ThetaCrypt - Threshold Cryptography Library in Rust

Thetacrypt is a WIP codebase that aims at providing threshold cryptography as a service.

• To dive into the details of the architecture of our service explore the src directory.
• To try a quick start and immediately explore the functionalities offered by thetacrypt, check the demo directory.
• To learn more about threshold cryptography and its theoretical background, remain on this page.

Theoretical background

What is threshold cryptography?

Threshold cryptography defines protocols to enhance the security of a cryptosystem by distributing the trust among a group of parties. Typically, it is used for sharing a secret across a predefined number of nodes so as to obtain fault-tolerance for a subset, or threshold, of them. More formally, a threshold cryptosystem is defined by a fixed number of parties $P = {P_1, \dots, P_n}$, who need to collaborate to perform a cryptographic operation such that at least a threshold of them, $(t+1)$-out-of- $n$, are able to successfully terminate, but $t$ will learn anything about the shared secret. This is achieved by using Shamir's secret sharing, i.e. a technique based on polynomial interpolation that enables the reconstruction of a polynomial of degree $t$ with at least $t+1$ points.

The generation and distribution of the secret $s$ are performed, in the easiest setting, by a trusted dealer $D$ $\notin P$. The dealer chooses at random the coefficients ${a_1, \dots, a_t}$ and defines the polynomial: $p(x) = s + a_1 x + \dots + a_t x^t$. The polynomial has a degree at most $t$ and its evaluation in $p(0)$ is the secret. The polynomial will be uniquely determined by $t+1$ point.

Threshold cryptosystems are known for public-key schemes only, where applying secret sharing is possible thanks to the algebraic assumption used in such schemes.