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Suppose a clock that is broken into four distinct pieces, that run from (12 - 9), (3-12), (6-3), (9-6). The clock can be reassembled from any two out of the four pieces, but no single piece can be used to create a full clock.

I’ve been trying to apply this idea to files and binary data, but have been having trouble finding a general formulation of the ability to take an object, divide it into multiple parts and reassemble with some portion of those parts (n out of m).

I understand that this cannot be done with only one clock. I’ve looked at Samir’s secret sharing - but I don’t think that would apply here. I’ve also spent a long time at a variety of different computer science techniques (file splitting, sharding, etc.) and I haven’t been able to find anything - so I’ve been going back to looking for a mathematical answer.

Are there general formulations of this problem? Can I use it to divide a clock into an arbitrary number of pieces (20) and then calculate how many pieces I would need to reassemble?

KReiser
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Prasanna
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  • I think this is too general a question so will not get good answers here. You might want to search for lattice of coverings and visit some of the links to see if anything is useful. – Ethan Bolker Nov 30 '19 at 18:19
  • Why it can't be with Shamir? Any secret sharing scheme that supports (n,2) can be used. In your case, however, I don't see any secrecy since any owner of the 3/4 part of the clock has the knowledge of 3/4 of the data which is not in Shamir or perfect secret sharing schemes. Analogous with your clock, you can easily convert it (4,2). Consider the data divided into four-part and each placed in one of the quadrants of the clock. Now use the clock pieces, you are done! – kelalaka Dec 01 '19 at 15:55

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