Write
31
edits
Quantum Coin: Difference between revisions
Jump to navigation
Jump to search
→Protocol Description
| Line 59: | Line 59: | ||
* The holder sends the identification number of the quantum coin to the TTP. | * The holder sends the identification number of the quantum coin to the TTP. | ||
* The TTP chooses uniformly at random a set <math>L_{bn}\subset[k]</math> of size <math>t</math>, and sends it to the coin holder. | * The TTP chooses uniformly at random a set <math>L_{bn}\subset[k]</math> of size <math>t</math>, and sends it to the coin holder. | ||
* The holder consults with P and chooses uniformly at random a set <math>L_{hl} \subset L_{bn}</math> consisting of <math>2t/3</math> yet unmarked positions. He sends <math>L_{hl}</math> to the bank and marks in <math>P</math> all the elements of <math>L_{hl}</math> as used. | * The holder consults with <math>P</math> and chooses uniformly at random a set <math>L_{hl} \subset L_{bn}</math> consisting of <math>2t/3</math> yet unmarked positions. He sends <math>L_{hl}</math> to the bank and marks in <math>P</math> all the elements of <math>L_{hl}</math> as used. | ||
* The TTP chooses at random <math>2t/3</math> values <math>m_i \in\{{0, 1}\}</math>, one for each <math>i \in L_{hl}</math> , and sends them to the coin holder. | * The TTP chooses at random <math>2t/3</math> values <math>m_i \in\{{0, 1}\}</math>, one for each <math>i \in L_{hl}</math> , and sends them to the coin holder. | ||
* The holder measures the quantum registers corresponding to the elements of <math>L_{hl}</math> in order to produce <math>2t/3</math> pairs <math>(a_i, b_i)</math> (refer to <math>HMP_4</math>-queries in Notations), such that <math>(x_i,m_i, a_i, b_i)\in HMP_4</math> for all <math>i \in L_{hl}</math>. He sends the list of <math>(a_i, b_i)</math>s to the TTP. | * The holder measures the quantum registers corresponding to the elements of <math>L_{hl}</math> in order to produce <math>2t/3</math> pairs <math>(a_i, b_i)</math> (refer to <math>HMP_4</math>-queries in Notations), such that <math>(x_i,m_i, a_i, b_i)\in HMP_4</math> for all <math>i \in L_{hl}</math>. He sends the list of <math>(a_i, b_i)</math>s to the TTP. | ||