# Measurement-Device-Independent Two-Party Cryptography with Error Estimation
###### Abstract  
We present an innovative method for quantum two-party cryptography. Our protocol introduces joint measurement and error estimation to improve the security of two-party cryptographic protocols. Our protocol removes the assumption of the attacker's limited power and catches the attacking actions through highly estimated bit error rate. Our protocol is formally proved to be secure against both eavesdroppers and dishonest communication parties. We also utilize our designed protocol to construct two specific two-party cryptographic applications: Quantum bit commitment and quantum password identification.  
quantum; two-party cryptography; measurement-device-independent 2020  
extended the model to the noisy storage model [2; 17], where the attacker possesses quantum storage with unlimited capacity, but the noise increases over time.  
Although [PERSON] manifested secure two-party cryptographic protocols are feasible under noisy bounded model [2; 17], we are still interested in designing two-party cryptographic protocols when the attacker possesses perfect quantum storage inspired by [PERSON]'s work [18]. We have discovered that two-party cryptographic protocols, like bit commitment, oblivious transfer, in Ref. [2; 11; 17] do not have the process of error estimation, which serves as a significant indicator of eavesdropping attack in QKD. The reasons are obvious: For one thing, the communication parties do not trust each other and for another, the information is asymmetric between parties during the communication process.  
Inspired by the foundations of measurement-device-independent QKD (MDI-QKD) [19; 20; 21] and phase-matching QKD (PM-QKD) [22; 23], we make it possible to introduce error estimation into two-party cryptographic protocols. In the QKD process, once there is an eavesdropper, the final key error rate will exceed the upper limit. Therefore, in encrypted communication between the two parties, if one party is dishonest, the information they previously negotiated will also have a higher error rate, which is difficult in avoiding detection by another party. In MDI-QKD, the measurement stage is independent of the final key. This de-emphasizes the assumptions for the attacker's quantum memory and enables us to discover the attacker by the increased quantum bit error rate during the estimation process.  
In this paper, we introduce joint measurement method in MDI-QKD and PM-QKD, and error estimation into two-party cryptographic protocols, and raise our improved weak string erasure (WSE) protocol and 1-2 random oblivious transfer (ROT) protocol. These two protocols are significant for other TPC (two-party cryptographic protocols) applications. Compared with existing WSE and 1-2 ROT protocol, our protocol does not make any assumption on the attacker's devices. Instead, we restrict the attacking behavior by the protocol itself, which offers greater security. In our protocol, the honest party does not need quantum storage devices and the devices are compatible with mainstream QKD platforms.  
The paper is organized as follows. Section 2 introduces the foundations of our research. Section 3, and Section 4 discuss our proposed WSE and 1-2 ROT respectively, and demonstrate their security. In Section 5, we probe into applications of two-party cryptographic protocols and propose two important practices, quantum bit commitment and password-based identification. Finally, the paper ends with a conclusion.