Quantum protocols for untrusted computations

In this paper, we propose new quantum arithmetic protocols among multiple parties. Let some parties have values. A problem is to find a protocol such that under the condition that any eavesdropper intercepting any quantum system being exchanged among the parties must not be able to acquire information, the parties compute an arithmetic operation such as addition and multiplication, and transfer its computing result to another party. One of main ideas to solve this problem is based on operating state phases. A quantum addition algorithm based on operating phases has been proposed by Draper, but his algorithm was not considered being eavesdropped. We propose secure quantum arithmetic protocols.