  Shor and Steane ancilla are two well-known methods for fault-tolerant logical
measurements, which are successful on small codes and their concatenations. On
large quantum low-density-parity-check (LDPC) codes, however, Shor and Steane
measurements have impractical time and space overhead respectively. In this
work, we widen the choice of ancilla codes by unifying Shor and Steane
measurements into a single framework, called homomorphic measurements. For any
Calderbank-Shor-Steane (CSS) code with the appropriate ancilla code, one can
avoid repetitive measurements or complicated ancilla state preparation
procedures such as distillation, which overcomes the difficulties of both Shor
and Steane methods. As an example, we utilize the theory of covering spaces to
construct homomorphic measurement protocols for arbitrary $X$- or $Z$-type
logical Pauli operators on surface codes in general, including the toric code
and hyperbolic surface codes. Conventional surface code decoders, such as
minimum-weight perfect matching, can be directly applied to our constructions.
