量子密码学：理论与实践的交汇

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"量子密码学-从理论到实践" 量子密码学是信息安全领域的一个前沿分支，它利用量子力学的原理来实现通信的安全性。这一领域的理论基础在于量子态的不可克隆性、测量的随机性和海森堡不确定性原理，这些特性使得量子密码学能够在理论上提供无条件的安全保障，即即使是最强大的攻击者，只要遵循物理定律，也无法不被发现地窃取信息。文章提到了arXiv上的一篇关于量子密码学的研究论文，由Hoi-Kwong Lo和Norbert Lütkenhaus共同撰写，他们分别来自多伦多大学和滑铁卢大学的量子信息和量子控制中心以及量子计算研究所。这篇论文回顾了量子密码学的理论和实践，同时也关注了一些近期的发展。量子密码学中最著名的协议是BB84协议，由Charles Bennett和Gilles Brassard在1984年提出。该协议利用量子比特（qubits）的不同基态进行编码和解码，通过检测接收方的量子态与发送方的不匹配，可以确定是否存在中间人攻击。此外，还有E91协议，这是第一个量子密钥分发（QKD）协议，它允许两个远程用户安全地生成共享密钥，即使在有潜在敌手存在的情况下。近年来，量子密码学的研究重点转向了实际应用和安全性分析。尽管理论上量子通信是安全的，但在实际操作中，可能会受到各种噪声、损耗和技术限制的影响。研究人员已经提出了各种方法来对抗这些挑战，例如使用纠错码和前向错误纠正策略，以提高在噪声环境下的通信效率和安全性。在实际系统中，量子密码学面临着诸多挑战，如量子信道的稳定性、探测器效率和误报率等问题。此外，实验实施通常需要精密的光学设备或超导电路，这限制了其商业化部署。然而，随着技术的进步，如量子点、线性光学系统和离子陷阱等新型量子信息处理平台的发展，量子密码学正逐步走向实用化。在安全性方面，量子密码学的实践安全性不仅依赖于物理原理，还涉及到协议的安全分析和攻击模型。例如，侧信道攻击是针对实现层的攻击，攻击者可能利用设备的物理特性获取信息。因此，对量子设备的安全评估和设计变得至关重要。量子密码学是一个充满活力且不断发展的领域，它将理论物理学与信息科学相结合，为未来的网络安全提供了新的可能性。随着量子技术的不断成熟，我们期待看到量子密码学在保障数据隐私和信息安全方面发挥更大的作用。

arXiv:quant-ph/0702202v3 13 Mar 2007

Quantum Cryptography: from Theory to Practice

Hoi-Kwong Lo and Norbert L¨utkenhaus

Center for Quantum Information and Quantum Control,

Department of Physics and Department of Electrical & Computer Engineering,

University of Toronto, Toronto,

Ontario, M5S 3G4, Canada

and

Institute for Quantum Computing & Department of Physics and Astronomy,

University of Waterloo,

200 University Ave. W. N2L 3G1

(Dated: March 17, 2016)

Quantum cryptography can, in principle, provide unconditional security guaranteed by the law

of physics only. Here, we survey the theory and practice of the subject and highlight some recent

developments.

PACS numbers:

”The human desire to keep secrets is almost as old as

writing itself.” [1] With the advent in electronic com-

merce, the importance of secure communications via en-

cryption is growing. Each time when we go on-line for

internet banking, we should be concerned with commu-

nication secur ity. Indeed, methods of secret communi-

cations were used in many ancient civilizations includ-

ing Mesopotamia , Eqypt, India and China. Legends say

that Julius Caesar used a simple substitution cipher in

his correspondences. Each letter is replaced by a letter

that followed it thr e e places alphabetically. For instance,

the word LOW is replaced by ORZ because the ﬁrst let-

ter ”L” in LOW is replaced by L → M → N → O, etc.

Regardless of the size of the shift, the illustrated method

is still called Caesar’s cipher.

Let us introduce the general problem of secure commu-

nication. Suppose a sender, Alice, would like to send a

message to a receiver, Bob. An eavesdropper, Eve, would

like to learn about the message. How can Alice prevent

Eve from learning her message?

A standard method is encryption. Alice uses her en-

cryption key (some secret information) to transform her

message (a plaintext) into something (a ciphertext) that

is unintelligible to Eve and sends the ciphertext throug h

a communica tio n channel. Bob, with his decry ption key,

recover s Alice’s message from the c iphertext. For in-

stance, in Caesar’s cipher, the key takes a value between

1 and 26, which denotes the size of the shift.

Since encryption machine s may be captured, in moder n

cryptography, it is standard to assume that the encryp-

tion method is known and the security of the message lies

on the security of the key. For instance, we assume that

Eve knows that Caesar’s cipher is being used, but she

does not a priori know the value of the key. Note that

Caesar’s cipher is not that secure because the number of

all poss ible key values is s o small (only 26) that Eve can

easily try all possible values.

Throughout the history of cryptography, many ciphers

have been invented and believed for a while to be un-

breakable. Almost all have subsequently been broken,

with disastrous consequences to the unsuspecting users.

For instance, in the Second World War, the Allies’ break-

ing of the German Enigma code contributed greatly to

the ultimate vic tory of the Allies. The ﬁrst lesson in

cryptography is: never under-estimate the ingenuity and

eﬀorts that your enemies are willing to spend on breaking

your codes.

Unbr eakable codes do exist in co nventional cryptogra-

phy. T hey are called o ne-time pads and were invented by

Gilbert Vernam in 1918: A message is ﬁrs t converted into

a binary form (i.e., a string consisting of 0’s and 1’s) by

a publicly known method. The key is ano ther sequence

of 0’s and 1’s of the same length. For encryption, Al-

ice combines each bit of the message with the re spec tive

bit of the key by using addition modulo 2 to generate

the ciphertext. For decryption, Bob combines each bit of

the ciphertext with the respective bit of the key by using

addition modulo 2 to generate the plaintext.

For one-time pad to be secure, it is important that

a key is never re-used. This is why it is ca lled a one-

time pad. Why re-using a key would ma ke the scheme

insecure? Suppose the same key, k, is use d to encrypt

two diﬀerent messages, m

and m

. Then, the cipher-

texts, c

= m

⊕ k and c

= m

⊕ k, are trans mitted

in public. An eavesdropper can simply take the addition

modulo 2 of the two cipher-texts to obtain c

⊕ c

⊕ k ⊕ m

⊕ k = m

⊕ m

. But, this allows Eve to

learn some non-trivial information, namely the parity,

about the two original messages.

I. KEY DISTRIBUTION PROBLEM

The one-time pad has a serious drawback: it pre -

supposes that Alice and Bob share a random string of

secret, a key, before the actual transmission o f the mes-

sage. So, the introduction of the one-time pad shifts the

problem of secure communication to the problem of se -

cure key distribution. This is called the key distribution

problem. In top secret applications, key distribution is

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