Download Quantum Cryptography

QUANTUM
CRYPTOGRAPHY
INTRODUCTION
•
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.
•
It relies on 2 major elements of quantum
mechanics:
i.e heisenberg uncertainity principle
and principle of photon polarization.
NEED OF QUANTUM CRYPTOGRAPHY
• Classical Cryptography relies heavily on the complexity of
factoring integers.
• Quantum Computers can use Shor’s Algorithm to efficiently
break today’s cryptosystems.
• We need a new kind of cryptography!
BASIC IDEA IN CRYPTOGRAPHY
•
Cryptography: “the coding and
decoding of secret messages.”
•
•
The basic idea is to modify a message
so as to make it unintelligible to
anyone but the intended recipient.
Cryptosystem (Cipher System) – method
of disguising messages so that only
certain people can read them
•
Cryptography – Art of creating and
using Cryptosystems
•
For message (plaintext) M,
e(M, K)
encryption - ciphertext
d[e(M, K), K] = M
decryption
•
Cryptanalysis – Art of breaking
Cryptosystems
•
Cryptography – study of Cryptography
and Cryptosystems
THE PROCESS
Key
Sender
Plaintext
Encryption
Cryptotext
Secure
transmission
Decryption
Recipient
Plaintext
Message encryption
Key ready for use
Secure key distribution
Hard Problem for conventional
encryption
THE CLASSIC CRYPTOGRAPHY
• Encryption algorithm and related key are kept secret.
• Breaking the system is hard due to large numbers of possible
keys.
• For example: for a key 128 bits long
128
38
• there are
2  10
keys to check
using brute force.
The fundamental difficulty is key distribution to parties
who want to exchange messages.
FACTORING A PRODUCT OF TWO LARGE PRIMES
• The best known conventional algorithm requires the
solution time
proportional to:
T (n)  exp[ c(ln n) (ln ln n)
1/ 3
2/3
]
For p & q 65 digits long T(n) is approximately
one month using cluster of workstations.
For p&q 200 digits long T(n) is astronomical.
QUANTUM COMPUTING ALGORITHM FOR FACTORING.
• In 1994 Peter Shor from the AT&T Bell Laboratory showed that in
principle a quantum computer could factor a very long product of
primes in seconds.
• Shor’s algorithm time computational complexity is
T (n)  O[(ln n) ]
3
Once a quantum computer is built the RSA
method would not be safe.
BINARY INFORMATION
• A user can suggest a key by sending a stream of randomly polarized photons.
• This sequence can be converted to a binary key.
• If the key was intercepted it could be discarded and a new stream of randomly
polarized photons sent.
QUANTUM KEY DISTRIBUTION
•
Quantum Key Distribution exploits the effects discussed in order
to thwart eavesdropping.
•
It enables two parties to produce a shared random bit string
known only to them, which can be used as a key for encryption
and decryption.
•
If an eavesdropper uses the wrong polarization basis to measure
the channel, the result of the measurement will be random.
SECURITY OF QUANTUM KEY DISTRIBUTION
• Quantum
cryptography obtains its fundamental security from the fact that
each qubit is carried by a single photon, and each photon will be altered as
soon as it is read.
• This makes impossible to intercept message without being detected.
NOISE
• The presence of noise can impact detecting attacks.
• Eavesdropper and noise on the quantum channel are
indistinguishable.
(1) Malicious eavesdropper can prevent communication.
(2) Detecting eavesdropper in the presence of noise is hard.
THE MAIN CONTRIBUTION OF QUANTUM
CRYPTOGRAPHY.
• It solved the key distribution problem.
• Unconditionally secure key distribution method proposed
by: Charles Bennett
and Gilles Brassard in 1984.
• The method is called BB84.
• Once
key is securely received it can be used to encrypt messages transmitted by
conventional channels.
STATE OF THE QUANTUM CRYPTOGRAPHY
TECHNOLOGY.
•
Experimental implementations have existed since 1990.
•
Current (2004) QC is performed over distances of 30-40 kilometers using
optical fiber.
In general we need two capabilities.
(1)
Single photon gun.
(2) Being able to measure single photons.
CONCLUSION
• Quantum cryptography promises to revolutionize secure communication by providing
security based on the fundamental laws of physics, instead of the current state of
mathematical algorithms or computing technology.
• The devices for implementing such methods exist and the performance of
demonstration systems is being continuously improved.
• Within the next few years, if not months, such systems could start encrypting some of
the most valuable secrets of government and industry.
THANK YOU