Amazon CloudSearch provides option to mandate HTTPS & minimum TLS version

Amazon CloudSearch now lets you configure your domains to require that all traffic be submitted over HTTPS so that you can ensure that communications between your clients and your domain are encrypted. You can also configure the minimum required TLS version to accept, with TLS 1.0 as the default. This option helps ensure that your clients are configured correctly. For information on enabling this feature, see the documentation.

Source:: Amazon AWS