feat: linux codesign with sigstore (#7674)

### Summary
Linux codesigning with sigstore and test run output at
https://github.com/openai/codex/actions/runs/19994328162?pr=7662.

Sigstore is one of the few ways for codesigning for linux platform.
Linux is open sourced and therefore binary/dist validation comes with
the build itself instead of a central authority like Windows or Mac.
Alternative here is to use GPG which again a public key included with
the bundle for validation. Advantage with Sigstore is that we do not
have to create a private key for signing but rather with[ keyless
signing](https://docs.sigstore.dev/cosign/signing/overview/).

This should be sufficient for us at this point and if we want to we can
support GPG in the future.

.github/actions/linux-code-sign/action.yml

@@ -0,0 +1,44 @@
+name: linux-code-sign
+description: Sign Linux artifacts with cosign.
+inputs:
+  target:
+    description: Target triple for the artifacts to sign.
+    required: true
+  artifacts-dir:
+    description: Absolute path to the directory containing built binaries to sign.
+    required: true
+
+runs:
+  using: composite
+  steps:
+    - name: Install cosign
+      uses: sigstore/cosign-installer@v3.7.0
+
+    - name: Cosign Linux artifacts
+      shell: bash
+      env:
+        COSIGN_EXPERIMENTAL: "1"
+        COSIGN_YES: "true"
+        COSIGN_OIDC_CLIENT_ID: "sigstore"
+        COSIGN_OIDC_ISSUER: "https://oauth2.sigstore.dev/auth"
+      run: |
+        set -euo pipefail
+
+        dest="${{ inputs.artifacts-dir }}"
+        if [[ ! -d "$dest" ]]; then
+          echo "Destination $dest does not exist"
+          exit 1
+        fi
+
+        for binary in codex codex-responses-api-proxy; do
+          artifact="${dest}/${binary}"
+          if [[ ! -f "$artifact" ]]; then
+            echo "Binary $artifact not found"
+            exit 1
+          fi
+
+          cosign sign-blob \
+            --yes \
+            --bundle "${artifact}.sigstore" \
+            "$artifact"
+        done

.github/workflows/rust-release.yml

@@ -50,6 +50,9 @@ jobs:
     name: Build - ${{ matrix.runner }} - ${{ matrix.target }}
     runs-on: ${{ matrix.runner }}
     timeout-minutes: 30
+    permissions:
+      contents: read
+      id-token: write
     defaults:
       run:
         working-directory: codex-rs
@@ -100,6 +103,13 @@ jobs:
       - name: Cargo build
         run: cargo build --target ${{ matrix.target }} --release --bin codex --bin codex-responses-api-proxy
 
+      - if: ${{ contains(matrix.target, 'linux') }}
+        name: Cosign Linux artifacts
+        uses: ./.github/actions/linux-code-sign
+        with:
+          target: ${{ matrix.target }}
+          artifacts-dir: ${{ github.workspace }}/codex-rs/target/${{ matrix.target }}/release
+
       - if: ${{ matrix.runner == 'macos-15-xlarge' }}
         name: Configure Apple code signing
         shell: bash
@@ -283,6 +293,11 @@ jobs:
             cp target/${{ matrix.target }}/release/codex-responses-api-proxy "$dest/codex-responses-api-proxy-${{ matrix.target }}"
           fi
 
+          if [[ "${{ matrix.target }}" == *linux* ]]; then
+            cp target/${{ matrix.target }}/release/codex.sigstore "$dest/codex-${{ matrix.target }}.sigstore"
+            cp target/${{ matrix.target }}/release/codex-responses-api-proxy.sigstore "$dest/codex-responses-api-proxy-${{ matrix.target }}.sigstore"
+          fi
+
       - if: ${{ matrix.runner == 'windows-11-arm' }}
         name: Install zstd
         shell: powershell
@@ -321,6 +336,11 @@ jobs:
               continue
             fi
 
+            # Don't try to compress signature bundles.
+            if [[ "$base" == *.sigstore ]]; then
+              continue
+            fi
+
             # Create per-binary tar.gz
             tar -C "$dest" -czf "$dest/${base}.tar.gz" "$base"