Information Theoretic Cryptography with Statistical Cheating Detection and Its Applications

本文研究了信息论密码学中的欺骗检测方法。特别地，我们阐明了（2，2）-门限秘密共享方案在模拟攻击中份额大小与成功概率指数之间的权衡关系。这个结果暗示了我们如何通过使每个共享冗余来轻松检测模拟。此外，我们还提出了一种防止可视秘密共享方案（VSSS）中欺骗的方法。我们还讨论了如何在实际环境中欺骗视觉秘密共享方案，重点是在没有计算机的情况下解密VSSS。除此之外，我们还阐明了信息论密码学的几个基本结果。

In this research, we investigated the way of detecting cheating in information theoretic cryptography. In particular, we clarified that the trade-off between share size and the exponent of the success probability in impersonation attack on (2,2)-threshold secret sharing schemes. This result implies how we can easily detect the impersonation by making each share redundant. In addition, we proposed a method of preventing the cheating in visual secret sharing schemes (VSSS). We also discussed how to cheat the visual secret sharing schemes in a practical setting by focusing on the situation where VSSS is decrypted without computers. Other than the above, we clarified several fundamental results on information theoretic cryptography.