            _ = self.point_at_infinity.to_bytes_uncompressed()
+        with self.assertRaises(AssertionError):
+            _ = self.point_at_infinity.to_bytes_compressed()
+        with self.assertRaises(AssertionError):
+            _ = self.point_at_infinity.to_bytes_xonly()
+
+    def test_not_on_curve_raises(self):
+        # for compressed and x-only GE deserialization, test with invalid x coordinate
+        for x in self.x_coords_not_on_curve:
+            x_bytes = x.to_bytes(32, 'big')
+            with self.assertRaises(ValueError):
+                _ = GE.from_bytes_compressed(b'\x02' + x_bytes)
+            with self.assertRaises(ValueError):
+                _ = GE.from_bytes_compressed(b'\x03' + x_bytes)
+            with self.assertRaises(ValueError):
+                _ = GE.from_bytes_compressed_with_infinity(b'\x02' + x_bytes)
+            with self.assertRaises(ValueError):
+                _ = GE.from_bytes_compressed_with_infinity(b'\x03' + x_bytes)
+            with self.assertRaises(ValueError):
+                _ = GE.from_bytes_xonly(x_bytes)
+
+        # for uncompressed GE serialization, test by invalidating either coordinate
+        for ge in self.group_elements_on_curve:
+            valid_x = ge.x
+            valid_y = ge.y
+            invalid_x = ge.x + 1
+            invalid_y = ge.y + 1
+
+            # valid cases (if point (x,y) is on the curve, then point(x,-y) is on the curve as well)
+            _ = GE.from_bytes_uncompressed(b'\x04' + valid_x.to_bytes() + valid_y.to_bytes())
+            _ = GE.from_bytes_uncompressed(b'\x04' + valid_x.to_bytes() + (-valid_y).to_bytes())
+            # invalid cases (curve equation y**2 = x**3 + 7 doesn't hold)
+            self.assertNotEqual(invalid_y**2, valid_x**3 + 7)
+            with self.assertRaises(ValueError):
+                _ = GE.from_bytes_uncompressed(b'\x04' + valid_x.to_bytes() + invalid_y.to_bytes())
+            self.assertNotEqual(valid_y**2, invalid_x**3 + 7)
+            with self.assertRaises(ValueError):
+                _ = GE.from_bytes_uncompressed(b'\x04' + invalid_x.to_bytes() + valid_y.to_bytes())
+
+    def test_affine(self):
+        # GE serialization and parsing round-trip (variants that only support serializing points on the curve)
+        for ge_orig in self.group_elements_on_curve:
+            # uncompressed serialization: 65 bytes, starts with 0x04
+            ge_ser = ge_orig.to_bytes_uncompressed()
+            self.assertEqual(len(ge_ser), 65)
+            self.assertEqual(ge_ser[0], 0x04)
+            ge_deser = GE.from_bytes_uncompressed(ge_ser)
+            self.assertEqual(ge_deser, ge_orig)
+
+            # compressed serialization: 33 bytes, starts with 0x02 (if y is even) or 0x03 (if y is odd)
+            ge_ser = ge_orig.to_bytes_compressed()
+            self.assertEqual(len(ge_ser), 33)
+            self.assertEqual(ge_ser[0], 0x02 if ge_orig.has_even_y() else 0x03)
+            ge_deser = GE.from_bytes_compressed(ge_ser)
+            self.assertEqual(ge_deser, ge_orig)
+
+            # x-only serialization: 32 bytes
+            ge_ser = ge_orig.to_bytes_xonly()
+            self.assertEqual(len(ge_ser), 32)
+            ge_deser = GE.from_bytes_xonly(ge_ser)
+            if not ge_orig.has_even_y():  # x-only implies even y, so flip if necessary
+                ge_deser = -ge_deser
+            self.assertEqual(ge_deser, ge_orig)
+
+    def test_affine_with_infinity(self):
+        # GE serialization and parsing round-trip (variants that also support serializing the point at infinity)
+        for ge_orig in self.group_elements:
+            # compressed serialization: 33 bytes, all-zeros for point at infinity
+            ge_ser = ge_orig.to_bytes_compressed_with_infinity()
+            self.assertEqual(len(ge_ser), 33)
+            if ge_orig.infinity:
+                self.assertEqual(ge_ser, b'\x00'*33)
+            else:
+                self.assertEqual(ge_ser[0], 0x02 if ge_orig.has_even_y() else 0x03)
