You can build and push docker/oci images without the need to execute a docker daemon (and requiring privileged containers) thanks to tools like kaniko and buildah

Using Kaniko

Basic image build

A basic task for building images using kaniko is this. Add --no-push if you don't want to push the image. This doesn't take care of registry authentication. See below for an example with registry authentication.

    tasks:
      # kaniko image doesn't have the git command installed
      - name: checkout code
        runtime:
          containers:
            - image: alpine/git
        steps:
          - clone:
          - save_to_workspace:
              contents:
                - source_dir: .
                  dest_dir: .
                  paths:
                    - '**'
      - name: build docker image
        runtime:
          containers:
            - image: gcr.io/kaniko-project/executor:debug
        shell: /busybox/sh
        steps:
          - restore_workspace:
              dest_dir: .
          #- run: /kaniko/executor --no-push
          - run: /kaniko/executor --destination registry/image
        depends:
          - checkout code

With authentication

For more information refer to the kaniko doc. Kaniko document some ways to authenticate to gcr and aws registries and its images already include a credential helper for amazon ecr.

At the end you should create a docker config.json config file with the required auth data:

    tasks:
      # kaniko image doesn't have the git command installed
      - name: checkout code
        runtime:
          containers:
            - image: alpine/git
        steps:
          - clone:
          - save_to_workspace:
              contents:
                - source_dir: .
                  dest_dir: .
                  paths:
                    - '**'
      - name: build docker image
        runtime:
          containers:
            - image: gcr.io/kaniko-project/executor:debug
        environment:
          DOCKERAUTH:
            from_variable: dockerauth
        shell: /busybox/sh
        steps:
          - restore_workspace:
              dest_dir: .
          - run:
              name: generate docker config
              command: |
                cat << EOF > /kaniko/.docker/config.json
                {
                  "auths": {
                    "https://index.docker.io/v1/": { "auth" : "$DOCKERAUTH" }
                  }
                }
                EOF
          - run: /kaniko/executor --destination registry/image
        depends:
          - checkout code

Using Buildah

TODO