基於密碼學的零知識證明協定

Protocols of Zero-Knowledge Proof Based on Cryptography

吳智羽(Zhi-Yu Wu)

指導教授 ： 涂世雄

中原大學/電機資訊學院/通訊工程碩士學位學程/碩士(2021年)

https://doi.org/10.6840/cycu202100016

摘要

本文提出了一些基於密碼學的零知識證明協議。我們在這些方案中加密秘密消息以執
行零知識證明交換。我們可以在沒有其他多餘信息的情況下確認秘密訊息。
本文提出了三種方案。在第一個方案中，我們提出了基於 RSA 密碼系統的零知識證明
協議。在該方案中，給出了五種協議。在這些協議中，秘密消息是通過我們的 RSA 函
數加密的，然後我們將其發布給中介或第三方認證。驗證者可以使用檢查公式進行驗
證。在這些協議中，這些秘密消息通過 RSA 的公開金鑰或其 Euler 函數進行加密。
對於第二種方案，我們提出了基於對數的零知識證明。在該方案中，給出了三種協
議。在這些協議上，秘密訊息通過我們的對數函數進行加密。該函數基於離散對數困
難。秘密訊息通過公開金鑰或其 Euler 函數進行加密。
對於第三種方案，我們提出了基於 Rabin 密碼系統的零知識證明。 Rabin 密碼系統也
是一個非對稱密碼系統，類似於 RSA，它使用大整數質因數分解困難。該方案給出了三
種協議。秘密訊息和交互式消息通過 Rabin 的公開金鑰或其 Euler 函數進行加密。
本文的主要貢獻如下。
（1）使用密碼學原理進行零知識證明。
（2）協議易於驗證。
（3）交互過程易於理解和操作。

關鍵字

密碼學 ； 零知識

並列摘要

In this thesis, we propose some protocols of zero-knowledge proof based on
cryptography. We encrypt the secret message in these schemes to perform zeroknowledge proof transformation. As results, we can transform the secret
message without additional information.
There are three schemes have been proposed in this thesis. At the first
scheme, we propose zero-knowledge proof protocols based on RSA
cryptosystem. In this scheme, there are five protocols have been given. In these
protocols, the secret message is encrypted by our RSA formula, then we publish
it to an intermediary or third-party certification. The verifier can use the check
formula to verify if the sender owns the secret message. In these protocols, the
secret message is encrypted by the public key of RSA or its Euler function.
For the second scheme, we propose zero-knowledge proofs based on
logarithm. In this scheme, there are three protocols have been given. On these
protocols, the secret message is encrypted by our logarithm formula. Each
formula is based on the logarithm problem. The secret message is encrypted by
the public prime key or its Euler function.
For the third scheme, we propose zero-knowledge proofs based on Rabin
cryptosystem. The Rabin cryptosystem is also an asymmetric cryptographic
system like RSA. It uses difficulty of integer factorization. In this scheme, there
are three protocols are given. The secret message and interactive message are
encrypted by the public key of Rabin or its Euler function.
In this thesis, the main contributions are as follows.
(1)The protocols of zero-knowledge is performed by sing the theory of
cryptography.
(2)The protocols are verified easily.
(3)The interactive process is easily understood and manipulated.

並列關鍵字

zero-knowledge

參考文獻

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