Short Abstract.
This is a story about how Alice ingeniously devises two different quantum cryptographic communication protocols (i.e., BB84 and B92) that prevent archvillainess Eve from eavesdropping on Alice's communications with Bob. How does Alice do this? Also, how does she implement her ideas in optics?
Long Abstract.
Alice and Bob wish to communicate without the archvillainess Eve eavesdropping on their conversation. Alice, decides to take two college courses, one in cryptography, the other in quantum mechanics. During the courses, she discovers she can use what she has just learned to devise a cryptographic communication system that automatically detects whether or not Eve is up to her villainous eavesdropping. Some of the topics discussed are Heisenberg's Uncertainty Principle, the Vernan cipher, the BB84 and B92 cryptographic protocols. The talk ends with a discussion of some of Eve's possible eavesdropping strategies, opaque eavesdropping, translucent eavesdropping, and translucent eavesdropping with entanglement.
1. Preface . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1. The Unique Contribution of Quantum Cryptography . . . . 1
1.2. A Note to the Reader . . . . . . . . . . . . . . . . . . . 2
2. Introduction . . . . . . . . . . . . . . . . . . . . . . . 2
3. A Course on Classical Cryptography . . . . . . . . . . . . 2
3.1. Alice's enthusiastic decision . . . . . . . . . . . . . . 2
3.2. Plaintext, ciphertext, key, and ... Catch 22 . . . . . . . 2
3.3. Practical Secrecy . . . . . . . . . . . . . . . . . . . . 3
3.4. Perfect Secrecy . . . . . . . . . . . . . . . . . . . . . 4
3.5. Computational Security . . . . . . . . . . . . . . . . . . 5
4. A Course on Quantum Mechanics . . . . . . . . . . . . . . 7
4.1. Alice's Reluctant Decision . . . . . . . . . . . . . . . . 7
4.2. The Classical World - Introducing the the Shannon Bit . . 7
4.3. The Quantum World - Introducing the Qubit . . . . . . . . 7
4.4. Where do qubits live? . . . . . . . . . . . . . . . . . . 8
4.5. Some Dirac notation - Introducing kets . . . . . . . . . . 8
4.6. Finally, a definition of a qubit . . . . . . . . . . . . . 8
4.7. More Dirac notation - Introducing bras and bra-c-kets . . 9
4.8. Activities in the quantum world - Unitary transformations 10
4.9. Observables in quantum mechanics - Hermitian operators . . 10
4.10. The Heisenberg uncertainty principle - A limitation on
what we can actually observe . . . . . . . . . . . . . . . 11
4.11. Young's two slit experiment - An example of Heisenberg's
uncertainty principle . . . . . . . . . . . . . . . . . . 12
5. The Beginnings of Quantum Cryptography . . . . . . . . . . 14
5.1. Alice has an idea . . . . . . . . . . . . . . . . . . . . 14
5.2. Quantum secrecy - The BB84 protocol without noise . . . . 15
5.3. Quantum secrecy - The BB84 protocol with noise . . . . . . 18
6. The B92 cryptographic protocol . . . . . . . . . . . . . . 20
7. There are many other quantum cryptographic protocols . . . 22
8. A comparison of quantum cryptography with classical and
public key cryptography . . . . . . . . . . . . . . . . . 22
9. Eavesdropping strategies and counter measures . . . . . . 22
9.1. Opaque eavesdropping . . . . . . . . . . . . . . . . . . . 23
9.2. Translucent eavesdropping without entanglement . . . . . . 23
9.3. Translucent eavesdropping with entanglement . . . . . . . 23
9.4. Eavesdropping based on implementation weaknesses . . . . . 23
10. Implementations . . . . . . . . . . . . . . . . . . . . . 24
11. Conclusions . . . . . . . . . . . . . . . . . . . . . . . 24
12. Acknowledgement . . . . . . . . . . . . . . . . . . . . . 25
References . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
