Do you have any information on Amazon bucket policies?

Yes! Give this a try if you're wanting to incorporate these into your integration method.
 

This policy will allow CloudFront to gain access to private content. 

{ 
"Version":"2008-10-17", 
"Id":"PolicyForCloudFrontPrivateContent", 
"Statement":[{ 
"Sid":" Grant CloudFront Origin Identity access to private content", 
"Effect":"Allow", 
"Principal":{ 
"AWS":"arn:aws:iam::cloudfront:user/CloudFront Origin Access Identity PRIVATE" // This is the origin ID specific to our account. 
}, 
"Action":"s3:GetObject", 
"Resource":"arn:aws:s3:::bucketname/*" 
} ]
}