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Problem with understanding Multi-party secure stable matching circuit

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I am reading the following paper:

MPCircuits: Optimized Circuit Generation for Secure Multi-Party Computation

https://eprint.iacr.org/2019/275.pdf

I have following questions:

1.     why Preference of group1 starts from L_0 where as preference list from group2 starts with L_(n/2+1)?

2.     Any reason why they used the priority encoder?

3.     What is the technique for the security of preference list?

Somebody please guide me. Zulfi.

 

 

 

How we have multiparty stable matching.jpg

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