We revisit the oblivious transfer (OT) capacities of noisy channels against the passive adversary, which have been identified only for a limited class of channels. In the literature, the general construction of oblivious transfer has been known only for generalized erasure channels (GECs); for other channels, we first convert a given channel to a GEC via alphabet extension and erasure emulation, and then apply the general construction for GEC. In this paper, we derive an improved lower bound on the OT capacity of the binary symmetric channel (BSC) and binary symmetric erasure channel (BSEC) by proposing a new protocol; by using interactive communication between the sender and the receiver, our protocol emulates erasure events recursively in multiple rounds. We also discuss a potential necessity of multiple rounds interactive communication to attain the OT capacity.

翻译：我们重新审视了针对被动攻击者的噪声信道的不经意传输（OT）容量，目前仅在有限的信道类别中确定了该容量。文献中，仅针对广义擦除信道（GEC）存在通用构造方案；对于其他信道，我们通常通过字母扩展和擦除模拟将给定信道转换为GEC，然后应用针对GEC的通用构造方案。本文通过提出一种新协议，推导了二元对称信道（BSC）和二元对称擦除信道（BSEC）的OT容量改进下界；利用发送方与接收方之间的交互通信，我们的协议通过多轮递归方式模拟擦除事件。我们还讨论了实现OT容量时多轮交互通信的潜在必要性。