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Multi-Database Classical Symmetric Private Information Retrieval with Quantum Key Distribution
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==Protocol Description== <!-- Mathematical step-wise protocol algorithm helpful to write a subroutine. --> '''Inputs:''' * User <math>U</math>: index of desired database item, <math>X=x</math>; randomness <math>R</math>; <math>f_{\text{query},1}</math>,<math>f_{\text{query},2}</math>,<math>f_\text{dec}</math>. * Data centre <math>D_1</math>: database <math>W=w</math>. * Data centre <math>D_2</math>: database <math>W=w</math>. '''Output:''' * User <math>U</math>: retrieved database element <math>\hat{w}_x</math> (it may be different from the desired database element <math>w_x</math> in the case of malicious parties). '''Protocol:''' * '''Sharing secret keys between parties:''' each pair of parties perform a single-round [[Quantum Key Distribution|quantum key distribution]] protocol (see e.g., [[Measurement Device Independent Quantum Key Distribution (MDI-QKD)|MDI-QKD]] and [https://www.nature.com/articles/ncomms4732 this] specific protocol), so that at the end of the secret sharing phase, data centre <math>D_1</math> and the user <math>U</math> share secret key pair <math>(S_1,S_2)</math>; data centre <math>D_2</math> and the user <math>U</math> share secret key pair <math>(S_3,S_4)</math>; and data centres <math>D_1</math> and <math>D_2</math> share secret key pair <math>(S_5,S_6)</math>. If any of the key distribution protocols abort, then the whole SPIR protocol aborts. ''The next steps are the same as for a generic one-round two-database classical SPIR protocol like this of [https://dl.acm.org/doi/abs/10.1145/276698.276723 Gertner et al (2000)].'' * '''Query:''' Query <math>Q_1=f_{\text{query},1} (x,R)</math> (resp. <math>Q_2=f_{\text{query},2} (x,R)</math>) is generated by the user and sent via QKD-secured (one-time pad encryption with QKD shared secret keys) classical channel <math>C_{U1}</math> (resp. <math>C_{U2}</math>) to data centre <math>D_1</math> (resp. <math>D_2</math>). * '''Answer:''' After receiving query <math>\tilde{Q}_1</math> (resp. <math>\tilde{Q}_2</math>), data centre <math>D_1</math> (resp. <math>D_2</math>) generates answer <math>A_1=f_{\text{ans},1} (\tilde{Q}_1,w,S_5)</math> (resp. <math>A_2=f_{\text{ans},2} (\tilde{Q}_2,w,S_6)</math>) and sends it to the user via <math>C_{U1}</math> (resp. <math>C_{U2}</math>). * '''Retrieval:''' The user decodes the received database element <math>\hat{w}_x</math> using <math>f_{\text{dec}}</math>: <math>\hat{w}_x=f_\text{dec} (\tilde{A}_1,\tilde{A}_2,Q_1,Q_2,x,R)</math>.
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