# Why do we use addition and multiplication in GMW protocol

I don't understand why the protocol evaluates the addition and the multiplication ?

Why not just the multiplication ?

I didn't find any information about the OT used in this protocol. Is this a basic one like Rabin's or not ?

• can you link to the document you are reading and which part exactly is not clear to you? It's currently a bit vague: to securely compute a function, you must securely compute all its gates, including the addition, but I suspect this is not your question. Jun 15, 2019 at 9:56
• cs.umd.edu/~jkatz/gradcrypto2/f13/lecture13.pdf and cis.upenn.edu/~nadiah/courses/cis800-02-f13/hemenway-otsmc.pdf. You answered my question. I didn't understand that all the gates must be securely compute. Jun 15, 2019 at 11:00

In GMW, a 1-out-of-4 OT is used to evaluate the AND gates (as I said above, XOR gates only require local computation - i.e., XORing the corresponding shares). This is the standard OT, i.e., not Rabin OT: the sender has 4 messages $$(m_i)_{i\leq 4}$$, and the receiver with input $$j \in \{1,2,3,4\}$$ learns $$m_j$$ without learning anything else; $$j$$ remains hidden to the sender.