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Shared Secrets

Create shares of a secret code which need to be reunited to reveal the secret.

This is a proof of concept and hasn't been properly evaluated for security.

I've recently been informed this is Shamir's Secret Sharing (1979).

Usage

This is a ruby library with an associated executable

# Create 7 shares of the password which require at least 3 to recreate
Secret.create("Howdy, partner!", shares: 7, required: 3)
# => [
        [0] "1-1112273582787975695074844380307169353741255382365",
        [1] "2-1875991816751276345070115490824050279206167488551",
        [2] "3-2886525393117596696571705091964438315320864997297",
        [3] "4-4143874311886936749579613183728333462085347908603",
        [4] "5-5648038573059296504093839766115735719499616222469",
        [5] "6-7399018176634675960114384839126645087563669938895",
        [6] "7-9396813122613075117641248402761061566277509057881"
    ]

# Combine the shares to restore the secret
Secret.restore(Secret.create("Howdy, partner!", shares: 7, required: 3))
# => "Howdy, partner!"

# The secret cannot be restored with too few shares
Secret.restore(Secret.create("Howdy, partner!", shares: 7, required: 3).take(2))
# => Secret::FailedDecodeError
# Create 7 shares of the password which require at least 3 to recreate
$ secret create 7 3 "Howdy, partner!"
1-1026197645290506249894399987748734333070887531064
2-1519067637302214266153992634504989515382450532105
3-2073980667262818795364669700682561085860817681862
4-2690936735172319837526431186281449044505988980335
5-3369935841030717392639277091301653391317964427524
6-4110977984838011460703207415743174126296744023429
7-4914063166594202041718222159606011249442327768050

# Combine the shares to restore the secret
$ secret create 7 3 "Howdy, partner!" | xargs secret restore
Howdy, partner!

# The secret cannot be restored with too few shares
$ secret create 7 3 "Howdy, partner!" | tail -2 | xargs secret restore
Unable to decode input

This encoding is based on a 2048-bit prime and has a message space around 192 bytes.

Under the Hood

This project was inspired by a homework assignment in EECS 376 (Foundations of Computer Science) at the University of Michigan.

Given the parameters of a secret, a number of shares, and a number of required shares, it's possible to generate a polynomial which has the secret as a y-intercept. To generate password shares, simply pull (x, y) coordinates from the equation. You can then reconstruct the polynomial and recover the secret using those coordinates and Lagrange interpolation.

This library accepts strings as secrets and encodes them as numbers which can be used in the equation. On decode, it reconstructs the polynomial, extracts the secret, and converts it back to a string.