Squashed 'src/secp256k1/' changes from 705ce7e..c545fdc

c545fdc Merge bitcoin-core/secp256k1#1298: Remove randomness tests b40e2d3 Merge bitcoin-core/secp256k1#1378: ellswift: fix probabilistic test failure when swapping sides c424e2f ellswift: fix probabilistic test failure when swapping sides 907a672 Merge bitcoin-core/secp256k1#1313: ci: Test on development snapshots of GCC and Clang 0f7657d Merge bitcoin-core/secp256k1#1366: field: Use `restrict` consistently in fe_sqrt cc55757 Merge bitcoin-core/secp256k1#1340: clean up in-comment Sage code (refer to secp256k1_params.sage, update to Python3) 600c5ad clean up in-comment Sage code (refer to secp256k1_params.sage, update to Python3) 981e5be ci: Fix typo in comment e9e9648 ci: Reduce number of macOS tasks from 28 to 8 609093b ci: Add x86_64 Linux tasks for gcc and clang snapshots 1deecaa ci: Install development snapshots of gcc and clang b79ba8a field: Use `restrict` consistently in fe_sqrt c9ebca9 Merge bitcoin-core/secp256k1#1363: doc: minor ellswift.md updates afd7eb4 Merge bitcoin-core/secp256k1#1371: Add exhaustive tests for ellswift (with create+decode roundtrip) 2792119 Add exhaustive test for ellswift (create+decode roundtrip) c7d900f doc: minor ellswift.md updates 332af31 Merge bitcoin-core/secp256k1#1344: group: save normalize_weak calls in `secp256k1_ge_is_valid_var`/`secp256k1_gej_eq_x_var` 9e6d1b0 Merge bitcoin-core/secp256k1#1367: build: Improvements to symbol visibility logic on Windows (attempt 3) 0aacf64 Merge bitcoin-core/secp256k1#1370: Corrected some typos b6b9834 small fixes 07c0e8b group: remove unneeded normalize_weak in `secp256k1_gej_eq_x_var` 3fc1de5 Merge bitcoin-core/secp256k1#1364: Avoid `-Wmaybe-uninitialized` when compiling with `gcc -O1` fb758fe Merge bitcoin-core/secp256k1#1323: tweak_add: fix API doc for tweak=0 c6cd2b1 ci: Add task for static library on Windows + CMake 020bf69 build: Add extensive docs on visibility issues 0196e8a build: Introduce `SECP256k1_DLL_EXPORT` macro 9f1b190 refactor: Replace `SECP256K1_API_VAR` with `SECP256K1_API` ae9db95 build: Introduce `SECP256K1_STATIC` macro for Windows users 7966aee Merge bitcoin-core/secp256k1#1369: ci: Print commit in Windows container a7bec34 ci: Print commit in Windows container 249c81e Merge bitcoin-core/secp256k1#1368: ci: Drop manual checkout of merge commit 98579e2 ci: