Quantum Cryptography Security Through Uncertainty

Quantum Cryptography – Security through Uncertainty Narayana Kashyap

QUANTUM CRYPTOGRAPHY – SECURITY THROUGH UNCERTAINTY NARAYANA D KASHYAP Spring 2003

ABSTRACT Quantum cryptography is governed by the laws of physics. It basically utilizes Heisenberg’s Uncertainty Principle. The way it works is by a system which includes a transmitter and receiver. A sender transmits photons which have been polarized (using either rectilinear polarization or diagonal polarization). The receiver at the other end measures this polarization for each photon by using any of the two types. The receiver records the measurement (rectilinear or diagonal). He announces the measurement but not the result and the sender announces back to the receiver which of the measurements were of the correct type. Both the parties keep the cases in which the receiver measurements were of the correct type. These cases are then translated into bits (1's and 0's) called qubits and thereby become the key. An eavesdropper is bound to introduce errors to this transmission because he/she does not know in advance the type of polarization of each photon and quantum mechanics does not allow him/her to acquire sharp values of two non-commuting observables (here rectilinear and diagonal polarizations). The two legitimate users of the quantum channel test for eavesdropping by revealing a random subset of the key bits and checking (in public) the error rate. Although they cannot prevent eavesdropping, they will never be fooled by an eavesdropper because any effort to tap the channel, however subtle and sophisticated, will be detected. Whenever they are not happy with the security of the channel they can try to set up the key distribution again.

1. INTRODUCTION Cryptography

Gentlemen do not read each other's mail - Henry Stimson, U.S. Secretary of State

During early days when people wanted information to be protected or to be destined for only a few designated people, they used to hide information in such a way that the onlooker would be puzzled and does not understand what the writing is. The earliest known technique is Caesar Cipher, a substitution technique where the letters of English were replaced with the letters further down the alphabet set. Such techniques and methods where information is not easy to perceive and understand leads to what is known as Cryptography.

With the usage of the internet, where information is exposed to everyone and could be tampered by anyone, the need for information hiding has become even more important and prioritized in the modern day society. Hackers and cryptanalysts find this information easy to watch, modify and sometimes even block the information from getting across to the destined person. Hence, a person who would like to have information sent across to only a few selected trusted parties takes help from

CS 265 Term Paper Page 1 of 5 April 14, 2003 Quantum Cryptography – Security through Uncertainty Narayana Kashyap organizations which help in hiding the information and securely transferring the information to the designated parties. These organizations use what is called as Public / Private Key Cryptography. The algorithms and the techniques used are quite robust and it would take a cryptanalyst considerable amount of time and effort to decipher the encrypted message. The time, in fact, is quite huge; a 128-bit key used for encryption is said to have a time factor of the order of millions of years to decipher using brute force methods. These algorithms are based on mathematical concepts, which can be solved or broken through better decryption techniques and faster and parallel computers in the future. One method goes beyond mathematics and its concepts and instead, the laws of physics govern the security of encrypted message. This form is called Quantum Cryptography.

Quantum Cryptography

I can't speak without an interception. This is private; please get off my line. Please tell me when I can have my privacy. - Ray and Dave Davies

This cryptographic technique allows a secure channel between two people who want to communicate in privacy. Here initial parameters are agreed in forefront and during the course of communication can change to the desired configuration or sometimes these parameters are not even needed. It is as powerful as classical cryptography and can take conventional cryptography to the next level, as Quantum Cryptography can sense even a passive attack or eavesdropping on the quantum channel.

“Quantum theory is believed to govern all objects, large and small, but its consequences are most conspicuous in microscopic systems such as individual atoms or subatomic particles. The act of measurement is an integral part of quantum mechanics, not just a passive, external process as in classical physics. So it is possible to design a quantum channel - one that carries signals based on quantum phenomena - in such a way that any effort to monitor the channel necessarily disturbs the signal in some detectable way.” (http://www.cyberbeach.net/~jdwyer/quantum_crypto/quantum1.htm)

This is due to Heisenberg’s Uncertainty Principle which asserts that certain pairs of physical properties are completely complimentary to each other, in the sense that measuring one of them disturbs the other property.

This principle can be applied to the quantum channel, which is used by Quantum Cryptography. The Quantum channel carries small particles called “Quantums” or “Photons” of light within them. Hence the name, Quantum Cryptography. When light travels, it generates oscillating electric field, and the direction of oscillation is known as the polarization of the photon.

