ohh interesting!
Are there any opensource implementations of homomorphic numerical processing?
Were there any efforts of combining both approaches?
Were there any efforts of combining both approaches?
With a less than operator and the ability to encrypt chosen plaintext values, you can decrypt arbitrary messages in a linear (in message size) number of steps.
Arithmetic operations can often be used to build gadgets that bootstrap comparison operations. For instance, with addition and equality you can implement a comparison operation for low-medium cardinality fields.
The field is littered with negative results that are being sold as secure, practical systems. Be careful when using them on important data.
Isn't this a big assumption? The way I envision it is
1. client encrypts data with their key
2. server computes on data without decrypting and without needing the key
3. client decrypts computation output with their key.
Or is it always required at step 2 that the server also has the key needed for encryption (but not decryption obviously)?
The standard resilience criteria for modern multi-purpose encryption suppose that your scheme should be resistant to adaptive chosen-cipher attack. Chosen plaintext is a way weaker attack (the hierarchy being: known plaintext < chosen plaintext < chosen cipher < adaptative chosen cipher).
It may be OK for some situations, but it requires to be much more cautious than with regular crypto (which is already error-prone…).
Fwiw, bootstrapping is actually what makes FHE slow, not the actual addition/multiplication etc