Physical Zero-Knowledge Proof for Nonogram Puzzles

• Main Authors: Yu-Feng Chien, 簡裕峰
• Other Authors: Wing-Kai Hon
• Format: Others
• Language: en_US
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/64177637153735718328

碩士 === 國立清華大學 === 資訊工程學系 === 96 === In daily life, we may want to convince others that we know a secret, while at the same time, we do not want to let them know what the secret is. In cryptography, there is a notion of zero-knowledge proof system, in which we can apply to achieve the goal. One may wonder if it is still possible to achieve the goal without using complicated theorems or powerful computational machines, and just by utilizing things that are easily reachable in our daily life? The answer is “yes.” This thesis studies various protocols for convincing others that “we know the solution of a Nonogram puzzle.” In other words, a person (called prover) who knows the solution of a particular Nonogram puzzle can apply our protocols to persuade another person (called verifier) that he knows the solution; at the same time he will not leak any information about the solution. Moreover, we show that our protocols can be implemented easily using only physical objects that are around us in our daily life. Our protocols are based on the traditional zero-knowledge proof system, together with a specially designed scratch-off card as our physical tool. The prover can then convince the verifier through a series of interaction between them. Yet, when the prover does not know the solution, there are some chances (called soundness probability) that a verifier wrongly believes this false prover. To counter this, we propose various strategies so that the soundness probability can be reduced. In summary, our final protocol can achieve perfect completeness (i.e., a prover knowing the solution can always convince the verifier), zero-knowledge property (i.e., no leakage of information) and 1/2 soundness (i.e., a false prover has only 1/2 chance to fool the verifier).