Shamir Secret Sharing Meaning

What is Secret Sharing?

Before we dive deep into Shamir Secret Sharing, let’s understand the Secret Sharing concept. Secret Sharing in cryptography is the technique of splitting private information (a secret) into smaller fragments or parts and distributing those parts across a group or network. Individually, the shares are useless. It ensures that no single entity can use their share to access the complete secret. This makes it effective for securing confidential or sensitive information such as private keys, personal data, and more.

Imagine you want to share the password to your safety deposit box with your heirs – Gigi, Ogee, and Georgie. However, you want to ensure that they all need to cooperate to reconstruct the password. You also don’t want any or all of them to know the complete password.

Assuming that the password is “pygmalion”, you could divide it into three parts randomly and share it with your heirs. For instance;

pyg___, _mal___,_ion

In scenarios where the shareholders cannot be completely trusted, the shares are encrypted before they are distributed. If one of the shares is compromised or lost, it’s difficult to reassemble all the shares to reconstruct the secret. This is where Shamir Secret Sharing(SSS) comes in.

Shamir Secret Sharing (SSS) Explained

Shamir Secret Sharing scheme, formulated by Adi Shamir in 1979, is an algorithm that enables a secret to be divided into multiple, distinct parts, but it only requires a certain threshold of the shares to reconstruct the entire secret. The shares are encrypted before they’re distributed in a group or network. No shareholder knows other participants’ encrypted shares.

Using the example above, you could decide on a threshold (say 2 of 3), which is the minimum number of shareholders required for the reconstruction. If Ogee forgot or lost his share of the password, Gigi and Georgie could combine their shares to reconstruct the password. This means that anything short of the threshold cannot reconstruct the original secret. With SSS, a higher threshold typically means there’s a higher level of security.

How does SSS Allow Reconstruction With Only a Fraction of the Shares?

SSS uses a method known as polynomial interpolation, which is a mathematical technique to find unknown data using known data points. This enables the complete reconstruction of a secret with a predetermined minimum number of data points.