Threshold Cryptography

Threshold Cryptography is a term used by NIST to describe cryptographic primitives implemented using Multiparty Computation.

MPC is a cryptographic technology that allows a number of MPC nodes, n, to collaboratively compute any function y=function(x1, x2, ..., xn) in a secure way, so each node Ni learns only on y and xi.

Secret Sharing

Secret sharing is a technique in cryptography that allows a secret value or message to be divided into multiple parts, called shares, where only certain subsets of the shares are sufficient to reconstruct the original secret. This allows the secret to be distributed among multiple parties, and no single party has access to the entire secret, still, the secret can be reconstructed if enough parties come together.

Threshold cryptography is a type of secret sharing where the shares are distributed among multiple parties. The secret can only be reconstructed if a minimum number of shares, called the threshold, are combined. This allows the secret to be protected against unauthorized access if the threshold is not reached.

For example, imagine that a secret message is divided into three shares and distributed among three parties with a threshold of two parties. In such a case the secret can only be reconstructed if at least two of the parties come together and combine their shares. If any of the parties tries to access the secret on their own, they will only have access to a single share, which is not sufficient to reconstruct the complete secret.

Threshold cryptography is used to provide secure and efficient access to sensitive data or resources, such as cryptographic keys, without requiring any single party to have complete access. It can also be used to enable secure multiparty computation, where multiple parties can jointly calculate encrypted data without revealing their inputs to each other.