Two-Cloud-Servers-Assisted Secure Outsourcing Multiparty Computation

Algorithm 1

(i) KeyGen(1^𝑘): sample a ring element vector 𝑎←𝑅^𝑛_𝑞 and a ring element 𝑠 from the

distribution 𝜒, denoted as 𝑠←𝜒, a ring element vector 𝑥 from the distribution 𝜒^𝑛, denoted

as 𝑥←𝜒^𝑛. Then, the private key is 𝑠𝑘=𝑠; the public key is 𝑝=𝑎𝑠+2𝑥∈𝑅^𝑛_𝑞.

(ii) Enc(𝑝𝑘,𝑚): sample 𝑒←𝜒^𝑛 and compute 𝑐₀∶=𝑝,𝑒+𝑚∈𝑅_𝑞 and 𝑐₁∶=⟨𝑎,𝑒⟩∈𝑅_𝑞. Output

the ciphertext 𝑐∶=𝑐₀,𝑐₁∈𝑅²_𝑞.

(iii) Dec(𝑠𝑘,𝑐): compute 𝜇=𝑐₀−𝑐₁𝑠∈𝑅_𝑞 and output 𝑚^′∶=𝜇(mod2).