A secret sharing scheme such as [Shamir's secret sharing][1] allow to perform addition and multiplication for secret values so far as there is at least 3 participants. Addition of two secret values is done locally at each party by adding the corresponding local shares, so it is possible to do addition even with only 2 parties. In the case of multiplication, a degree reduction step is obligatory, because multiplication increases the degree of the shares and this makes it impossible for 2 parties to perform multiplications without the aid of a third one.

It is possible to construct a multiplicative sharing scheme that works for two parties, but it wouldn't be additive. 

> Is any one aware of a secret sharing
> scheme for two parties (without the
> need for a third party) that is BOTH
> additive and multiplicative, or is it
> impossible ?

So far I know that it is impossible to construct scalar product protocol with unconditional security for two parties. But I don't suppose that it necessarily prevents the construction of an algebraic (additive+multiplicative) secret sharing scheme.


  [1]: http://en.wikipedia.org/wiki/Shamir's_Secret_Sharing