(Adapted from the upstream project)
Captcha can be enabled for this home server. This file explains how to do that. The captcha mechanism used is Google's ReCaptcha. This requires API keys from Google.
Requires a site/secret key pair from:
http://www.google.com/recaptcha/admin
Must be a reCAPTCHA v2 key using the "I'm not a robot" Checkbox option
Once registered as above, set the following values:
matrix_synapse_enable_registration_captcha: true
matrix_synapse_recaptcha_public_key: 'YOUR_SITE_KEY'
matrix_synapse_recaptcha_private_key: 'YOUR_SECRET_KEY'