Symmetric-key cryptography requires a shared key to be known between the two parties. A simple way to encrypt a message is XOR encryption. This method repeatedly applies the XOR operation on the message using the key. The receiver performs the same operation to decipher the message.
But how does one transmit a key over an insecure channel? Sending it as plain text means it can be intercepted by a malicious eavesdropper. And we can’t encrypt it because it leads to a chicken- and-egg problem, since this operation would also require a key.
A classical solution to this problem is Diffie-Helman key-exchange algorithm. With the advent of quantum computing, however, novel technologies have been developed. Quantum computing manipulates quantum bits (qubits), instead of classical bits. Qubits are subject to quantum mechanical laws of physics. In this assignment, you’ll implement and test the Quantum Key Exchange (QKE) algorithm.
QKE assumes the existence of a quantum communication channel over which qubits can be transferred. A qubit can be encoded via a photon’s polarization. For example, we can define counterclockwise polarization ↺ as 1, and clockwise polarization ⟳ as 0. However, this is not the only option, a photon could also be polarized in a linear fashion; thus, we can define an upwards polarization ↑ as 1, and a downwards polarization ↓ as 0. Crucially, because of quantum mechanics, the internal state of a qubit can only be measured by interacting with it through a polarization filter of a specific type.
| Qubit Value 1 | Qubit Value 2 | |
|---|---|---|
| Linear Polarization | ↑ | ↓ |
| Cirular Polarization | ↻ | ↺ |
The key quantum mechanical observation is that these two types of polarization (circular vs. linear) are orthogonal to each other. This means that if a photon is polarized in a circular manner, it has an equal 50-50 chance to be measured as ↑ or ↓ when measured linearly (and vice-versa).
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The transmitter sends a stream of qubits and for each, it records the value and polarization type, which are both picked randomly with equal chances.
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The receiver receives the stream of qubits and for each, it selects a random polarization type to measure it, and records the results
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The transmitter and receiver exchange the polarization types the used for the stream. The secret key is formed by the recorded qubit values where both happened to use the same polarization type. Thus, for these qubits both have recorded the same value but none but they know what that value actually is
To run program
git clone https://github.com/HK-Transfield/Quantum-Key-Exchange
cd Quantum-Key-Exchange
python3 Main.py
To run tests
git clone https://github.com/HK-Transfield/Quantum-Key-Exchange
cd Quantum-Key-Exchange
pip install -r Requirements.txt
python3 -m pytest