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

Questions

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