Drop manual checkout of merge commit 5b9f37f ci: Add `CFLAGS: -O1` to task matrix a6ca76c Avoid `-Wmaybe-uninitialized` when compiling with `gcc -O1` 0fa84f8 Merge bitcoin-core/secp256k1#1358: tests: introduce helper for non-zero `random_fe_test()` results 5a95a26 tests: introduce helper for non-zero `random_fe_test` results 304421d tests: refactor: remove duplicate function `random_field_element_test` 3aef6ab Merge bitcoin-core/secp256k1#1345: field: Static-assert that int args affecting magnitude are constant 4494a36 Merge bitcoin-core/secp256k1#1357: tests: refactor: take use of `secp256k1_ge_x_on_curve_var` 799f4ee Merge bitcoin-core/secp256k1#1356: ci: Adjust Docker image to Debian 12 "bookworm" c862a9f ci: Adjust Docker image to Debian 12 "bookworm" a178209 ci: Force DWARF v4 for Clang when Valgrind tests are expected 7d8d5c8 tests: refactor: take use of `secp256k1_ge_x_on_curve_var` 8a72734 Help the compiler prove that a loop is entered fd491ea Merge bitcoin-core/secp256k1#1355: Fix a typo in the error message ac43613 Merge bitcoin-core/secp256k1#1354: Add ellswift to CHANGELOG 67887ae Fix a typo in the error message 926dd3e Merge bitcoin-core/secp256k1#1295: abi: Use dllexport for mingw builds 1083683 Merge bitcoin-core/secp256k1#1336: Use `__shiftright128` intrinsic in `secp256k1_u128_rshift` on MSVC 7c7467a Refer to ellswift.md in API docs c32ffd8 Add ellswift to CHANGELOG 3c1a0fd Merge bitcoin-core/secp256k1#1347: field: Document return value of fe_sqrt() 5779137 field: Document return value of fe_sqrt() be8ff3a field: Static-assert that int args affecting magnitude are constant efa76c4 group: remove unneeded normalize_weak in `secp256k1_ge_is_valid_var` 5b7bf2e Use `__shiftright128` intrinsic in `secp256k1_u128_rshift` on MSVC 05873bb tweak_add: fix API doc for tweak=0 6ec3731 Simplify test PRNG implementation fb5bfa4 Add static test vector for Xoshiro256++ 723e8ca Remove randomness tests bc7c8db abi: Use dllexport for mingw builds git-subtree-dir: src/secp256k1 git-subtree-split: c545fdc
fanquake · Jul 18, 2023 · ff061fd · ff061fd
1 parent 901336e
commit ff061fd
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Showing 36 changed files with 373 additions and 331 deletions.
diff --git a/.cirrus.yml b/.cirrus.yml
@@ -54,12 +54,6 @@ cat_logs_snippet: &CAT_LOGS
     cat_ci_env_script:
       - env
 
