Homomorphism of an elementwise sum and dot product

[NotASmurf]

∑ab is needed but is impractical to implement.

Specifically ∑_i a_i.10^i-|i| in any form where I can work with ∑_i a_i = α and ∑_i 10^i-|i| separately.

Is there a homomorphic function I can run it through such that ∑ab can be expressed as ∑a∑b? Note: for current problem i cannot simply set it up such that ∑a∑b - ∑ab polynomial expansion saves the day, any help appreciated.

 

[Svein]

No. A simple counterexample: Let all a_i=1 and all b_i=1 Then Σab = Σa = Σb.