Suppose $n$ actors each hold a plaintext $p_i$. We wish to find $\sum p_i$, without leaking any information about individual $p_i$. Any actor (or any link in the network) could be controlled by an active adversary. More precisely, these protocols can be proved secure against a polynomial time bounded adversary who can corrupt a set of less than $n/2$ parties initially, and then make them behave as he likes, we say that the adversary is active.
In article Multiparty Computation from Threshold Homomorphic Encryption there is approach to multiparty computation (MPC) basing it on homomorphic threshold crypto-systems. I'm unsure how to make multiparty sum secure in malicious model (against less than $n/2$ active adversaries) following this approach. I'm under impression that it's quite simple:
- each player uses additive homomorphic encryption to calculate ciphertext $E(p_i)$ of his own imput, sends the ciphertext to other parties and attach proof of plaintext knowledge to the ciphertext
- verify proofs, add ciphertexts to calculate $E(\sum p_i)$
- decrypt sum $E(\sum p_i)$ using threshold decryption to calculate $\sum p_i$
Could you confirm that what I described above is secure in malicious model (against less than $n/2$ active colluding adversaries)?