-merge_base_script_snippet: &MERGE_BASE
-  merge_base_script:
-    - if [ "$CIRRUS_PR" = "" ]; then exit 0; fi
-    - git fetch --depth=1 $CIRRUS_REPO_CLONE_URL "pull/${CIRRUS_PR}/merge"
-    - git checkout FETCH_HEAD  # Use merged changes to detect silent merge conflicts
-
 linux_container_snippet: &LINUX_CONTAINER
   container:
     dockerfile: ci/linux-debian.Dockerfile
@@ -68,12 +62,12 @@ linux_container_snippet: &LINUX_CONTAINER
     # Gives us more CPUs for free if they're available.
     greedy: true
     # More than enough for our scripts.
-    memory: 1G
+    memory: 2G
 
 task:
   name: "x86_64: Linux (Debian stable)"
   << : *LINUX_CONTAINER
-  matrix: &ENV_MATRIX
+  matrix:
     - env: {WIDEMUL:  int64,  RECOVERY: yes}
     - env: {WIDEMUL:  int64,                 ECDH: yes, SCHNORRSIG: yes, ELLSWIFT: yes}
     - env: {WIDEMUL: int128}
@@ -86,14 +80,18 @@ task:
     - env: {BUILD: distcheck, WITH_VALGRIND: no, CTIMETESTS: no, BENCH: no}
     - env: {CPPFLAGS: -DDETERMINISTIC}
     - env: {CFLAGS: -O0, CTIMETESTS: no}
+    - env: {CFLAGS: -O1, RECOVERY: yes, ECDH: yes, SCHNORRSIG: yes, ELLSWIFT: yes}
     - env: { ECMULTGENPRECISION: 2, ECMULTWINDOW: 2 }
     - env: { ECMULTGENPRECISION: 8, ECMULTWINDOW: 4 }
   matrix:
     - env:
         CC: gcc
     - env:
         CC: clang
-  << : *MERGE_BASE
+    - env:
+        CC: gcc-snapshot
+    - env:
+        CC: clang-snapshot
   test_script:
     - ./ci/cirrus.sh
   << : *CAT_LOGS
@@ -111,7 +109,6 @@ task:
         CC: i686-linux-gnu-gcc
     - env:
         CC: clang --target=i686-pc-linux-gnu -isystem /usr/i686-linux-gnu/include
-  << : *MERGE_BASE
   test_script:
     - ./ci/cirrus.sh
   << : *CAT_LOGS
@@ -125,20 +122,22 @@ task:
     HOMEBREW_NO_INSTALL_CLEANUP: 1
     # Cirrus gives us a fixed number of 4 virtual CPUs. Not that we even have that many jobs at the moment...
     MAKEFLAGS: -j5
-  matrix:
-    << : *ENV_MATRIX
   env:
     ASM: no
     WITH_VALGRIND: no
     CTIMETESTS: no
+    CC: clang
   matrix:
-    - env:
-        CC: gcc
-    - env:
-        CC: clang
+    - env: {WIDEMUL:  int64,  RECOVERY: yes, ECDH: yes, SCHNORRSIG: yes, ELLSWIFT: yes}
+    - env: {WIDEMUL:  int64,  RECOVERY: yes, ECDH: yes, SCHNORRSIG: yes, ELLSWIFT: yes, CC: gcc}
+    - env: {WIDEMUL: int128_struct, ECMULTGENPRECISION: 2, ECMULTWINDOW: 4}
+    - env: {WIDEMUL: int128,                 ECDH: yes, SCHNORRSIG: yes, ELLSWIFT: yes}
+    - env: {WIDEMUL: int128,  RECOVERY: yes,            SCHNORRSIG: yes}
+    - env: {WIDEMUL: int128,  RECOVERY: yes, ECDH: yes, SCHNORRSIG: yes, ELLSWIFT: yes, CC: gcc}
+    - env: {WIDEMUL: int128,  RECOVERY: yes, ECDH: yes, SCHNORRSIG: yes, ELLSWIFT: yes, CPPFLAGS: -DVERIFY}
+    - env: {BUILD: distcheck}
   brew_script:
     - brew install automake libtool gcc
-  << : *MERGE_BASE
   test_script:
