Thetacrypt - Threshold Cryptography Distributed Service 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 cryptographic scheme 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 a secret $s$ is 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.

Implemented Schemes and References

Scheme Name	Scheme Type	Reference
SG02	Cryptosystem	Securing Threshold Cryptosystems against Chosen Ciphertext Attack (ZK-based)
BZ03	Cryptosystem	Simple and Efficient Threshold Cryptosystem from the Gap Diffie-Hellman Group (Pairing-based)
BLS04	Signature	Short Signatures from the Weil Pairing (Pairing-based)
FROST	Signature	FROST: Flexible Round-Optimized Schnorr Threshold Signatures (ZK-based)
SH00	Signature	Practical Threshold Signatures (Threshold RSA)
CKS05	Coin-flip	Random Oracles in Constantinople: Practical Asynchronous Byzantine Agreement Using Cryptography (ZK-based)