Quantum Cryptography Scott Roberts CSE 599 03/01/2001

Overview Classical Cryptography Quantum Cryptography BB84 Quantum Key Distribution Scheme Demo Here is an overview of what I will talk be talking about today. First, I will talk about classical cryptography and the problems inherent in the two most common cryptosystems. Then, I will discuss quantum cryptography and how it solves the problems of classical cryptography. Then, I will talk about the BB84 quantum key distribution scheme which is the most popular quantum cryptography algorithm. Finally, I will demonstrate a BB84 simulation application that I created.

Classical Cryptography Private-key cryptography Based on secrecy of the key Problem: key distribution Public-key cryptography Based on one-way functions Problem: Based on unproven mathematical assumptions In danger due to recent advances in quantum computing – namely Shor’s algorithm. In private-key cryptosystems, the sender, who we typically refer to as Alice, and the receiver, who we refer to as Bob, share a common key that is kept private from all untrusted parties. This key is used both for encryption and decryption. The main problem with private-key cryptography is key distribution. Alice needs to transmit the key to Bob without revealing the key to an eavesdropper, who we call Eve. It’s impossible to completely prevent eavesdropping from occurring when transmitting the key over classical delivery channels, such as the Internet. If Alice chooses to send the key to Bob via a courier, how do Alice and Bob know that the courier can be trusted. With public-key cryptography, the encryption and decryption key are different. The encryption key is public and the decryption key is private. Therefore, anybody can encrypt a msg using the encryption key but only the person with the decryption key can decrypt the msg. PKC is based on the concept of one-way functions. These are functons that are easier to compute in one direction than the other. i.e., given x you can easily compute f(x) but given f(x) you cannot easily compute x. (At least there is not a known polynomial time algorithm to do so.) An example is the factoring of large integers. The problem is that PKC is based on unproven math assumptions.

Quantum Cryptography (a.k.a. Quantum Key Distribution) Enables Alice to send a key to Bob and detect eavesdropping. Really about key distribution (QKD). QKD based on an unchangeable law of physics: the Heisenberg Uncertainty Principle. For any two incompatible observables, A and B, reducing the uncertainty of A forces the uncertainty of B to increase, and vice versa. i.e., measuring one of the observables interferes with the measurement of the other This is key to QKD

QKD (cont’d) QKD uses photons to transmit key data If Eve attempts to measure a photon that is in transit from Alice to Bob, and Eve uses a measurement (rectilinear or diagonal) that is incompatible with the polarity of the photon, that measurement will randomly change the polarity of that photon. Eve cannot measure the photon both rectilinearly and diagonally due to Heisenberg Therefore, eavesdropping is easy to detect.

BB84 Scheme for QKD Created by Bennett and Brassard in 1984. Uses a quantum channel for transmitting the key Uses a public channel for key reconciliation. In the real world, Alice and Bob share a small secret key that is used for authentication in public channel.

BB84 Steps Alice sends Bob photons with polarizations chosen at random. For each photon, Bob chooses at random the type of measurement – rectilinear or diagonal. Bob records the results of his measurements but keeps them a secret.

BB84 Steps (cont’d) Bob publicly announces the type of measurements (not polarities) he made and Alice tells him which measurements were of the correct type. Alice and Bob keep all cases in which Bob measured the correct type. Should have same photon polarities. These are translated into bits (0º and 45º = 0, 90º and 135º = 1.

BB84 Steps (cont’d) Bob and Alice test for eavesdropping by publicly comparing and discarding a randomly selected subset of their polarization data. Problem: can result in a small key As an alternative Alice and Bob could test the parity of a randomly chosen subset of the key data. This allows for a much larger key.

BB84 Demo Demonstrates the BB84 QKD scheme. Allows user to see the effects that eavesdropping has on BB84. Can test both standard technique and parity modification.

Conclusion Classical Cryptography has served us well thus far but is inherently flawed. Private-key: keys must be private Public-key: based on unproven mathematical assumptions In danger due to Shor’s algorithm for factoring large integers Quantum Cryptography is totally secure Based on unbreakable laws of physics Easily able to detect eavesdropping