Quantum Cryptography with Classical Cryptography Introduction

1
Quantum Cryptographywith Classical Cryptography
Introduction
Aaron Holladay and Joshua Pugh
2
Cryptography Concepts

• Plaintext the original message
• Ciphertext the disguised message
• Encryption any procedure to convert plaintext
  into ciphertext
•  
• Decryption any procedure to convert ciphertext
  into plaintext
•  
• Key label for a specific algorithm in the whole
  collection of algorithms in a cryptosystem

3
An Introduction

• Cryptography the art of creating and using
  cryptosystems
• Cryptosystem or cipher system a method of
  disguising messages so that only certain people
  can see through the disguise

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2 Types of Cryptosystems

• Symmetric - use the same (secret) key to encrypt
  and decrypt a message
• Asymmetric - use one key (the public key) to
  encrypt a message and a different key (the
  private key) to decrypt it. Asymmetric
  cryptosystems are also called public key
  cryptosystems.

5
Symmetric Example and History

• Traditionally, the 2 parties would exchange 1 key
  in private to each other or over a secure
  connection and then the same key would be used to
  encrypt and decrypt the message.
• Supposedly, cryptography began when Julius Caesar
  sent messages to his trusted acquaintances, he
  didn't trust the messengers. So he replaced
  every A by a D, ever B by an E, and so on through
  the alphabet. Only someone who knew the "shift
  by 3" rule could decipher his messages.

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Caesar-like Example

• Text HELLO WORLD
• Key Shift each ASCII character right by 3
• Encrypted Text KHOORZRUOG
• To Decrypt Shift each character left by 3

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Public-Key Cryptography

• introduced by Diffie and Hellman in 1976
• Each person has a public and private key that are
  mathematical inverses of each other
• So, if the public key does something like Caesar
  did, then each character would be shifted right
  by 3. The private key then shifts the characters
  left by 3.
• want your function to be something that someone
  else could not find the inverse of

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Problems??

• An absolute security of information cannot be
  guaranteed. It has to be possible to figure out
  the mathematical inverse, but this could be quite
  timely.
• Cant verify the author of a message
• Wont know if the message has been read by an
  eavesdropper or not

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Digital SignaturesSecond Problem Solved!

• Example Bob and Alice create their
  public/private key pairs and exchange public
  keys. Then, Bob can use his private key to
  digitally sign his messages and Alice can use
  Bob's public key to verify the message is from
  Bob. Bob encrypts messages with Alice's public
  key and sends them to her and she decrypts them
  with her private key.

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Current Uses

• The main public-key algorithm is RSA and was
  developed by Ron Rivest, Adi Shamir, and Leonard
  Adleman in 1977. This algorithm is included as
  part of web browsers from Netscape and Microsoft.

11
Quantum Cryptography
12
Quantum Concepts

• Quantum entanglement a phenomenon in which the
  superposition of states (all possible states) of
  two or more systems allows the system to
  influence one another regardless of their spatial
  separation

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Quantum Concepts cont

• EPR (Einstein, Poldolsky and Rosen) paradox - As
  long as both photons remain unobserved, their
  properties remain indefinite, in a superposition
  of all states. But because of their common
  origin, the properties of the photons are
  correlated, or entangled.
• Ex. Through simple conservation of momentum, one
  knows that if one photon heads north, the other
  headed south. Consequently, measuring the
  momentum of one photon instantaneously determines
  the momentum of the other photon even if it has
  traveled to the opposite end of the universe.
  While the two measurements remain probabilistic,
  they nevertheless are correlated.

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Polarization of Photons

• There are four different polarizations of
  photons
• Rectilinear polarizations
• -0 degrees
• -90 degrees
• Diagonal polarizations
• -45 degrees
• -135 degrees

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2 Encryption Techniques

• Parity Bits
• Keys

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Parity Bits

• One technique is to use parity bits throughout
  the transmission and if the polarization of the
  parity bits are not correct, then you know there
  was an eavesdropper.

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Keys

• The sender sends photons with one of the four
  polarizations which are chosen at random. For
  each incoming photon, the receiver chooses at
  random the type of measurement either
  rectilinear or diagonal. The receiver records
  the results and keeps them secret. The receiver
  then publicly announces the type of measurement,
  but not results and the sender tells the receiver
  which measurements were correct. The parties
  keep all cases in which the receivers
  measurements were correct, converts the
  measurements to binary, and this becomes the key.

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Eavesdropping

• Quantum no-cloning theorem states that it is
  impossible to make an exact copy of an unknown
  quantum state
• Thus it is virtually impossible to eavesdrop by
  reading photons from an entangled pair and then
  continue sending that photon in the stream
  without being detected.

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The Reason

• The fundamental problem with classic private
  channel message/key transfers is that it can be
  monitored passively without the sender/receiver
  knowing.
• The act of measurement is an integral part of
  quantum mechanics, not just passive. The way that
  the quantum channel is designed it uses the
  theories of quantum mechanics so that any attempt
  to monitor the channel will disrupt the data in a
  detectable way.

20
Problems

• Single photons on demanda beam of light produced
  by a laser contains approximately 100 million
  billion photons per secondSOLVEDan individual
  photon can be released from a quantum dot
  embedded in a microdisk.
• Distinguishing between line noise and
  eavesdropping
• Sending photons over a large distance, but this
  problem has recently become less of an issue with
  the use of Quantum Repeaters

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Future Use

• Future applications are in the most secure
  communication lines for bank-to-ATM transactions,
  financial information protection over the
  internet, and military and government
  communications including the use for
  ship-to-ship, ground-to-satellite, and
  satellite-to-satellite communication.

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References

• Cryptography FAQ http//www.faqs.org/faqs/crypto
  graphy-faq/
•  
• Cryptography The Study of Encryption
  http//world.std.com/franl/crypto.html
•  
• Public Key Cryptography http//www.trustedweb.co
  m/intro/public-key-cryptography.html
•  
• What is Quantum Cryptography?
  http//www.qubit.org/intros/crypt.html
•  
• Quantum Cryptography, Scientific American, July
  1992, http//dhushara.tripod.com/book/quantcos/aq/
  qcrypt.htm
• Quantum Cryptography and Communications
  http//photon.bu.edu/sergienko/crypto.html
• Quantum Entanglement http//www.wikipedia.com/wi
  ki/quantumentanglement
• Unconditional Security of Quantum Key
  Distribution over Arbitrarily Long Distances
  http//www.sciencemag.org, March 26, 1999, Vol.
  283.
• First Device That Produces Light One Photon At
  a Time http//ptg.djnr.com/ccroot/asp/publib/sto
  ry.asp
• Did A Mouse Give Birth To The Universe?
  http//www.uoregon.edu/rlz/QM.html