By Qasim Mahmood Raja
The third and last talk in a series of talks by final year students of BSc Physics hosted by NPAS was held on 10th May. Yagana Syed gave a talk titled Quantum Secret Sharing, her final year project.
Cryptography
Yagana began by giving a basic intro to Cryptography as “the art of secret information exchange”. As she explained it, we aim to securely send a message from say Alice to Bob. An encrypted message is sent to Bob. Decoding this requires Alice to send a key to Bob securely.
How is this done quantum mechanically?
This is where we enter into the world of Quantum cryptography which is, as Yagana puts it “flawless unless the laws of quantum mechanics are proven wrong”.
Quantum Cryptography
Yagana then described the E91 protocol which allows us to generates a secure key, using an animated video titled “Quantum cryptography, animated”
Link: https://www.youtube.com/watch?v=LaLzshIosDk
Here is a summary “Both Bob and Alice each receive one half of the entangled pair, then randomly choose the polarization filter for each photon that arrives at the detector. Then over a classical communication channel, compare the orientation for each filter and note the ones that were the same. The ones that are the same (i.e. in terms of the orientation of the filter) make up the shared key for Alice and Bob. Another interesting feature is that the mismatches can be used to check for an eavesdropper (for the advanced readers, this relies on whether or not Bell’s inequality is satisfied). This results in a quantitative measure of the error rate and if such error does not exceed an agreed upon threshold (because environmental disturbances can also change quantum states and there is no distinction between them and an actual eavesdropper) then the key is accepted otherwise the procedure is repeated.”
After this review, Yagana Syed began to describe her final year project.
Secret Sharing
(n,n) Threshold Scheme
Here, we have a message and this time we want to share it not with one person but an ‘n’ number of people. Our general idea is that we send a key to each of the n players and the actual message is encrypted in such a way that only if all n members combine their keys can they decrypt the message, what’s called as the (n,n) threshold scheme.
Objective of QSS
The goal is to ensure protection against not only eavesdroppers but also against dishonest players (those who we are distributing the keys to)
Yagana used a clip from “The Imitation game” to further elaborate on this.
Continuous vs Discrete Variables
Yagana then remarked on the advantages offered by Continuous variable approach to quantum sharing as opposed to the standard discrete variable approach. The major one being that there are chances of bit flips (e.g. a 0 turning to 1) due to environmental disruptions in the discrete variable approach not encountered while using continuous variables thus resulting in minimum error via this approach.
In this protocol, for instance, we’ll be using x and p, denoting position and momentum respectively as continuous variables. The values of these two are chosen randomly and quantum states of a certain type called a coherent state with these average position and momentum values are created in the implementation of the protocol.
The Protocol for QSS
Finally, she concluded the talk after explaining the actual protocol as mentioned in the paper “Quantum Secret sharing using weak coherent states”.
References:
For those interested in reading the paper, here is the link
Also
E91 protocol
If you are curious (and have taken a course on quantum mechanics), read up on the E91 protocol in detail here
https://en.wikipedia.org/wiki/Quantum_key_distribution#E91_protocol:_Artur_Ekert_(1991)
if you haven’t taken quantum mechanics, watch this video
Both protocols for key distribution BB84 and E91 are explained at the end
Also do take a look at Sabine Hossenfelder’s youtube channel for more stuff on quantum cryptography
npasofficial.com 