Secret Shares With Chinese Remainder Theory (CRT)

Asmuth–Bloom and Mignotte secret sharing using CRT

The general asked his army to arrange themselves into groups of 100, and the remainder was 25, then into groups of 101, and the remainder was 17, and then into groups of 102, and the remainder was 82. He announced that “We are 657,325 strong, let’s march! Here’s his solution:

With secret shares, we can take a secret, and then split it into a number of shares (n). Then we can define an algorithm to recover the secret using a threshold value (t). Thus we can split a secret in shares for Bob, Alice, Carol and Dave, and then define a thresold of three, so that Bob, Alice and Carol can come together with their shares and recover the value. Shamir used polynomials to share points, and where a curve can be recovered with enough points.

So let’s look at Shamir’s Secret Shares (SSS), and then look at regenerating with Chinese Remainer Theory (CRT). Both are defined as perfect secret sharing, as it should not be possible to regenerate the secret, without bringing together at…