Socialist Millionaire Problem

https://en.wikipedia.org/wiki/Socialist_millionaires

by vs4vijay • 6 years ago

75 31 6 years ago

en.wikipedia.org

In an episode of Curb Your Enthusiasm, the protagonist has to find the total weight of all the passengers for an airplane, but every passenger is uncomfortable sharing their weight. To me this seems like a problem that could be solved cryptographically, as it seems reminiscent of the SMP or distributed key generation. Does anyone from the crypto community know if there exists a solution for a problem like that?

Fjolsvith2• 6 years ago

Weigh the airplane without passengers, load them and then weigh it.

Otherwise you're guessing.

lonelappde• 6 years ago

It's not often practical to get a loaded plane on a scale.

Also it is useful to balance the weight across the sides of a plane, not just get total weight.

Thorrez• 6 years ago

If you do things physically, you can do it easily.

For example you could have a hat with pieces of paper in it each with a number. The numbers sum to 0 (some are positive, some are negative). Each person draws a piece of paper, adds his or her weight to it, then says that number. The numbers that each person says are summed and that's the total sum.

srfa• 6 years ago

Could use a similar technique remotely using a random number generator. Provided there are enough passengers the sum would approximately equal the true total weight.

There might be behavioural issues here though - perhaps people would keep generating a random number until they are provided one that makes their weight look 'better' (and 'better' probably means 'smaller' for most people).

Edit: comicjk made a great point about large numbers. Perhaps using large random numbers (eg a normal distribution with a mean of 4550 and a std deviation of 20-30) would help reduce the behavioural issue.

comicjk2• 6 years ago

I like this better than my solution. The technique of adding random numbers has a more crypto feel to it. It would help to use big numbers, so that they would conceal the underlying number better (clearly single-digit numbers would be no help, might as well extend that and use 5-digit numbers).

sl8r• 6 years ago

Won't you possibly get some information about some passengers by doing this, if you know / can figure out the distribution of the random numbers?

E.g., say that the random numbers are uniformly distributed between -200 and 200. If somebody says a number like 425, then I know they weigh at least 225 pounds. And the probability they weigh more than 225 - k pounds is 1 - k/400.

emilfihlman2• 6 years ago

This doesn't actually hide the information in edge cases.

comicjk2• 6 years ago

It seems like a plain anonymization problem, much like a voting with a secret ballot. If I encountered this problem in real life, I would just use slips of paper and a box with a slit in it. Possible strengthening techniques would involve removing the handwriting, for instance using multiple choice 0-9 for each digit.

mistrial9• 6 years ago

hmm not from the crypto-community, but .. find the passengers that are comfortable sharing their weight; gather those, mark them in the total list with a tag, a certainty estimate from 0.0 to 1.0, and a weight. Now use the rest of the list to estimate weights based on similarity, assigning some reasonable certainty; show the other passenger those results, tell them again how the group benefits, and they personally benefit; iterate.. If an individual does not want to publicly share their weight, then show them how they can enter the weight without being named to the group. Iterate that, with their consent.

The reason I say this is because you are not talking to machine parts or to secret financial players, in this problem, to you are talking to human beings. By reducing human beings to machine parts to solve a problem, you are losing information that is critical to your own humanity ! and to theirs ! super-bad results can happen when people in power and their adjuncts, are successfully rewarded for reducing human beings to machine parts in their solutions ! Junior programmers finish your studies, but all humans please take note -- no cryptography required here !

garrettgrimsley2• 6 years ago

I'm not a cryptographer, much less from the cryptography community, but I think what you're looking for is known as Fully Homomorphic Encryption. Check it out at https://en.wikipedia.org/wiki/Homomorphic_encryption

What is SMP?

iheartblocks2• 6 years ago

I meant the Socialist Millionaire Problem

baby3• 6 years ago

I think it's easier if you just put everybody on a big scale, like that episode of the office.

casefields• 6 years ago

Or just get one of those carnival weight guessers. They get surprisingly good from practice.

Melting_Harps4• 6 years ago

Does anyone from the crypto community know if there exists a solution for a problem like that?

Technically it can be done, and in an obfuscated way no less without relying on self-reporting, which is always going to skew things; consider the following:

- At boarding have a scale underneath a padded area when scanning each and every passenger (calibration required): this will create a unique ID that corresponds with the boarding pass and seat number and weight while the ticket is being scanned, how long this takes is anyone guess as I'm not an engineer.

- Upon acquiring the weight of each passenger, create a hash for that ID and measured weight, and use that to associate the measured weight rather than the ID, such that it creates an aggregate of each and every boarded passenger with info rather than Jane Doe 55Kg (ID/weight). Record that info into a DLT/blockchain held by a series of parties to validate independently.

- With that info you can discern individual weights, without actually having an identity attached to said weight measurement. And in real time, no less.

This, albeit crudely lined out as its a rather lengthy process to describe, is the basis for why blockchain technology/DLT could be useful for voting as it was used in Sierra Leone's 2018 election:

https://techcrunch.com/2018/03/14/sierra-leone-just-ran-the-...

https://www.agora.vote/

PS: I don't think a token is necessary, simply having the hashed info recorded onto a blockchain is enough, assuming its held by independent parties to be able to validate.

emilfihlman2• 6 years ago

What's the blockchain for? It serves no purpose here.

BoiledCabbage3• 6 years ago

Really? A blockchain? It's parody at this point.

The goal is to get the summed weight of all the passengers. In step 1 of your plan you weigh each and every passenger. If that really is your plan then step 2 is to sum them! Call the sum() function! How in the world did you turn that into 5 steps involving a blockchain?

It's the epitome of the blockchain obsessed. Create unrelated problems just to claim "see a blockchain fixed them."

You've already weighed the passengers! The way to get their summed weight is to sum them!

Fjolsvith2• 6 years ago

Relying on passengers to tell you their true weight is begging for trouble. My wife has never told me her true weight.

Cyberdog• 6 years ago

My eyes are glossing over trying to understand the equations in this article, but isn't the solution as easy as comparing a cryptographic hash of Alice's wealth with a cryptographic hash of Bob's wealth for equality?

The fact that Alice could guess Bob's wealth within a certain range, even if that range is "between $0 and $1 trillion," and then have a finite range to search for a collision could be mitigated with a sufficiently slow hashing algorithm and/or an absurd number of iterations.

baby3• 6 years ago

"could be mitigated"

This is the issue with your solution, it isn't really mitigated in such problems because the domain is too small.

roenxi• 6 years ago

Expanding on this observation - mitigating in this manner means the two parties would have to use absurd amounts of time and computing power to calculate the initial hashes to communicate. Not very practical in many cases.

Socialist Millionaire Problem

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