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arXiv 1608.01909cs.CR
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在两轮中完全安全的消息传输

Perfectly Secure Message Transmission in Two Rounds

Gabriele Spini, Gilles Zémor

摘要:

在被称为“完全安全消息传输”(PSMT)的模型中,发送方Alice通过n个并行的双向通道连接到接收方Bob。一个计算能力无限的对手夏娃控制着这些通道中的t个,这意味着她可以获取和改变通过这些通道传输的任何数据。发送者Alice希望私下和可靠地向Bob传送秘密消息,即以这样的方式,Eve将不会获得关于消息的任何信息,而Bob将能够完全恢复它。在本文中,我们专注于工作在两个传输轮n= 2t+1的协议。我们打破了以前的工作,通过以下一个概念上更简单的蓝图实现PSMT协议。我们降低了以前最著名的通信复杂性,即传输1位秘密所需的位数,从O(n^3 log n)到O(n^2 log n)。我们的协议还回答了Kurosawa和Suzuki提出的一个问题,迄今为止还没有解决:他们的协议对于大小为O(n^2 log n)位的秘密达到了最佳传输速率,作者提出了降低这个阈值的问题。因此,时间复杂度为O(n log n)。此外,我们展示了我们的协议可以适应网络编码的背景下。

英文摘要:

In the model that has become known as "Perfectly Secure Message Transmission"(PSMT), a sender Alice is connected to a receiver Bob through n parallel two-way channels. A computationally unbounded adversary Eve controls t of these channels, meaning she can acquire and alter any data that is transmitted over these channels. The sender Alice wishes to communicate a secret message to Bob privately and reliably, i.e. in such a way that Eve will not get any information about the message while Bob will be able to recover it completely. In this paper, we focus on protocols that work in two transmission rounds for n= 2t+1. We break from previous work by following a conceptually simpler blueprint for achieving a PSMT protocol. We reduce the previously best-known communication complexity, i.e. the number of transmitted bits necessary to communicate a 1-bit secret, from O(n^3 log n) to O(n^2 log n). Our protocol also answers a question raised by Kurosawa and Suzuki and hitherto left open: their protocol reaches optimal transmission rate for a secret of size O(n^2 log n) bits, and the authors raised the problem of lowering this threshold. The present solution does this for a secret of O(n log n) bits. Additionally, we show how our protocol can be adapted to a Network Coding context.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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