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good morning everyone, today im gonna present to you our new and intersting work on high dimensional semi quantum cryptography. So what is the big question that we are trying to answer here? As you already know that most of our existing encryption system that is used in the internet is based on unproven computational assumptions, right? RSA is one example. Peter Shor has shown back in 1992 that with the help of a quantum computer, these systems can be broken, risking existing digital infrastructure. You are also aware of the recent developments of quantum computers right? What we need now is encryption system that are 'quantum-safe'.

To answer this question, we take a look at quantum cryptography, wchich provides unconditional security. So even with the advent of a quantum computer, our encryption systems woudl still be safe. There are many variants of quantum cryptography, each with its own advantages and disadvantages. We choose to use high dimensional qkd and try to make it more economical by essentially halving one parties capabilities. which is called semi-quantum cryptography.

Now here we describe our protocol. Without any technicalities, the protocol looks like this:

so here are the two parties, alice and bob. alice prepares these two basis states, eve attacks the forward channel, bob measures or resends and then eve attacks again.


So how do we prove the unconditinoal security of our protocol?
Here is the proof sketch:
As you can imagine, two way analysis is hard for cryptographic protocols. But we prove a theorem that in our case, an one way analysis would be suffiecient to prove the security in two way protocol. Then we use the entropic uncertainty relation that basically says it is not possible to know both the position and moementum of some particle with arbitrary precision at the same time. This is a depiction of our conversion to one way from two way. With the help of this special operator rw that we have derived, we can show that the view for all parties at time t* is the same in both of these cases and for any attack against this two way protocol, there is an equivalent attack against this one way protocol such that eve gets no advantage.


Then we move on to actually demonstrate our result. So what I was referring to as noise tolerance, this is measured from this equation. We say that for which attack of the adversary the key rate goes to zero. In the first comparison, we show how using a higher dimension does increase the noise tolerance. In the second case, we show how does it compare against the fully quantum hd-bb84 protocol. here we also see a almost comparable result. Although the decrease in key rate is to be expected because we are operating at a much lower capacity.

so to conclude, we have proposed a new hd-sqkd protocol, which is the first ussage of higher dimensinoal systems in a semi quantum protocol. and proved its unconditional security.
	good morning everyone, today im gonna present to you our new and intersting work on high dimensional semi quantum cryptography. So what is the big question that we are trying to answer here? As you already know that most of our existing encryption system that is used in the internet is based on unproven computational assumptions, right? RSA is one example. Peter Shor has shown back in 1992 that with the help of a quantum computer, these systems can be broken, risking existing digital infrastructure. You are also aware of the recent developments of quantum computers right? What we need now is encryption system that are 'quantum-safe'.

	To answer this question, we take a look at quantum cryptography, wchich provides unconditional security. So even with the advent of a quantum computer, our encryption systems woudl still be safe. There are many variants of quantum cryptography, each with its own advantages and disadvantages. We choose to use high dimensional qkd and try to make it more economical by essentially halving one parties capabilities. which is called semi-quantum cryptography.

	Now here we describe our protocol. Without any technicalities, the protocol looks like this:

	so here are the two parties, alice and bob. alice prepares these two basis states, eve attacks the forward channel, bob measures or resends and then eve attacks again.



	So how do we prove the unconditinoal security of our protocol?
	Here is the proof sketch:
	As you can imagine, two way analysis is hard for cryptographic protocols. But we prove a theorem that in our case, an one way analysis would be suffiecient to prove the security in two way protocol. Then we use the entropic uncertainty relation that basically says it is not possible to know both the position and moementum of some particle with arbitrary precision at the same time. This is a depiction of our conversion to one way from two way. With the help of this special operator rw that we have derived, we can show that the view for all parties at time t* is the same in both of these cases and for any attack against this two way protocol, there is an equivalent attack against this one way protocol such that eve gets no advantage.



	Then we move on to actually demonstrate our result. So what I was referring to as noise tolerance, this is measured from this equation. We say that for which attack of the adversary the key rate goes to zero. In the first comparison, we show how using a higher dimension does increase the noise tolerance. In the second case, we show how does it compare against the fully quantum hd-bb84 protocol. here we also see a almost comparable result. Although the decrease in key rate is to be expected because we are operating at a much lower capacity.

	so to conclude, we have proposed a new hd-sqkd protocol, which is the first ussage of higher dimensinoal systems in a semi quantum protocol. and proved its unconditional security.