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0 pointsDylan168075y ago0 comments

While it's a clever method, it's also worth noting that for moderately-sized groups you can achieve the same thing with a much simpler method and almost no math.

Let's say you have a 256 bit key as the secret, and you want any 5 out of 15 people to have access.

For each combination of 5 people, pick 4 random 256 bit numbers. 4 people get those and 1 gets the key encrypted with those numbers as a one time pad.

Once you do every combination, each person will end up with a list of a thousand numbers. Any 5 of them can get together, each grab their number for that group, and XOR them to access the secret.

That's only 32KB of data to hang onto. With 15 people the absolute max is 107KB. Even printed as plain text it would need less than 20 sheets of paper.

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DennisP5y ago

Oh that's great. At one point I wanted to use SSS just for two out of three. I can't believe it never occurred to me to just say "if you're pairing with Jack, xor his number with this one." It's even simple enough to do by hand.

StavrosK5y ago

What happens if 5 people who have encrypted random numbers (and no key) get together?

Dylan16807OP5y ago

What's an "encrypted random number"?

If they have 5 random numbers and XOR them together, then they won't get the key as output.

StavrosK5y ago

So then it's not "any" 5 out of 15, it's "any group of these three", which is a significant disadvantage compared to SSS.

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0 pointsDylan168075y ago0 comments

While it's a clever method, it's also worth noting that for moderately-sized groups you can achieve the same thing with a much simpler method and almost no math.

Let's say you have a 256 bit key as the secret, and you want any 5 out of 15 people to have access.

For each combination of 5 people, pick 4 random 256 bit numbers. 4 people get those and 1 gets the key encrypted with those numbers as a one time pad.

Once you do every combination, each person will end up with a list of a thousand numbers. Any 5 of them can get together, each grab their number for that group, and XOR them to access the secret.

That's only 32KB of data to hang onto. With 15 people the absolute max is 107KB. Even printed as plain text it would need less than 20 sheets of paper.

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DennisP5y ago

StavrosK5y ago

What happens if 5 people who have encrypted random numbers (and no key) get together?

Dylan16807OP5y ago

What's an "encrypted random number"?

If they have 5 random numbers and XOR them together, then they won't get the key as output.

StavrosK5y ago

So then it's not "any" 5 out of 15, it's "any group of these three", which is a significant disadvantage compared to SSS.

1 more reply

j / k navigate · click thread line to collapse