Quantum Cryptography: Secure Communication through Quantum Mechanics, Lecture notes of Computer Science

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Quantum Cryptography

By Roshan Pawar AC- Under Supervision of Dr. Shweta Jain Under Supervision of Dr. Dhirendra Pratap Singh

M.tech 1st year

2017-

Maulana Azad National Institute of Technology

 Cryptography

 Limitations of Modern Cryptosystems

 Quantum Cryptography

 Quantum Key Distribution

 Advantages

 Limitations

 Conclusion

 References

Contents

 (^) It is used to secure communication by protecting the sensitive data and provides confidentiality and integrity of messages.  (^) Messages are made secret by transforming them from “plain-text” into “cipher-text”.  (^) There are two types of cryptography

1. In symmetric key cryptography, the same key is used for both encryption and decryption. The major difficulty of symmetric key cryptography is to provide the secret keys to legitimate parties without divulging the keys to eavesdroppers.
2. In Public key cryptography there are two keys, one for encrypting and another key for decrypting, and only one key is intended to be

Cryptography



Modern cryptography algorithms are based over the

fundamental process of factoring large integers into

their primes, which is said to be “INTRACTABLE”.

 But modern cryptography is vulnerable to both

technological progress of computing power and

evolution in mathematics to quickly reverse one-way

functions such as that of factoring large integers.

 Current public key cryptosystems may be “good

enough” to provide a reasonably strong level of

confidentiality today, there is exposure to a handful of

risks.

Limitations of Modern Cryptosystems

 (^) Rather than depending on the complexity of factoring large numbers, quantum cryptography is based on the fundamental and unchanging principles of quantum mechanics.  (^) In fact, quantum cryptography rests on two principles of quantum mechanics:

• The Heisenberg Uncertainty principle,
• Principle of photon polarization.  (^) According the Heisenberg Uncertainty principle, it is not possible to measure the quantum state of any system

Quantum Cryptography

 (^) Certain pairs of physical properties are related in such a way that measuring one property prevents the observer from knowing the value of the other.  (^) The photon polarization principle describes how light photons can be oriented or polarized in specific directions. Moreover, a photon filter with the correct polarization can only detect a polarized photon or else the photon will be destroyed.

 It is this “one-way-ness” of photons along

with the Heisenberg Uncertainty principle

that make quantum cryptography an

attractive option for ensuring the privacy of

data and defeating eavesdroppers.

 (^) In Quantum cryptography ,there are two channels,

• Optical channel,
• Public channel.  (^) Optical channel is used for transferring photons between sender and receiver.  (^) Public channel is used for discussing about which polarizer is both sender and receiver using.

 (^) Light waves are propagated as discrete quanta called, photons. They are massless and have energy, momentum and angular momentum called spins.  (^) Spin carries the polarization.  (^) If the sender and receiver using the same polarizer, then match occurred and that bit value become one of the bit of the key.

 There are two polarizers, vertical polarizer

and horizontal polarizer. In vertical polarizer if

photon movement is in 90 then bit value

become 1 and if photon movement is in 0

,then bit value will be 0.In case of diagonal

polarizer photon movement is in 45, bit value

will be 1 and if photon movement is in 135,

bit value becomes 0.

 An encryption key could be created depending

on the amount of photons reaching a recipient

and how they were received.

 These photons can be polarized at various

orientations, and these orientations can be

used to represent bits representing ones and

zeros.

 (^) This example includes a sender, “Alice”, a receiver, “Bob”, and a malicious eavesdropper, “Eve”.  (^) Alice begins by sending a message to Bob using a photon gun to send a stream of photons randomly chosen in one of four polarizations that correspond to vertical, horizontal or diagonal in opposing directions (0,45,90 or 135 degrees).  (^) For each individual photon, Bob will randomly choose a filter and use a photon receiver to count and measure the polarization which is either rectilinear (0 or 90 degrees) or diagonal (45 or 135 degrees), and keep a log of the results.

Quantum Key Distribution

 (^) While a portion of the stream of photons will disintegrate over the distance of the link, only a predetermined portion is required to build a key sequence.  (^) Bob will inform Alice to the type of measurement made and which measurements were of the correct type without mentioning the actual results.  (^) The photons that were incorrectly measured will be discarded, while the correctly measured photons are translated into bits based on their polarization. These photons are used to form the basis of a key for sending encrypted information.

 It is important to point out that neither Alice nor Bob are

able to determine what the key will be in advance because

the key is the product of both their random choices. Thus,

quantum cryptography enables the distribution of a one-time

key exchanged securely.

 Now let us suppose that a malicious attacker attempts to

infiltrate the cryptosystem and defeat the quantum key

distribution mechanisms.

 (^) If this malicious attacker, named Eve, tries to eavesdrop, she too must also randomly select either a rectilinear or diagonal filter to measure each of Alice’s photons.  (^) Hence, Eve will have an equal chance of selecting the right and wrong filter, and will not be able to confirm with Alice the type of filter used.  (^) Even if Eve is able to successfully eavesdrop while Bob confirms with Alice the protons he received, this information will be of little use to Eve unless she knows the correct polarization of each particular photon.

There are three significant advantages of this system:

 First, the Heisenberg Uncertainty principle means that

information regarding photons cannot be duplicated

because photons will be destroyed once they are measured

or tampered with. Since photons are indivisible, once it hits

a detector, the photon no longer exists.

 Secondly, Alice and Bob must calculate beforehand the

amount of photons needed to form the encryption key. If

there is a deviation for the predetermined fixed number,

Bob can be certain that traffic is being sniffed or something

is wrong in the system. This is the result of the fact that if

Eve detects a photon, it will no longer exist to be detected

by Bob.

Advantages

 If Eve attempts to create and pass on to

Bob a photon, she will have to randomly

choose its orientation, and on average be

incorrect about 50 percent of the time –

enough of an error rate to reveal her

presence.

 (^) Point to Point links and Denial of Service: X and Y have to be at each end of it, with their photon sources and detectors. The point-to-point nature of QKD restricts potential growth, and gives rise to the possibility of a denial-of- service attack: if Z can’t obtain key information, then cutting the physical link will mean X and Y can’t either, which might serve Z’s purposes just as well.  (^) Key Distribution Rate : The length of the quantum channel also has an effect on the achievable rate of key distribution. The rate at which key material can be sent decreases exponentially with respect to distance, and is regarded as another limiting factor in the usability of QKD systems. Limitations of Quantum Cryptography

 Quantum cryptography does not provide

digital signature and related features.

 Distance Limitation :

Currently, quantum key distribution

distances are limited to tens of kms because

optical amplification destroys the bit state

 (^) Quantum cryptography ensure secure communication by providing security based on the fundamental law of physics, instead of the current state of mathematical algorithms or computing technology.  (^) Unlike classical encryption algorithm quantum cryptography does not depend factoring large integers into primes but on the fundamental principles of quantum physics.  (^) Quantum cryptography is more secure, because an intruder is not able to replicate the photon to recreate the key

Conclusion

 C. Bennett and G. Brassard, “Quantum Cryptography:

Public Key Distribution and Coin Tossing,”

International Conference on Computers, Systems, and

Signal Processing, Bangalore, India, 1984.

 Quantum Cryptography: Realizing next generation

information security, (IJAIEM) Volume 3, Issue 2,

February 2014

 Quantum Cryptography: Lavanya Varghese, (IJCSIT)

International Journal of Computer Science and

Information Technologies, Vol. 6 (1) , 2015, 14-17

References