     - ./ci/cirrus.sh
   << : *CAT_LOGS
@@ -157,7 +156,6 @@ task:
     SCHNORRSIG: yes
     ELLSWIFT: yes
     CTIMETESTS: no
-  << : *MERGE_BASE
   test_script:
     # https://sourceware.org/bugzilla/show_bug.cgi?id=27008
     - rm /etc/ld.so.cache
@@ -180,7 +178,6 @@ task:
   matrix:
     - env: {}
     - env: {EXPERIMENTAL: yes, ASM: arm32}
-  << : *MERGE_BASE
   test_script:
     - ./ci/cirrus.sh
   << : *CAT_LOGS
@@ -198,7 +195,6 @@ task:
     SCHNORRSIG: yes
     ELLSWIFT: yes
     CTIMETESTS: no
-  << : *MERGE_BASE
   test_script:
     - ./ci/cirrus.sh
   << : *CAT_LOGS
@@ -216,7 +212,6 @@ task:
     SCHNORRSIG: yes
     ELLSWIFT: yes
     CTIMETESTS: no
-  << : *MERGE_BASE
   test_script:
     - ./ci/cirrus.sh
   << : *CAT_LOGS
@@ -237,7 +232,6 @@ task:
     - name: "i686 (mingw32-w64): Windows (Debian stable, Wine)"
       env:
         HOST: i686-w64-mingw32
-  << : *MERGE_BASE
   test_script:
     - ./ci/cirrus.sh
   << : *CAT_LOGS
@@ -280,7 +274,6 @@ task:
         CC: /opt/msvc/bin/x86/cl
         AR: /opt/msvc/bin/x86/lib
         NM: /opt/msvc/bin/x86/dumpbin -symbols -headers
-  << : *MERGE_BASE
   test_script:
     - ./ci/cirrus.sh
   << : *CAT_LOGS
@@ -325,7 +318,6 @@ task:
     - env:
         HOST: i686-linux-gnu
         CC: i686-linux-gnu-gcc
-  << : *MERGE_BASE
   test_script:
     - ./ci/cirrus.sh
   << : *CAT_LOGS
@@ -352,7 +344,6 @@ task:
         ECMULTGENPRECISION: 2
         ECMULTWINDOW: 2
         CFLAGS: "-fsanitize=memory -g -O3"
-  << : *MERGE_BASE
   test_script:
     - ./ci/cirrus.sh
   << : *CAT_LOGS
@@ -369,7 +360,6 @@ task:
     RECOVERY: yes
     SCHNORRSIG: yes
     ELLSWIFT: yes
-  << : *MERGE_BASE
   test_script:
     - ./ci/cirrus.sh
   << : *CAT_LOGS
@@ -401,11 +391,17 @@ task:
     # Ignore MSBuild warning MSB8029.
     # See: https://learn.microsoft.com/en-us/visualstudio/msbuild/errors/msb8029?view=vs-2022
     IgnoreWarnIntDirInTempDetected: 'true'
-  merge_script:
-    - PowerShell -NoLogo -Command if ($env:CIRRUS_PR -ne $null) { git fetch $env:CIRRUS_REPO_CLONE_URL pull/$env:CIRRUS_PR/merge; git reset --hard FETCH_HEAD; }
+  matrix:
+    - env:
+        BUILD_SHARED_LIBS: ON
+    - env:
+        BUILD_SHARED_LIBS: OFF
+  git_show_script:
+    # Print commit to allow reproducing the job outside of CI.
+    - git show --no-patch
   configure_script:
     - '%x64_NATIVE_TOOLS%'
-    - cmake -E env CFLAGS="/WX" cmake -G "Visual Studio 17 2022" -A x64 -S . -B build -DSECP256K1_ENABLE_MODULE_RECOVERY=ON -DSECP256K1_BUILD_EXAMPLES=ON
+    - cmake -E env CFLAGS="/WX" cmake -A x64 -B build -DSECP256K1_ENABLE_MODULE_RECOVERY=ON -DSECP256K1_BUILD_EXAMPLES=ON -DBUILD_SHARED_LIBS=%BUILD_SHARED_LIBS%
   build_script:
     - '%x64_NATIVE_TOOLS%'
     - cmake --build build --config RelWithDebInfo -- -property:UseMultiToolTask=true;CL_MPcount=5

