# Generation and Distribution of Quantum Oblivious Keys for Secure Multiparty Computation
### State of the Art  
Classical OT implementations are based on the use of asymmetric keys, and suffer from two types of problems. The first one is the efficiency: asymmetric cryptography relies on relatively complex key generation, encryption, and decryption algorithms [12] (Chapter 1) and [13] (Chapter 6). This limits achievable rates of OTs, and since implementations of SMC require a very large number of OTs [3; 10], this has hindered the development of SMC-based applications. The other serious drawback is that  
Figure 1: In secure multiparty computation, N parties compute a function preserving the privacy of their own input. Each party only has access to their own input–output pair.  
asymmetric cryptography, based on integer number factorization or discrete-logarithm problems, is insecure in the presence of quantum computers, and therefore, it has to be progressively abandoned. There are strong research efforts in order to find other hard problems that can support asymmetric cryptography [4]. However, the security of these novel solutions is still not fully understood.  
A possible way to circumvent this problem is by using quantum cryptography to improve the efficiency and security of current techniques. Quantum solutions for secure key distribution, Bit Commitment (BC) and OT have been already proposed [14]. The former was proved to be unconditionally secure (assuming an authenticated channel) and realizable using current technology. Although, it was shown to be impossible to achieve unconditionally secure quantum BC and OT [15; 16; 17], one can impose restrictions on the power of adversaries in order to obtain practically secure versions of these protocols [18; 19]. These assumptions include physical limitations on the apparatuses, such as noisy or bounded quantum memories [20; 21; 22]. For instance, quantum OT and BC protocols have been developed and implemented (see [23; 24; 25]) under the noisy storage model. Nevertheless, solutions based on hardware limitations may not last for long, because as quantum technology improves the rate of secure OT instances will decrease. Other solutions include exploring relativistic scenarios using the fact that no information can travel faster than light [26; 27; 28]. However, at the moment, these solutions do not seem to be practical enough to allow the large dissemination of SMC.  
In this work, we explore the resulting security and efficiency features of implementing oblivious transfer using a well known quantum protocol [5] supported by using a cryptographic hash based commitment scheme [29]. We call it a hybrid approach, since it mixes both classical and quantum cryptography. We analyse the protocol stand alone security, as well as its composable security in the random oracle model. Additionally, we study its computational complexity and compare it with the complexity of alternative public key based protocols. Furthermore, we show that, while unconditional information-theoretic security cannot be achieved, there is an advantage (both in terms of security and efficiency) of using quantum resources in computationally secure protocols, and as such, they are worth consideration for practical tasks in the near future.  
This paper is organized as follows. In Section 2, we present a quantum protocol to produce OT given access to a collision resistant hash function, define the concept of oblivious keys, and explain how having pre-shared oblivious keys can significantly decrease the computational cost of OT during SMC. The security and efficiency of the protocol is discussed in Section 3. Finally, in Section 4 we summarize the main conclusions of this work.