- 學位論文
具完美安全與訊息驗證的量子密碼系統
A Quantum Cryptosystem with Perfect Secrecy and Message Authentication
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摘要
在傳統密碼學中, 已經有釵h研究學者發展出相當多不同的密碼系統, 這些密碼系統都有一個共同點, 他們的安全性全都是由一些計算難度上的假設來保證的, 這其實相當的不安全, 因為至今沒有人能保證這些假設的可靠性, 也就是說, 即便是目前廣泛使用的RSA, DES演算法, 也有可能在某一天被破解. 而量子密碼系統即可跳脫這些限制與缺點, 而純粹利用量子力學的物理定律來保證密碼系統的安全性. 在這篇論文中, 我們發展出一個量子密碼系統, 他不僅可以安全的讓兩方秘密通訊, 更可保證訊息來源的可靠性, 這避免掉攻擊者攔截整個傳輸通的可能. 而我們也在論文中證明了我們的密碼系統具備完美安全, 並且即使攻擊者不想偷得資訊而退一步只想破壞系統都是不可能發生的. 可以這麼說, 除非量子力學有再修正的必要, 否則我們的量子密碼系統是保證安全的.
並列摘要
In classical cryptography, many researcher have invented several useful cryptosytems. But, all of them are based on different classical computational assumptions, like the hardness of factoring or discrete logarithm. Nobody knows when the assumption is broken. In quantum cryptography, we can construct the quantum cryptosystem based on the laws of quantum physics to avoid the drawback above. In this thesis, we investigate a quantum cryptosystem with perfect secrecy and message authentication. In an insecure quantum channel that Bob communicates with Alice, we provide a cryptosystem allowing Alice to encrypt and authenticate an $n$-qubit message by $2n$ qubits with probability at least $1-frac{1}{2^{O(n)}}$ that Alice and Bob can detect eavesdropper(Eve), and we prove our quantum cryptosystem has perfect secrecy, that is, we can guarantee that nobody can steal any useful information from encrypted message.
參考文獻
1 Feymann, R. Simulating physics with computers.
3 Shor, P.W. Alogorithms for quantum computation:
Annual Symposium on Foundations of Computer Science} (Nov.),
124-134. Institute of Electrical and Electronic Engineers Computer
Society Press.