diff --git a/CHANGELOG.md b/CHANGELOG.md
@@ -7,6 +7,16 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ## [Unreleased]
 
+#### Added
+ - New module `ellswift` implements ElligatorSwift encoding for public keys and x-only Diffie-Hellman key exchange for them.
+   ElligatorSwift permits representing secp256k1 public keys as 64-byte arrays which cannot be distinguished from uniformly random. See:
+   - Header file `include/secp256k1_ellswift.h` which defines the new API.
+   - Document `doc/ellswift.md` which explains the mathematical background of the scheme.
+   - The [paper](https://eprint.iacr.org/2022/759) on which the scheme is based.
+
+#### Changed
+ - When consuming libsecp256k1 as a static library on Windows, the user must now define the `SECP256K1_STATIC` macro before including `secp256k1.h`.
+
 ## [0.3.2] - 2023-05-13
 We strongly recommend updating to 0.3.2 if you use or plan to use GCC >=13 to compile libsecp256k1. When in doubt, check the GCC version using `gcc -v`.
 

diff --git a/Makefile.am b/Makefile.am
@@ -153,7 +153,7 @@ endif
 if USE_EXAMPLES
 noinst_PROGRAMS += ecdsa_example
 ecdsa_example_SOURCES = examples/ecdsa.c
-ecdsa_example_CPPFLAGS = -I$(top_srcdir)/include
+ecdsa_example_CPPFLAGS = -I$(top_srcdir)/include -DSECP256K1_STATIC
 ecdsa_example_LDADD = libsecp256k1.la
 ecdsa_example_LDFLAGS = -static
 if BUILD_WINDOWS
@@ -163,7 +163,7 @@ TESTS += ecdsa_example
 if ENABLE_MODULE_ECDH
 noinst_PROGRAMS += ecdh_example
 ecdh_example_SOURCES = examples/ecdh.c
-ecdh_example_CPPFLAGS = -I$(top_srcdir)/include
+ecdh_example_CPPFLAGS = -I$(top_srcdir)/include -DSECP256K1_STATIC
 ecdh_example_LDADD = libsecp256k1.la
 ecdh_example_LDFLAGS = -static
 if BUILD_WINDOWS
@@ -174,7 +174,7 @@ endif
 if ENABLE_MODULE_SCHNORRSIG
 noinst_PROGRAMS += schnorr_example
 schnorr_example_SOURCES = examples/schnorr.c
-schnorr_example_CPPFLAGS = -I$(top_srcdir)/include
+schnorr_example_CPPFLAGS = -I$(top_srcdir)/include -DSECP256K1_STATIC
 schnorr_example_LDADD = libsecp256k1.la
 schnorr_example_LDFLAGS = -static
 if BUILD_WINDOWS

diff --git a/ci/cirrus.sh b/ci/cirrus.sh
@@ -4,7 +4,8 @@ set -eux
 
 export LC_ALL=C
 
-# Print relevant CI environment to allow reproducing the job outside of CI.
+# Print commit and relevant CI environment to allow reproducing the job outside of CI.
+git show --no-patch
 print_environment() {
     # Turn off -x because it messes up the output
     set +x
@@ -53,6 +54,22 @@ if [ -n "$WRAPPER_CMD" ]; then
     $WRAPPER_CMD --version
 fi
 
+# Workaround for https://bugs.kde.org/show_bug.cgi?id=452758 (fixed in valgrind 3.20.0).
+case "${CC:-undefined}" in
+    clang*)
+        if [ "$CTIMETESTS" = "yes" ] && [ "$WITH_VALGRIND" = "yes" ]
+        then
+            export CFLAGS="${CFLAGS:+$CFLAGS }-gdwarf-4"
+        else
+            case "$WRAPPER_CMD" in
+                valgrind*)
+                    export CFLAGS="${CFLAGS:+$CFLAGS }-gdwarf-4"
+                    ;;
+            esac
+        fi
+        ;;
+esac
+
 ./autogen.sh
 
 ./configure \

diff --git a/ci/linux-debian.Dockerfile b/ci/linux-debian.Dockerfile
@@ -1,5 +1,7 @@
 FROM debian:stable
 
+SHELL ["/bin/bash", "-c"]
+
 RUN dpkg --add-architecture i386 && \
     dpkg --add-architecture s390x && \
     dpkg --add-architecture armhf && \
@@ -9,11 +11,11 @@ RUN dpkg --add-architecture i386 && \
 # dkpg-dev: to make pkg-config work in cross-builds
 # llvm: for llvm-symbolizer, which is used by clang's UBSan for symbolized stack traces
 RUN apt-get update && apt-get install --no-install-recommends -y \
-        git ca-certificates \
+        git ca-certificates wget \
         make automake libtool pkg-config dpkg-dev valgrind qemu-user \
-        gcc clang llvm libc6-dbg \
+        gcc clang llvm libclang-rt-dev libc6-dbg \
         g++ \
-        gcc-i686-linux-gnu libc6-dev-i386-cross libc6-dbg:i386 libubsan1:i386 libasan6:i386 \
+        gcc-i686-linux-gnu libc6-dev-i386-cross libc6-dbg:i386 libubsan1:i386 libasan8:i386 \
         gcc-s390x-linux-gnu libc6-dev-s390x-cross libc6-dbg:s390x \
         gcc-arm-linux-gnueabihf libc6-dev-armhf-cross libc6-dbg:armhf \
         gcc-aarch64-linux-gnu libc6-dev-arm64-cross libc6-dbg:arm64 \
@@ -23,9 +25,44 @@ RUN apt-get update && apt-get install --no-install-recommends -y \
         sagemath
 
