S3 buckets don't support HTTPS?
Buckets support HTTPS, but not directly in conjunction with the static web site hosting feature.
See Website Endpoints in the S3 Developer Guide for discussion of the feature set differences between the REST endpoints and the web site hosting endpoints.
Note that if you try to directly connect to your web site hosting endpoint with your browser, you will get a timeout error.
The REST endpoint https://your-bucket.s3.amazonaws.com
will work for providing HTTPS between bucket and CDN, as long as there are no dots in the name of your bucket
Or if you need the web site hosting features (index documents and redirects), you can place CloudFront between Akamai and S3, encrypting the traffic inside CloudFront as it left the AWS network on its way to Akamai (it would still be in the clear from S3 to CloudFront, but this is internal traffic on the AWS network). CloudFront automatically provides HTTPS support on the dddexample.cloudfront.net
hostname it assigns to each distribution.
I admit, it sounds a bit silly, initially, to put CloudFront behind another CDN but it's really pretty sensible -- CloudFront was designed in part to augment the capabilities of S3. CloudFront also provides Lambda@Edge, which allows injection of logic at 4 trigger points in the request processing cycle (before and after the CloudFront cache, during the request and during the response) where you can modify request and response headers, generate dynamic responses, and make external network requests if needed to implement processing logic.