It is easy to see that both Paillier and Goldwasser-Micali are homomorphic addition schemes and are secure, but what would be the advantages of choosing one over the other?


1 Answer 1


They're both additively homomorphic, but over different groups.

With Goldwasser-Micali, you can, given $E(x)$ and $E(y)$, compute $E(x \oplus y)$ (where $\oplus$ is exclusive or)

With Pallier, you can, given $E(x)$ and $E(y)$, compute $E(x + y \bmod n)$, where $n$ is a large integer; this implies that, given $E(x)$ and $k$, you can compute $E(kx \bmod n)$

Which is appropriate depends on what operation you need to perform on the encrypted data.

In my experience, we almost always want the operations that Pallier provides.

  • $\begingroup$ so basically goldwasser micali can only do homomorphic xor but not homomorphic addition? $\endgroup$
    – Daniel K
    Feb 14, 2020 at 14:47
  • 2
    $\begingroup$ @DanielK: that is correct (unless you mean addition in $GF(2)$, which is xor…) $\endgroup$
    – poncho
    Feb 14, 2020 at 15:46

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