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Re:Republicans Push Bill Requiring Tech Companies Give Encry... by rectang on Wednesday June 24, 2020 @02:21PM (#23631807)
Algorithmically speaking, Shamir's Secret Sharing seems of interest to your "combination of private keys" option.

• https://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing

• https://cs.jhu.edu/~sdoshi/crypto/papers/shamirturing.pdf

I agree with the sibling commentators though that it just isn't strong enough to withstand a threat model of "people motivated to get the master key to vast amounts of encrypted communication". Even if such a scheme couldn't be cracked algorithmically, it wouldn't hold up against the relentless social engineering efforts that would be thrown at it.

Re:Republicans Push Bill Requiring Tech Companies Give Encry... by jonny_eh on Wednesday June 24, 2020 @02:27PM (#23631911)
> people motivated to get the master key

Or, more likely, people charged with protecting the master key being negligent.

One of potentially many examples: https://www.renderlab.net/advisories/mta-key/