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（Oblivious Transfer，OT）是安全双方计算的基本原语。众所周知，若双方仅能访问无噪声通信信道，即使在量子情形下，OT也无法实现信息论安全性。为此，学术界研究了OT的弱化变体。在本工作中，我们严格论证了防欺骗OT的不可实现性——在该场景中，不诚实方可实施欺骗，但需承担被检测到的风险。我们构造了一种针对任意量子协议的通用攻击方法，该攻击使接收方能够计算发送方的所有输入，并给出了此攻击成功概率的显式上界。这一结果意味着，统计信息论安全下的防欺骗量子对称私密信息检索不可实现。基于证明过程中发展的技术，我们推导了安全函数求值所需原语的熵界，进而得到关于将OT作为资源进行协议设计的不可行性结论。该结果显著改进了现有界值，并为1-out-of-n OT到资源原语的归约给出了紧致界。我们的结论尤其适用于有限个原语间的变换以及任意错误率情形。