First decide a directory on your Synology NAS where to store the Restic repository. I’ve chosen /volume1/restserver.

Download rest server for linux armv7l from the rest-server releases page and decompress it to the designated dir above. Something like:

wget -q https://github.com/restic/rest-server/releases/download/v0.10.0/rest-server_0.10.0_linux_armv7.tar.gz -O - | tar -C /volume1/restserver --strip-components=1 -xzf -

Create an authentication file on your local computer and copy it to the Synology in /volume1/restserver. To generate a password:

htpasswd -B -c .htpasswd your-http-username

Create systemd unit file /usr/local/lib/systemd/system/rest-server.service with this content:

[Unit]
Description=Start REST server
After=network.target

[Service]
ExecStart=/volume1/restserver/rest-server --path /volume1/restserver/ --listen :8765
Restart=on-failure
Type=simple
User=http

[Install]
WantedBy=multi-user.target

Then run

systemctl enable rest-server
systemctl start rest-server

To check if it’s running:

journalctl -fu rest-server