How to Share a Secret in Public
— by Friedger Müffke, Ryder
Demo
- Choose a secret number
- Take number to the power of your secret
- Divide by prime number
- Subtract the whole number part
- Multiply by prime number
- Tell the result
Step 1
- Use your friend's number
- Take number to the power of your secret
- Divide by prime number
- Subtract the whole number part
- Multiply by prime number
- Keep the result for you
Step 2
Basics
Finite Fields
Prime number as base
Backup Seed Phrases
Store parts of it at different places, with different people, ...
defy alarm exclude online voyage wrong avocado squeeze off near year cradle
Defy the dawn and silence the alarm,
Exclude the shadows from the online storm.
Embark upon a voyage where right and wrong
Blend like the green of a ripe avocado’s charm.
Squeeze the moments before they slip off,
Stay near the heart where dreams are spun.
Mark each passing day within the year,
Cradle hopes beneath the setting sun.
Shamir's Secret Sharing
- Distribute secret among a group
- Recover using a minimum of shares
- Based on "Number of points define degree of polynomial"
- Efficient
- Limited number of shares
Methods
Shamir Secret Sharing
Based on Lagrange Interpolation Theorem
Formulated by Adi Shamir in 1979
SSS
Diffie–Hellman–Merkle
One of the earliest key exchange methods
Based on work from 1969 by James Ellis, Clifford Cocks and Malcolm Williamson
DHM
Pallier Cryptosystem
Composite residuosity class problem by Pascal Pallier, 1999, generalization Damgård–Jurik in 2001
Work on threshold algorithms since 2018
PC
Shamir's Secret Sharing Today
Used in secure data storage, cryptographic key management, and distributed systems.
Shamir39 Tool
Hardware Wallets
Trezor
CypherRock
Ryder
Blockchain Commons
Sharded Secret Key Reconstruction
Collaborative Seed Recovery (CSR)
Blockchain Commons Depository