HElib with negative numbers

[nbarlowATI]

context-helib gives the wrong answer when dealing with negative numbers. e.g. with inputs and outputs int8_t, if we do: 3 ADD -4 we get the answer 0 instead of -1 3 MULTIPLY -4 we get -11 instead of -12 5 NEGATE we get -4 instead of -5

i.e. the answer is always (correct_answer+1)

I don't think this is actually a problem with HElib, but just a consequence of HElib returning the decrypted plaintext as a long modulo p followed by us casting this into a signed integer..

[nbarlowATI]

(Finding this out now is an illustration of inadequate tests - the HElib subtraction test only looked at positive numbers - need to add more corner cases!)

[nbarlowATI]

I think a reasonable solution (that seems to work on the extensive set of new tests!) is:

• Ensure that the plaintext space used internally in HElib (i.e. 0 to p-1) is at least twice as large as the input plaintext space specified by the user.
  • If not, can split plaintext inputs into elements of a vector with smaller bitwidth elements (TBD).
• If the output of the homomorphic operation is > p/2, we can assume that the result was negative, and therefore subtract p, giving us a signed long, which we then cast into the user-specified plaintext type.

[ots22]

Can we close this?