1. QUANTUM CRYPTOGRAPHY

2. Cryptography.
Transmitting information with access restricted to the intended recipient even if the message is intercepted by others.
Cryptography is of increasing importance
in our technological age using broadcast, network communications, Internet , ,
cell phones which may transmit sensitive information related to finances, politics, business and private confidential matters.

3. The process Key Plaintext Encryption Crypto text Plaintext Decryption
Secure
transmission
Key ready for use
Plaintext
Decryption
Message encryption
Secure key distribution

4. The classic cryptography
Encryption algorithm and related key are kept secret.
Breaking the system is hard due to large numbers of possible keys.
For example: for a key 128 bits long
there are
The fundamental difficulty is key distribution to parties who want to exchange messages.

5. PKC :the modern cryptography
In 1970s the Public Key Cryptography emerged.
Each user has two mutually inverse keys,
The encryption key is published;
The decryption key is kept secret.
Anybody can send a message to Bob
but only Bob can read it.

6. RSA Algorithm
The most widely used PKC is the RSA algorithm based on the difficulty of factoring a product ot two large primes
Choose two large prime numbers p and q.
Compute N=p*q.
Choose e(<<<N) such that e and (p-1)(q-1)
is relatively prime
Choose d such that (e*d) mod [(p-1)(q-1)]
is equal to 1;

7. EXAMPLE Let the Private key is (119,77)and Public key is (119,5).
If we want to send B then the ciphertext
c = 25 mod 119
= 32
Then the Plaintext
p = mod 119
= 2

8. Factoring a product of two large primes
The best known conventional algorithm requires the solution time proportional to:
For p & q 65 digits long T(n) is approximately
one month using cluster of workstations.
For p&q 200 digits long T(n) is astronomical.

9. Quantum Computing algorithm for factoring.
In 1994 Peter Shor from the AT&T Bell Laboratory showed that in principle a quantum computer could factor a very long
product of primes in seconds.
Shor’s algorithm time computational complexity is
Once a quantum computer is built the RSA method would not be safe.

10. Elements of the Quantum Theory
Light waves are propagated as discrete quanta called photons.
They are mass less and have energy, momentum and angular momentum called spin.
If on its way we put a polarization filter a photon may pass through it or may not.

11. Photon Polarization
Tilted filter at
the angle
Vertical filter
The probability of a photon appearing after the second
filter depends on the angle and becomes 0 at
= 90 degrees.
The first filter randomizes the measurements of the second filter.

12. Heisenberg Uncertainty Principle
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.
When measuring the polarization of a photon, the choice of what direction to measure affects all subsequent measurements.
If a photon passes through a vertical filter it will have the vertical orientation regardless of its initial direction of polarization

13. EXAMPLE

14. Quantum key distribution
Both Alice and Bob have two polarizers each.
One with the 0-90 degree basis (+) and one with degree basis ( )
(a) Alice uses her polarizers to send randomly photons to Bob in one of the four possible polarizations 0,45,90,135 degree.
(b) Bob uses his polarizers to measure each
polarization of photons he receives.
He can use the( + )basis or the ( ) but not both simultaneously.

15. EXAMPLE CONTD. Where λ is probability of error.
Stage 1: Communication over a quantum channel.
Stage 2:Communication in two phases in public channel
Phase 1:Extraction of raw key
Phase 2:Detection of Eve’s intrusion through error calculation
Where λ is probability of error.
m is the no of places where comparison takes place
If λ is 1 and m is 200 then

16. Eavesdropper Eve
If Eve uses the filter aligned with Alice’s she can recover the original polarization of the photon.
If she uses the misaligned filter she will receive no information about the photon Also she will influence the original photon and be unable to retransmit it with the original polarization.
Bob will be able to deduce Eve’s presence.

17. KEY DISTRIBUTION IN PRESENCE OF EAVESDROPPER

18. QUANTUM KEY DISTRIBUTION IN NOISY CHANNEL
Stage 1: Communication over a quantum channel.
Stage 2: Detection of Eve’s intrusion or noise by calculating error.
Phase 1: Same as above method.
Phase 2: Estimation of error.
Phase 3: Extraction of reconciled key.
Phase 4: Privacy amplification i.e. Extraction of final secret key.
The secret key may contain n-k-s.
n : the number of keys present in the reconciled key
k : the number of place where there is error
s : the security parameter sender and receiver have decided to maintain.

19. Binary information
A user can suggest a key by sending a stream of randomly polarized photons.
This sequence can be converted to a binary key.
If the key was intercepted it could be discarded and a new stream of randomly polarized photons sent.

20. Security of quantum key distribution
Quantum cryptography obtains its fundamental security from the fact that each qubit is carried by a single photon, and each photon will be altered as soon as it is read.
This makes impossible to intercept message without being detected.

21. State of the QC technology.
Experimental implementations have existed since 1990.
Current QC is performed over distances of kilometers using optical fiber
In general we need two capabilities.
Single photon gun.
(2) Being able to measure single photons.
Efforts are being made to use Pulsed Laser Beam with low intensity for firing single photons.
Detecting and measuring photons is hard.
The most common method is exploiting Avalanche Photodiodes where single photon triggers a detectable electron avalanche.

22. State of the QC technology.
Key transmissions can be achieved for about 80 km distance.
For longer distances we can use repeaters. But practical repeaters are a long way in the future.
Another option is using satellites .But the satellites distance from earth is in hundreds of kilometers.

23. Commercial QC providers
id Quantique, Geneva Switzerland
Optical fiber based system
Tens of kilometers distances
MagiQ Technologies, NY City
Optical fiber-glass
Up to 100 kilometers distances
NEC Tokyo 150 kilometers
QinetiQ Farnborough, England
Through the air 10 kilometers.
Supplied system to BBN in Cambridge Mass.

24. CONCLUSION
For the first time in history, the security of cryptography does not depend any more on the computing resources of the adversary, nor does it depend on mathematical progress. Quantum cryptography allows exchanging encryption keys, whose secrecy is future-proof and guaranteed by the laws of quantum physics. Its combination with conventional secret-key cryptographic algorithms allows raising the confidentiality of data transmissions to an unprecedented level .Recognizing this fact, the MIT Technology Review and Newsweek magazine identified quantum cryptography as one of the “ten technologies that will change the world.

25. References google.com yahoo.com wikipedia.com webopedia.com
idquantique.com
csee.umbc.edu

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