Re: Secret sharing algorithm with chosen keys

Lethal Possum <lethal.possum@xxxxxxxxx> wrote:

James, concerning your first suggestion: I am not sure it would be
secure. When you say "instead of public keys, you'd have the XORed
token set for each T people", now let's say we have N = 3 and T = 2.
Let's call the keys A, B and C. Let's call the symmetric key S. If I
understood your proposition correctly, you compute A + B + S, A + C +
S and B + C + S and put that with the message encrypted by S.

Yes, that's the idea.

The issue is that for example (A + B + S) + (A + C + S) + (B + C + S)
= S. In other words you can derive the main symmetric encryption key
from the decryption keys.

Hmmm, I see the problem.

But I'll have to think is there is a way to make it work
maybe using something less reversible than XOR to create
the decryption keys.

Perhaps each "decryption key" as you call it, should be a ciphered copy
of the symmetric key S and this cipher should be keyed on the XORed
combination of the T tokens. That way, even knowing all the decryption
keys doesn't help you derive the symmetric key without actually having
the relevant XORed combination to reverse the cipher protecting a
decryption key.

Hope that helps. Unfortunately, the other responses went over my head,
but I feel confident they are worth considering in more depth than my
novice ideas.

--
James Taylor
.

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