 WORKDIR /root
-# The "wine" package provides a convience wrapper that we need
+
+# Build and install gcc snapshot
+ARG GCC_SNAPSHOT_MAJOR=14
+RUN wget --progress=dot:giga --https-only --recursive --accept '*.tar.xz' --level 1 --no-directories "https://gcc.gnu.org/pub/gcc/snapshots/LATEST-${GCC_SNAPSHOT_MAJOR}" && \
+    wget "https://gcc.gnu.org/pub/gcc/snapshots/LATEST-${GCC_SNAPSHOT_MAJOR}/sha512.sum" && \
+    sha512sum --check --ignore-missing sha512.sum && \
+    # We should have downloaded exactly one tar.xz file
+    ls && \
+    [[ $(ls *.tar.xz | wc -l) -eq "1" ]] && \
+    tar xf *.tar.xz && \
+    mkdir gcc-build && cd gcc-build && \
+    apt-get update && apt-get install --no-install-recommends -y libgmp-dev libmpfr-dev libmpc-dev flex && \
+    ../*/configure --prefix=/opt/gcc-snapshot --enable-languages=c --disable-bootstrap --disable-multilib --without-isl && \
+    make -j $(nproc) && \
+    make install && \
+    ln -s /opt/gcc-snapshot/bin/gcc /usr/bin/gcc-snapshot
+
+# Install clang snapshot
+RUN wget -qO- https://apt.llvm.org/llvm-snapshot.gpg.key | tee /etc/apt/trusted.gpg.d/apt.llvm.org.asc && \
+    # Add repository for this Debian release
+    . /etc/os-release && echo "deb http://apt.llvm.org/${VERSION_CODENAME} llvm-toolchain-${VERSION_CODENAME} main" >> /etc/apt/sources.list && \
+    # Install clang snapshot
+    apt-get update && apt-get install --no-install-recommends -y clang && \
+    # Remove just the "clang" symlink again
+    apt-get remove -y clang && \
+    # We should have exactly two clang versions now
+    ls /usr/bin/clang* && \
+    [[    $(ls /usr/bin/clang-?? | sort | wc -l) -eq "2" ]] && \
+    # Create symlinks for them
+    ln -s $(ls /usr/bin/clang-?? | sort | tail -1) /usr/bin/clang-snapshot && \
+    ln -s $(ls /usr/bin/clang-?? | sort | head -1) /usr/bin/clang
+
+# The "wine" package provides a convenience wrapper that we need
 RUN apt-get update && apt-get install --no-install-recommends -y \
         git ca-certificates wine64 wine python3-simplejson python3-six msitools winbind procps && \
+# Workaround for `wine` package failure to employ the Debian alternatives system properly.
+    ln -s /usr/lib/wine/wine64 /usr/bin/wine64 && \
+# Set of tools for using MSVC on Linux.
     git clone https://github.com/mstorsjo/msvc-wine && \
     mkdir /opt/msvc && \
     python3 msvc-wine/vsdownload.py --accept-license --dest /opt/msvc Microsoft.VisualStudio.Workload.VCTools && \

