Arithmetic cryptography protocol for secure multi-party computation (non-refereed)

In this paper, we propose a cryptographic solution for secure multi-party computation (SMC). SMC is also called secure function evaluation, which is extensively studied in classical cryptography. SMC protocol allows n participants p(1),...p(n) to compute an n-input data through trusted third party (TTP) without revealing the information of the parties. All the parties may perform secure communication with TTP for computation. During the computation, TTP may undesirably extract data of all the parties for misuse. It may be risky if the data is sent out. To achieve security in SMC, numbers of solutions are available, but they use cryptography as secure communication between the parties and not for the computation. Basically cryptography is used for the secure communication but in our protocol, we use it for the secure communication as well as for computation. TTP computes entire encrypted data received by all the parties without being aware that the data is encrypted so that if data is disclosed by TTP to others even than no one can reveal the actual data of the party. In this protocol, we have tried to remove the concept of hiding the data using anonymizer. Our earlier protocol uses the anonymizer between parties and TTP to hide the identity of parties. Even after enforcing all these securities, the anonymizer can become malicious, causing leakage of data. To prevent this, we require some additional measures. Thus we propose a new cryptographic protocol that causes a secure communication between the parties and the TTP as well as perform secure computation using encryption. The protocol uses a polynomial to encrypt data by party itself before sending to TTP for computation. It also embeds some dummy data at random places. The purpose of dummy data is to check the honesty of TTP because result of dummy data is known to the party. All the data send to TTP is in the form of numbers as it is assumed that TTP performs only arithmetic computation to produce the result. After computation, TTP sends result to respective parties and each party will removes all dummies to get the actual result as well as check the honesty of TTP by dummies. If any other party wants to reveal the actual data then the probability of breaking the data will be of the order 1/m(n), which is quite high and cannot be done in a polynomial time. The security is the most important factor in SMC that is why this protocol meets our requirements. Only limitation of protocol is encryption time. By choosing proper polynomials and their constants, we can reduce the encryption time.