# (n-1) Group Password -- something with polynomials?

**URL:** <https://boards.straightdope.com/t/n-1-group-password-something-with-polynomials/504478>\
**Category:** Factual Questions\
**Created:** [July 27, 2009, 8:44pm UTC](https://boards.straightdope.com/t/n-1-group-password-something-with-polynomials/504478 "2009-07-27T20:44:49Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![erislover](https://avatars.discourse-cdn.com/v4/letter/e/71e660/32.png) [@erislover](https://boards.straightdope.com/u/erislover)\
**Post date:** [July 27, 2009, 8:44pm UTC](https://boards.straightdope.com/t/n-1-group-password-something-with-polynomials/504478/1 "2009-07-27T20:44:49Z")

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Some time ago I read about a means of a group–let’s say a group of 4 people could use to secure a password such that _at least 3_, and any 3, of the 4 were required to recover it. I swear the implementation was based on properties of a polynomial that each individual’s secret key helped compose, but I cannot remember enough details to tease the solution out of google.

Does anyone know what I’m talking about so I may revisit this topic?

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**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\
**Post date:** [July 27, 2009, 9:14pm UTC](https://boards.straightdope.com/t/n-1-group-password-something-with-polynomials/504478/2 "2009-07-27T21:14:42Z")

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One way you could do it is to pick three of the four passwords, and make the system require all three of those passwords to open up. Then, you construct the fourth password by taking the parity bit of the other three passwords. With any three such keys, no matter which they are, you can reconstruct the missing one, and thereby have all the information the system is asking for.

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**Author:** ![ftg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ftg/32/2801_2.png) [@ftg](https://boards.straightdope.com/u/ftg)\
**Post date:** [July 27, 2009, 9:38pm UTC](https://boards.straightdope.com/t/n-1-group-password-something-with-polynomials/504478/3 "2009-07-27T21:38:20Z")

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[Start here.](http://en.wikipedia.org/wiki/Secret_sharing#Shamir.27s_scheme)

Note carefully the use of terminology: it doesn’t go the way non-experts think it might.

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**Author:** ![gotpasswords](https://avatars.discourse-cdn.com/v4/letter/g/c57346/32.png) [@gotpasswords](https://boards.straightdope.com/u/gotpasswords)\
**Post date:** [July 27, 2009, 9:44pm UTC](https://boards.straightdope.com/t/n-1-group-password-something-with-polynomials/504478/4 "2009-07-27T21:44:19Z")

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Sounds like you’re thinking of partial-key escrow.

There’s a synopsis of a whole bunch of PKE schemes [here](http://www.cs.georgetown.edu/~denning/crypto/Appendix.html).

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**Author:** ![erislover](https://avatars.discourse-cdn.com/v4/letter/e/71e660/32.png) [@erislover](https://boards.straightdope.com/u/erislover)\
**Post date:** [July 27, 2009, 10:31pm UTC](https://boards.straightdope.com/t/n-1-group-password-something-with-polynomials/504478/5 "2009-07-27T22:31:51Z")

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**ftg** , that’s exactly it. **gotpasswords** , excellent followup. Thanks.