diff --git a/configure.ac b/configure.ac
@@ -127,12 +127,6 @@ AC_DEFUN([SECP_TRY_APPEND_DEFAULT_CFLAGS], [
       SECP_TRY_APPEND_CFLAGS([-wd4267], $1) # Disable warning C4267 "'var' : conversion from 'size_t' to 'type', possible loss of data".
       # Eliminate deprecation warnings for the older, less secure functions.
       CPPFLAGS="-D_CRT_SECURE_NO_WARNINGS $CPPFLAGS"
-      # We pass -ignore:4217 to the MSVC linker to suppress warning 4217 when
-      # importing variables from a statically linked secp256k1.
-      # (See the libtool manual, section "Windows DLLs" for background.)
-      # Unfortunately, libtool tries to be too clever and strips "-Xlinker arg"
-      # into "arg", so this will be " -Xlinker -ignore:4217" after stripping.
-      LDFLAGS="-Xlinker -Xlinker -Xlinker -ignore:4217 $LDFLAGS" 
     fi
 ])
 SECP_TRY_APPEND_DEFAULT_CFLAGS(SECP_CFLAGS)

diff --git a/doc/ellswift.md b/doc/ellswift.md
@@ -88,7 +88,7 @@ $$
 \begin{array}{lcl}
 X(u, t) & = & \left\\{\begin{array}{ll}
   \dfrac{g(u) - t^2}{2t} & a = 0 \\
-  \dfrac{g(u) + h(u)(Y_0(u) + X_0(u)t)^2}{X_0(u)(1 + h(u)t^2)} & a \neq 0
+  \dfrac{g(u) + h(u)(Y_0(u) - X_0(u)t)^2}{X_0(u)(1 + h(u)t^2)} & a \neq 0
 \end{array}\right. \\
 Y(u, t) & = & \left\\{\begin{array}{ll}
   \dfrac{X(u, t) + t}{u \sqrt{-3}} = \dfrac{g(u) + t^2}{2tu\sqrt{-3}} & a = 0 \\
@@ -329,7 +329,7 @@ $t$ value for multiple $c$ inputs (thereby biasing that encoding):
     it requires $g(u)=0$ which is already outlawed on even-ordered curves and impossible on others; in the second it would trigger division by zero.
 * Curve-specific special cases also exist that need to be rejected, because they result in $(u,t)$ which is invalid to the decoder, or because of division by zero in the encoder:
   * For $a=0$ curves, when $u=0$ or when $t=0$. The latter can only be reached by the encoder when $g(u)=0$, which requires an even-ordered curve.
-  * For $a \neq 0$ curves, when $X_0(u)=0$, when $h(u)t^2 = -1$, or when $2w(u + 2v) = 2X_0(u)$ while also either $w \neq 2Y_0(u)$ or $h(u)=0$.
+  * For $a \neq 0$ curves, when $X_0(u)=0$, when $h(u)t^2 = -1$, or when $w(u + 2v) = 2X_0(u)$ while also either $w \neq 2Y_0(u)$ or $h(u)=0$.
 
 **Define** a version of $G_{c,u}(x)$ which deals with all these cases:
 * If $a=0$ and $u=0$, return $\bot.$

diff --git a/examples/CMakeLists.txt b/examples/CMakeLists.txt
@@ -6,9 +6,6 @@ target_link_libraries(example INTERFACE
   secp256k1
   $<$<PLATFORM_ID:Windows>:bcrypt>
 )
-if(NOT BUILD_SHARED_LIBS AND MSVC)
-  target_link_options(example INTERFACE /IGNORE:4217)
-endif()
 
 add_executable(ecdsa_example ecdsa.c)
 target_link_libraries(ecdsa_example example)

diff --git a/examples/examples_util.h b/examples/examples_util.h
@@ -95,7 +95,7 @@ static void secure_erase(void *ptr, size_t len) {
      *    As best as we can tell, this is sufficient to break any optimisations that
      *    might try to eliminate "superfluous" memsets.
      * This method used in memzero_explicit() the Linux kernel, too. Its advantage is that it is
-     * pretty efficient, because the compiler can still implement the memset() efficently,
+     * pretty efficient, because the compiler can still implement the memset() efficiently,
      * just not remove it entirely. See "Dead Store Elimination (Still) Considered Harmful" by
      * Yang et al. (USENIX Security 2017) for more background.
      */