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

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zak100
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Hi,
I am reading a research paper in the context of stable matching which reduces the problem. I am looking for an exampe
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.
 
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zak100 said:
Do you have any better idea with example?
An example of XOR secret sharing?

I have 2 sons who are traveling 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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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.
 
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.
 
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.
 
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].