To test whether a secret value $[x]$ is zero, where $x \in [0,2^{k−1}]$, SPDZ uses the a based on the method of Catrina and de Hoogh [1].

This method requires to working on a field with modulus $p>2^{k+s}$, where $s$ is a is a statistical security parameter.

Does another method exist that perform this comparison but eliminate the need for security bits (performance is not my #1 concern)?

Thanks.

[1]-https://www1.cs.fau.de/filepool/publications/octavian_securescm/smcint-scn10.pdf