Reducing the Stable Matching (SM) problem: XOR secret sharing: Example?

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zak100
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Summary:

Hi,
I am reading a research paper in the context of stable matching which reduces the problem. I am looking for an exampe

Main Question or Discussion Point

Hi,
I am reading the following paper:
Toward Practical Secure Stable Matching: https://encrypto.de/papers/RSSSK17.pdf.

According to the paper:

We can make the process of stable matching secure by utilizing Secure Function Evaluation (SFE) protocols.
SFE allows to evaluate a function on private inputs from multiple parties where each party wants to keep
her own inputs private.
and at other place:

Secure SM is inherently a multiparty SFE problem where multiple parties provide their inputs. However, we use
a known technique based on XOR-secret-sharing that translates this problem into two-party SFE.
Somebody please provide me an example for this model i.e reducing from multiparty data into 2-party data.

Zulfi.
 

Answers and Replies

  • #2
pbuk
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Not sure what example might help - what are you expecting to gain from reading this paper?
 
  • #4
pbuk
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Do you have any better idea with example?
An example of XOR secret sharing?

I have 2 sons who are travelling abroad and I want them to be able to access money on an ATM card after a month but only when they are together. I give one of them the card and the secret 8265 and the other one the secret 5467.

[Edit: terminolgy corrected]
The PIN on the card (the message) is 1234. I encrypt the message by taking 1234 ^ 8265 ^ 5467 = 12736 where ^ is the symbol for a binary XOR operation, and publish the encrypted message on the internet after a month.

When my sons are together, they XOR the encrypted message with both of their secrets (they can do this without sharing them with each other by using a tool like this one; because XOR is commutative it doesn't matter which order the secrets were applied in encryption or decryption) to retrieve the unencrypted PIN.
 
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  • #5
zak100
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Hi,
Good idea. Can you please show me the Maths how it works (for multi-party) both for encryption and decryption?

For two party, we have one-time Pad. But how can we use one time pad for muti-party, this is what I want to now.

Zulfi.
 
  • #6
pbuk
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  • #7
zak100
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Hi,
Thanks you are right. We already have One-time Pad. But how can we use One-time pad for multiple party this is my question.

Zulfi.
 
  • #8
pbuk
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This is not a 'one-time pad', the keys are reusable. I have explained multi-party use in #4.
 
  • #9
zak100
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Hi,
Yes you are right one-time pad is used only one time. I am talking about multiparty in the context of stable matching. Two groups and each group has 'n' elements. Each one of the 'n' elements have preference list. I have to encrypt this data so that the other group can't see the see the matching information. The other group can decrypt the information specific to its need. I need an example for this.

Zulfi.
 
  • #10
pbuk
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Have you considered the examples in the paper you linked?
The National Residency Matching Program (NRMP) matches around 32k graduatingmedical students to residency programs in the US every year [23, 33]. The New York City Department of Education (NYCDOE) matches over 90k entering students to public high schools [1]. Also there are many financial applications that require SM, such as vertical networks and their application in supply chains [25].
 

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