+            ge_deser = GE.from_bytes_compressed_with_infinity(ge_ser)
+            self.assertEqual(ge_deser, ge_orig)
@@ -0,0 +1,20 @@
+index,secret key,public key,aux_rand,message,signature,verification result,comment
+0,0000000000000000000000000000000000000000000000000000000000000003,F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9,0000000000000000000000000000000000000000000000000000000000000000,0000000000000000000000000000000000000000000000000000000000000000,E907831F80848D1069A5371B402410364BDF1C5F8307B0084C55F1CE2DCA821525F66A4A85EA8B71E482A74F382D2CE5EBEEE8FDB2172F477DF4900D310536C0,TRUE,
+1,B7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,0000000000000000000000000000000000000000000000000000000000000001,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,6896BD60EEAE296DB48A229FF71DFE071BDE413E6D43F917DC8DCF8C78DE33418906D11AC976ABCCB20B091292BFF4EA897EFCB639EA871CFA95F6DE339E4B0A,TRUE,
+2,C90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B14E5C9,DD308AFEC5777E13121FA72B9CC1B7CC0139715309B086C960E18FD969774EB8,C87AA53824B4D7AE2EB035A2B5BBBCCC080E76CDC6D1692C4B0B62D798E6D906,7E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C,5831AAEED7B44BB74E5EAB94BA9D4294C49BCF2A60728D8B4C200F50DD313C1BAB745879A5AD954A72C45A91C3A51D3C7ADEA98D82F8481E0E1E03674A6F3FB7,TRUE,
+3,0B432B2677937381AEF05BB02A66ECD012773062CF3FA2549E44F58ED2401710,25D1DFF95105F5253C4022F628A996AD3A0D95FBF21D468A1B33F8C160D8F517,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,7EB0509757E246F19449885651611CB965ECC1A187DD51B64FDA1EDC9637D5EC97582B9CB13DB3933705B32BA982AF5AF25FD78881EBB32771FC5922EFC66EA3,TRUE,test fails if msg is reduced modulo p or n
+4,,D69C3509BB99E412E68B0FE8544E72837DFA30746D8BE2AA65975F29D22DC7B9,,4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703,00000000000000000000003B78CE563F89A0ED9414F5AA28AD0D96D6795F9C6376AFB1548AF603B3EB45C9F8207DEE1060CB71C04E80F593060B07D28308D7F4,TRUE,
+5,,EEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E17776969E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B,FALSE,public key not on the curve
+6,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,FFF97BD5755EEEA420453A14355235D382F6472F8568A18B2F057A14602975563CC27944640AC607CD107AE10923D9EF7A73C643E166BE5EBEAFA34B1AC553E2,FALSE,has_even_y(R) is false
+7,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,1FA62E331EDBC21C394792D2AB1100A7B432B013DF3F6FF4F99FCB33E0E1515F28890B3EDB6E7189B630448B515CE4F8622A954CFE545735AAEA5134FCCDB2BD,FALSE,negated message
+8,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E177769961764B3AA9B2FFCB6EF947B6887A226E8D7C93E00C5ED0C1834FF0D0C2E6DA6,FALSE,negated s value
+9,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,0000000000000000000000000000000000000000000000000000000000000000123DDA8328AF9C23A94C1FEECFD123BA4FB73476F0D594DCB65C6425BD186051,FALSE,sG - eP is infinite. Test fails in single verification if has_even_y(inf) is defined as true and x(inf) as 0
+10,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,00000000000000000000000000000000000000000000000000000000000000017615FBAF5AE28864013C099742DEADB4DBA87F11AC6754F93780D5A1837CF197,FALSE,sG - eP is infinite. Test fails in single verification if has_even_y(inf) is defined as true and x(inf) as 1
+11,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D69E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B,FALSE,sig[0:32] is not an X coordinate on the curve
+12,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F69E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B,FALSE,sig[0:32] is equal to field size
+13,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E177769FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141,FALSE,sig[32:64] is equal to curve order
+14,,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC30,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E17776969E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B,FALSE,public key is not a valid X coordinate because it exceeds the field size
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