Oblivious transfer (OT) is a fundamental primitive for secure two-party computation. It is well known that OT cannot be implemented with information-theoretic security if the two players only have access to noiseless communication channels, even in the quantum case. As a result, weaker variants of OT have been studied. In this work, we rigorously establish the impossibility of cheat-sensitive OT, where a dishonest party can cheat, but risks being detected. We construct a general attack on any quantum protocol that allows the receiver to compute all inputs of the sender and provide an explicit upper bound on the success probability of this attack. This implies that cheat-sensitive quantum Symmetric Private Information Retrieval cannot be implemented with statistical information-theoretic security. Leveraging the techniques devised for our proofs, we provide entropic bounds on primitives needed for secure function evaluation. They imply impossibility results for protocols where the players have access to OT as a resource. This result significantly improves upon existing bounds and yields tight bounds for reductions of 1-out-of-n OT to a resource primitive. Our results hold in particular for transformations between a finite number of primitives and for any error.

翻译：不经意传输（OT）是安全两方计算的基础原语。众所周知，即使是在量子情形下，如果两个参与者仅能访问无噪声通信信道，OT也无法以信息论安全性实现。因此，人们研究了OT的较弱变体。在本工作中，我们严格确立了作弊敏感OT的不可能性，其中不诚实方可以作弊，但需承担被检测的风险。我们针对任何允许接收者计算发送者所有输入的量子协议构造了一种通用攻击，并给出了该攻击成功概率的显式上界。这意味着作弊敏感的量子对称私有信息检索无法以统计信息论安全性实现。利用我们证明过程中设计的技术，我们为安全函数求值所需原语提供了熵界。这些熵界意味着在参与者能够以OT作为资源的协议中存在不可能性结果。该结果显著改进了现有界限，并为从资源原语归约到1选n OT提供了紧致界限。我们的结果尤其适用于有限数量原语之间的转换以及任意误差情形。