I recently heard about the concept of zero-knowledge proof. However, I still do not get how it is possible to make it a solution to some real-world problems. One thing I heard is that zero-knowledge proof can be utilized in Elections. But my question is what is the use, or how can we implement zero-knowledge proof system in elections?
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This is far too broad a subject to cover in one answer, so I will give you a recommendation for where you can learn more.
I highly recommend this talk from Ben Adida: https://www.youtube.com/watch?v=ZDnShu5V99s. He discusses cryptography in elections, including zero-knowledge proofs and other cryptographic primitives, at a holistic level. Zero-knowledge proofs are used to verify the correctness of decryption and that the mixnet worked correctly, and he shows an example zero knowledge proof for the latter. You might also be interested to take a look at https://crypto.stackexchange.com/q/6647/351 and https://crypto.stackexchange.com/search?q=%5Bvoting%5D+zero+knowledge, where you can find some pointers into the research literature.
D.W.
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