An Information Theoretic Approach to Secret Sharing
An Information Theoretic Approach to Secret Sharing
复制标题
秘密共享的信息论方法
DOI：
10.1109/tit.2015.2421905
复制
发表时间：
2014
影响因子：
2.5
通讯作者：
S. Shamai
中科院分区：
文献类型：
--
作者：
Shaofeng Zou;Yingbin Liang;L. Lai;S. Shamai
提出了一种新的信息论方法来解决秘密共享问题。在该问题中，一个分发者以这样一种方式在一组参与者之间分配一个或多个秘密：对于每个秘密，只有合格的用户集合能够通过汇集他们的份额来恢复这个秘密，而不合格的用户集合即使汇集他们的份额也无法获得关于该秘密的任何信息。虽然现有的秘密共享系统（隐含地）假设分发者和参与者之间的通信是无噪声的，但本文采用了一个更实际的假设，即分发者通过一个有噪声的广播信道向参与者传递份额。因此，与主要基于数论工具的现有解决方案不同，提出了一种信息论方法，该方法利用份额传递过程中的信道随机性作为额外资源来实现秘密共享的要求。通过这种方式，秘密共享问题可以通过窃听信道模型重新表述为等效的安全通信问题，并且因此可以通过采用强大的信息论安全技术来解决。这种方法首先针对经典的秘密共享问题而开发，在该问题中只有一个秘密需要共享。这个经典问题被证明等同于复合窃听信道上的一个通信问题。因此，复合信道的保密容量的下限和上限为秘密共享率提供了相应的界限，并且为复合信道设计的保密方案提供了秘密共享方案。这种方法的威力通过一个更一般的分层多秘密共享问题进一步得到证明，该问题被证明等同于具有分层解码和保密约束的退化广播多输入多输出（MIMO）信道。退化的MIMO广播信道的保密容量区域得到了刻画，这为秘密共享容量区域提供了依据。此外，实现保密容量区域的安全编码方案为共享秘密提供了一种信息论方案。
A novel information theoretic approach is proposed to solve the secret sharing problem, in which a dealer distributes one or multiple secrets among a set of participants in such a manner that for each secret only qualified sets of users can recover this secret by pooling their shares together while nonqualified sets of users obtain no information about the secret even if they pool their shares together. While existing secret sharing systems (implicitly) assume that communications between the dealer and participants are noiseless, this paper takes a more practical assumption that the dealer delivers shares to the participants via a noisy broadcast channel. Thus, in contrast to the existing solutions that are mainly based on number theoretic tools, an information theoretic approach is proposed, which exploits the channel randomness during delivery of shares as additional resources to achieve secret sharing requirements. In this way, secret sharing problems can be reformulated as equivalent secure communication problems via wiretap channel models, and can hence be solved by employing the powerful information theoretic security techniques. This approach is first developed for the classic secret sharing problem, in which only one secret is to be shared. This classic problem is shown to be equivalent to a communication problem over a compound wiretap channel. Thus, the lower and upper bounds on the secrecy capacity of the compound channel provide the corresponding bounds on the secret sharing rate, and the secrecy scheme designed for the compound channel provides the secret sharing schemes. The power of the approach is further demonstrated by a more general layered multisecret sharing problem, which is shown to be equivalent to the degraded broadcast multiple-input multiple-output (MIMO) channel with layered decoding and secrecy constraints. The secrecy capacity region for the degraded MIMO broadcast channel is characterized, which provides the secret sharing capacity region. Furthermore, the secure encoding scheme that achieves the secrecy capacity region provides an information theoretic scheme for sharing the secrets.
DOI：
10.1007/978-3-319-04268-8
发表时间：
2013
期刊：
Seg Technical Program Expanded Abstracts
影响因子：
--
作者：
Carles Padró
通讯作者：
Carles Padró