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Device-Independent Oblivious Transfer: Difference between revisions
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Device-Independent Oblivious Transfer (edit)
Revision as of 17:38, 22 January 2022
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* The protocol consists of multiple rounds, which are randomly chosen for testing or string generation | * The protocol consists of multiple rounds, which are randomly chosen for testing or string generation | ||
* The testing rounds are carried out to ensure that the devices used are following the expected behaviour. The self-testing protocol used is a modification of the one used in DIQKD. This modification is necessary as, unlike the DIQKD scenario, the parties involved in OT may not trust each other to cooperate. The self-testing protocol uses the computational assumptions associated with ''Extended noisy trapdoor claw-free'' (ENTCF) function families to certify that the device has created the desired quantum states. If the fraction of failed testing rounds exceeds a certain limit, the protocol is aborted. | * The testing rounds are carried out to ensure that the devices used are following the expected behaviour. The self-testing protocol used is a modification of the one used in DIQKD. This modification is necessary as, unlike the DIQKD scenario, the parties involved in OT may not trust each other to cooperate. The self-testing protocol uses the computational assumptions associated with ''Extended noisy trapdoor claw-free'' (ENTCF) function families to certify that the device has created the desired quantum states. If the fraction of failed testing rounds exceeds a certain limit, the protocol is aborted. | ||
* | * At the end of the protocol, the honest sender outputs two randomly generated strings of equal length, and the honest receiver outputs their chosen string out of the two. | ||
==Notation== | ==Notation== | ||
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* <math>c</math>: A bit denoting the receiver's choice | * <math>c</math>: A bit denoting the receiver's choice | ||
* For any bit <math>r</math>, ['''Computational, Hadamard''']<math>_r = \begin{cases}\mbox{Computational, if } r = 0\\ \mbox{Hadamard, if } r = 1\end{cases}</math> | * For any bit <math>r</math>, ['''Computational, Hadamard''']<math>_r = \begin{cases}\mbox{Computational, if } r = 0\\ \mbox{Hadamard, if } r = 1\end{cases}</math> | ||
* <math>\sigma_X = \begin{pmatrix}0 & 1 \\ 1 & 0 \end{pmatrix} </math> | |||
* <math>\sigma_Z = \begin{pmatrix}1 & 0 \\ 0 & -1 \end{pmatrix} </math> | * <math>\sigma_Z = \begin{pmatrix}1 & 0 \\ 0 & -1 \end{pmatrix} </math> | ||
* For bits <math>v^{\alpha},v^{\beta}: |\phi^{(v^{\alpha},v^{\beta})}\rangle = (\sigma_Z^{v^{\alpha}}\sigma_X^{v^{\beta}} \otimes I) \frac{|00\rangle+|11\rangle}{\sqrt{2}}</math> | * For bits <math>v^{\alpha},v^{\beta}: |\phi^{(v^{\alpha},v^{\beta})}\rangle = (\sigma_Z^{v^{\alpha}}\sigma_X^{v^{\beta}} \otimes I) \frac{|00\rangle+|11\rangle}{\sqrt{2}}</math> | ||