The Quantum channel can be constructed with the help of two polarizing filters which are placed at either ends; one is the sender and the other is the receiver. These crystals are made of birefringent crystal (such as calcite). The sender can place his crystal in a

CS 265 Term Paper Page 2 of 5 April 14, 2003 Quantum Cryptography – Security through Uncertainty Narayana Kashyap direction that he wants the photons to be polarized and transmitted. The receiver on the other hand places his crystal in a direction he wishes to receive the photons.

A photon encountering a calcite crystal behaves in one of two ways depending on its polarization in relation to the crystal. The photon may pass through the crystal perpendicular to the axis of the crystal or it may pass through the crystal parallel to the axis but slightly shifted along the axis. If the photons are not in any of these two directions, then the photons arriving out of the calcite crystal may take a direction that is random in nature and hence it may be perpendicular to the axis or parallel to the axis. If the photons are not at all polarized before they enter into the crystal, then the crystal polarizes them depending on the direction of entry into the crystal.

2. WORKING OF QUANTUM CRYPTOGRAPHY

Nobody understands quantum theory. - Richard Feynman, Nobel prize-winning physicist

The polarizations are of two types: 1. Rectilinear Polarization (0 or 90) (vertical or horizontal) 2. Diagonal Polarization (45 or 135)

According to Quantum theory, Rectilinear and Diagonal polarizations are complementary properties, such that an apparatus set up to test the rectilinear polarizations cannot be used to test diagonally polarized photons. But the same can be identified by a similar apparatus that has been rotated 45 degrees from the original orientation. Thus, one property randomizes the other property.

Bennett and Brassard in 1984 proposed an algorithm for Quantum Key Distribution and was termed as BB84. This algorithm uses a quantum channel as well as a classical public channel through which the participants can send regular messages.

We consider three participants in the system Alice -> sender Bob -> receiver Eve -> eavesdropper

Alice and Bob would like to exchange their secret key. Hence they use Quantum cryptography to exchange. The system involves a transmitter and a receiver (each side consists of a laser emitter of light along with a filter to polarize/select the polarized photons) Alice uses the transmitter to send photons in one of the four polarizations: 0,45, 90 or 135 degrees. Bob uses the receiver to measure the polarization. According to the laws of Quantum Mechanics, the receiver can distinguish between rectilinear polarizations or horizontal polarizations, but not both polarizations together.

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The scenario of the key distribution is as follows:

Pre - agreed arrangement: 45 and 90 are 1’s, 0 and 135 are 0’s

The key distribution requires several steps.

1. Alice sends photons with one of four polarizations, which she has chosen in random.

2. For each photon, Bob chooses at random the type of measurement: either rectilinear (+) or diagonal (x).

3. Bob records the result of the measurement and keeps it as a secret

4. Bob publicly announces the types of measurements that he made, and Alice tells him which measurements were correct; this announcement is made over the classic public channel.

    

5. Alice and bob keep all the cases in which Bob measured the correct type. These cases are translated into bits (1 or 0) and eventually become the key.

6. Finally the key agreed on is:

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1 0 0 1 1

Some interesting things to be noted here are: 1. Bob announces publicly, for each photon, which type of measurement he has made (rectilinear or diagonal) but not the measurement result (for example, 0, 45, 90 or 135 degrees). 2. Alice and Bob both discard the cases in which Bob had made a wrong measurement or the cases in which the detectors (filters) failed to register the photon at all (the reason behind this is because the filters are not 100% efficient)

3. CONCLUSION

1. It is possible to send a secret key using single photon burst, without unnoticeably being intercepted. 2. 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. 3. The wide spread use and acceptance of Quantum Cryptography is just a matter of time. Currently the size and expense of the quantum equipment makes it infeasible for use in a home environment.

4. REFERENCES: 1. R. Rivest, A. Shamir, and L. Adleman, "On Digital Signatures and Public-Key Cryptosystems", MIT Laboratory for Computer Science, Technical Report, MIT/LCS/TR-212 (January 1979). 2. C.H. Bennett, G. Brassard, and A.K. Ekert, "Quantum cryptography", Scientific American, October 1992, p. 50.

5. WEBSITES: 1. http://www.cyberbeach.net/~jdwyer/quantum_crypto/quantum1.htm 2. http://www.cs.dartmouth.edu/~jford/crypto.html 3. http://www.cki.au.dk/experiment/qrypto/doc/QuCrypt/bb84coding.html 4. http://www.qubit.org 5. www.vad1.com/qcr 6. http://qso.lanl.gov/qc 7. www.quantum.univie.ac.at/research/crypto 8. http://www.csa.com/hottopics/crypt/oview.html

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