Advances In Cryptography

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Basic Ideas in Cryptography• Cryptography is the study of sending and receiving secret messages through the help of

cryptosystem.• The basic idea is to modify a message so as to make it unintelligible to anyone but the intended

recipient

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• It’s the transmitting information with access restricted to the intended recipient even if the message is intercepted by others.

• A typical application of cryptography in network security is to enable two parties to communicate confidentially over a non-physically secured communication platform such as radio waves, the internet, etc.

• “A little knowledge is a dangerous thing” Very true in cryptography

• Cryptography is of increasing importance in our technological age Broadcast Network communications Internet E-mail Cell phones

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Advancements in cryptography

[Today’s Talk] Quantum Cryptography Elliptic Curve Cryptography

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I. Quantum Cryptography

• Quantum cryptography is the single most successful application of Quantum Computing/Information Theory.

• For the first time in history, we can use the forces of nature to implement perfectly secure cryptosystems.

• Quantum cryptography describes the use of quantum mechanical effects to perform cryptographic tasks or to break cryptographic systems.

• The use of classical (i.e., non-quantum) cryptography to protect against quantum attackers is also often considered as quantum cryptography.

• Classical Cryptography relies heavily on the complexity of factoring integers.

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Ideas from the Quantum World

• Light waves are propagated as discrete quanta called photons.

• They are massless and have energy momentum and angular momentum called spin.

• Spin carries the polarization.

• If on its way we put a polarization filter a photon may pass through it or may not.

• We can use a detector to check of a photon has passed through a filter.

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Quantum key distribution

• The main key distribution of quantum cryptography is to solve the key distribution system problem.

• Alice communicates with Bob via a quantum channel sending him photons.• Then they discuss results using a public channel.• After getting an encryption key Bob can encrypt his messages and send them by any public

channel.• Both Alice and Bob have two polarizers each.• One with the 0-90 degree basis (+) and one with 45-135 degree basis ( )• Alice uses his polarizers to send randomly photons to Bob in one of the four possible

polarizations 0,45,90,135 degree.

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• Bob uses his polarizers to measure each polarization of photons he receives.• He can use the( + )basis or the ( ) but not both simultaneously

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presence of eavesdropping

• If Eve uses the filter aligned with Alice’s he can recover the original polarization of the photon.• If he uses the misaligned filter he will receive no information about the photon .• Also he will influence the original photon and be unable to retransmit it with the original

polarization.• Bob will be able to deduce Ave’s presence.

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II. Elliptic Curve Cryptography

• Elliptic curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields.

• ECC was proposed independently by cryptographers Victor Miller (IBM) and Neal Koblitz (University of Washington) in 1985.

• It is based on the difficulty of solving the Elliptic Curve Discrete Logarithm Problem (ECDLP)Like the prime factorization problem.

• ECDLP is another "hard" problem that is simple to state: Given two points, P and Q, on an elliptic curve, find the integer n, if it exists, such that p= nQ.

• Elliptic curves combine number theory and algebraic geometry.

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Cont..

• An elliptic curve consists of the set of real numbers (x, y) that satisfies the equation:

• The set of all of the solutions to the equation forms the elliptic curve.

• Elliptic curves have the interesting property that adding two points on the elliptic curve yields a third point on the curve.

• The point Q is calculated as a multiple of the starting point P Q = nP An attacker might know P and Q but finding the integer, n, is a difficult problem to solve. Q is the public key, then, and n is the private key.

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Advantages & Disadvantages

• Advantages• fast and compact implementation in hardware• Shorter keys than RSA • Disadvantages• Complex mathematical description• Short period of research in cryptanalysis (breaking cipher)

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References

• http://en.wikipedia.org/wiki/Quantum_cryptography• www.google.com• http://www.springerreference.com/docs/html/chapterdbid/71039.html

Thank You

Shailesh TyagiDeveloperwww.rareinput.com