# QUANTUM CRYPTOGRAPHY

Document Sample

```					  QUANTUM
CRYPTOGRAPHY

Matthew Suhre
Overview
   History of Cryptography
   Cryptography Basics
   RSA Encryption
   Algorithm
   Example
   Quantum Cryptography
   History
   Process
   Pros and Cons
   Open Air Cryptography
Cryptography History
   Dates Back to Julius Ceaser
 Didn’t trust messanger
 Used “Shift by 3” method
Cryptography Basics
   Cryptosystem (Cipher System) – method of
disguising messages so that only certain people can
   Cryptography – Art of creating and using
Cryptosystems
   Cryptanalysis – Art of breaking Cryptosystems
   Cryptography – study of Cryptography and
Cryptosystems
Cryptography Basics
   Symmetric Cryptosystems use the same key to
encrypt and decrypt
   You need to send the key securely
   Asymmetric Cryptosystems use a public key to
encrypt and a private key to decrypt
RSA Encryption
   Invented in 1978 by Ron Rivest, Adi Shamir and
   Algorithm for public key encryption
RSA Encryption Algorithm
   1. Find P and Q two large prime numbers
   2. Choose E such that: 1<E<PQ
 E does not have to be prime, but must be odd
 (P-1)(Q-1) and E must not have no prime factors in
common
   3. Compute D such that (DE-1) is evenly
divisible by (P-1)(Q-1)
RSA Encyrption Algorithm
   4. Encryption function is C = (T^E) mod PQ
 C is the ciphertext (positive integer)
 T is the plaintext (positive integer)
 T must be less then the modulus PQ

   5. Decryption function is T = (C^D) mod PQ
 C is the ciphertext (positive integer)
 T is the plaintext (positive integer)
 D is the private key
Example of RSA Encryption
RSA Encryption
   Relying on
 No one can solve
 Would take to long to solve

   Theoretically Can be Broken
Quantum Cryptography History
   Early 1970’s Stephen Wiesner wrote “Conjugate
Coding”
   1979 Charles H. Bennett and Gilles Brassard
wrote various papers on the subject
   Basis: Takes advantage of Heisenberg’s principle
in which measuring a quantum system disturbs it
and yields incomplete information
Quantum Cryptography Setup
   Most widely used is the BB84 Protocol
developed by IBM
   The sending apparatus consists of a green light-
emitting diode, a lens, a pinhole and mirrors that
provide a collimated beam of horizontally
polarized light. Next, electronic devices known
as Pockels Cells are used to change the original
horizontal polarization to any of four standard
polarization states under the users control
Quantum Cryptography Setup
   The receiving apparatus contains a similar
Pockels cell, which allows the user to choose the
type of polarization he will measure. After the
beam passes through hte Pockels Cell, it is split
by a calcite prism into two perpendicularly
polarized beams, which are directed into two
photomultiplier tubes for the purpose of
detecting individual photons
Alice Sends Polarizations

Bob randomly chooses measurement

Bob records the results

They Check the results

This then becomes the
key
Quantum Cryptography
   If someone tries to steal the signal
 Measurements are changed
 Signal is slower/weaker

 Sender/Reciever can stop
Pros
   Nearly Impossible to steal
   Detect if someone is listening
   “Secure”
Cons
   Price limits length
 Normally just for a local network about 10km
 Record set by Los Almos is 31 miles

 Longer length, signal is absorbed, noise increased

   Availability
   If was a straight pipe, distance could be limitless
Free Space
   Being developed for longer distances
   May be possible to send from ground satellites
to space satellites
   Longest recorded is ½ km, at Los Almos
Summary
   History of Cryptography
   Cryptography Basics
   RSA Encryption
   Algorithm
   Example
   Quantum Cryptography
   History
   Process
   Pros and Cons
   Open Air Cryptography
Bibliography
   http://www.cs.mcgill.ca/~crepeau/CRYPTO/Biblio-QC.html
   http://www.qubit.org/intros/crypt.html
   http://www.faqs.org/faqs/cryptography-faq
   http://world.std.com/~franl/crypto.html
   http://www.lanl.gov/orgs/pa/science21/QuantumCrypto.html