Advances In Cryptography

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


Advancements in cryptography
[Today’s Talk]
 Quantum Cryptography
 Elliptic Curve Cryptography


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.


 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.


 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.


•

•

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


 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.


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.


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.


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)


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


Thank
You
Shailesh Tyagi
Developer
www.rareinput.com

Advances In Cryptography

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