Advances In
Cryptography
Basic Ideas in Cryptography

• Cryptography is the study of sending and receiving secret messages through the help of
cryp...
• It’s the transmitting information with access restricted to the intended recipient even if the message is
intercepted by...
Advancements in cryptography
[Today’s Talk]
 Quantum Cryptography
 Elliptic Curve Cryptography

Brought To You By www.ra...
I.

Quantum Cryptography

• Quantum cryptography is the single most successful application of Quantum
Computing/Informatio...
 Ideas from the Quantum World
• Light waves are propagated as discrete quanta called photons.
• They are massless and hav...
 Quantum key distribution
• The main key distribution of quantum cryptography is to solve the key distribution system
pro...
•

•

Bob uses his polarizers to measure each polarization of photons he receives.
He can use the( + )basis or the ( ) but...
 presence of eavesdropping
• If Eve uses the filter aligned with Alice’s he can recover the original polarization of the ...
II. Elliptic Curve Cryptography
• Elliptic curve cryptography (ECC) is an approach to public-key
cryptography based on the...
Cont..
• An elliptic curve consists of the set of real numbers (x, y) that satisfies the equation:

•

The set of all of t...
Advantages & Disadvantages
• Advantages
• fast and compact implementation in hardware
• Shorter keys than RSA
• Disadvanta...
 References
• http://en.wikipedia.org/wiki/Quantum_cryptography
• www.google.com
• http://www.springerreference.com/docs/...
Thank
You
Shailesh Tyagi
Developer
www.rareinput.com
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Advances In Cryptography

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  • Changing a and b changes the shape of the curve, and small changes in these parameters can result in major changes in the set of (x,y) solutions.
  • Advances In Cryptography

    1. 1. Advances In Cryptography
    2. 2. 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 Brought To You By www.rareinput.com
    3. 3. • 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 Brought To You By www.rareinput.com
    4. 4. Advancements in cryptography [Today’s Talk]  Quantum Cryptography  Elliptic Curve Cryptography Brought To You By www.rareinput.com
    5. 5. 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. Brought To You By www.rareinput.com
    6. 6.  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. Brought To You By www.rareinput.com
    7. 7.  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. Brought To You By www.rareinput.com
    8. 8. • • Bob uses his polarizers to measure each polarization of photons he receives. He can use the( + )basis or the ( ) but not both simultaneously Brought To You By www.rareinput.com
    9. 9.  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. Brought To You By www.rareinput.com
    10. 10. 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. Brought To You By www.rareinput.com
    11. 11. 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. Brought To You By www.rareinput.com
    12. 12. 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) Brought To You By www.rareinput.com
    13. 13.  References • http://en.wikipedia.org/wiki/Quantum_cryptography • www.google.com • http://www.springerreference.com/docs/html/chapterdbid/71039.html Brought To You By www.rareinput.com
    14. 14. Thank You Shailesh Tyagi Developer www.rareinput.com

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