>It is possible to compute over encrypted data without access to the secret key
This is counter intuitive to me. For one, I don't consider the Caesar Cipher to be an encryption scheme that I would actually use for data.
In addition, when I want to "compute" data, I want to do things like identify sentiment analysis in free form text or identify key themes in a paragraph - and I'm not sure this actually IS possible with data that is encrypted
Maybe a simpler example would be doing a not operation on a ciphertext for a one time pad? When you decrypt it you will get the plain text with all of the bits flipped.
Doing computations on cipher text is very limited which is why it's not very efficient to do complicated operations.
This is counter intuitive to me. For one, I don't consider the Caesar Cipher to be an encryption scheme that I would actually use for data.
In addition, when I want to "compute" data, I want to do things like identify sentiment analysis in free form text or identify key themes in a paragraph - and I'm not sure this actually IS possible with data that is encrypted