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

[zak100]

TL;DR

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.

 

[pbuk]

Not sure what example might help - what are you expecting to gain from reading this paper?

 

[zak100]

Hi,
One more link:

https://crypto.stackexchange.com/questions/11372/xor-secret-sharing-schemeOf course, I want to understand the implemented security.

Do you have any better idea with example?

Zulfi.

 

[pbuk]

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.

 

[zak100]

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.

 

[pbuk]

The maths is simply the binary XOR function.

 

[zak100]

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.

 

[pbuk]

This is not a 'one-time pad', the keys are reusable. I have explained multi-party use in #4.

 

[zak100]

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.

 

[pbuk]

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].