A Distribution Protocol for Dealerless Secret Distribution

Abstract

As the value of bitcoin increases, more incidents such as those involving Mt Gox and Bitfinex will occur in standard centralised systems. The addition of group-based threshold cryptography with the ability to be deployed without a dealer and which supports the non-interactive signing of messages provides for the division of private keys into shares that can be distributed to individuals and groups to provide additional security. This scheme creates a distributed key generation system for bitcoin that removes the necessity for any centralised control list minimising any threat of fraud or attack. In the application of threshold-based solutions for DSA to ECDSA, we have created an entirely distributive signature system for bitcoin that mitigates against any single point of failure. When coupled with retrieval schemes involving CLTV and multisig wallets, our solution provides an infinitely extensible and secure means of deploying bitcoin. Using group and ring-based systems, we can implement blind signatures against issued transactions.

Appendix

To compute $\frac{{\beta = Exp - Interpolate(w_{i} , \ldots ,w_{n} )}}{Exp - Interpolate(\,)\quad \to *}$

If $\{ w_{i} , \ldots ,w_{n} \} (n \ge 2t + 1)$ is a set of values, such that at most, t are null and the remaining are of the form $G \times a_{i}$ where the $a_{i}$’s lie on some $(k - 1)$-degree Polynomial $H( \cdot )$, then $\beta = G \times H(\emptyset )$. This is computed using:

$$\begin{aligned} \beta & =\Sigma _{i \in v} w_{i} \times \lambda_{i} \\ & =\Sigma _{i \in v} (G \times H(i)) \times \lambda_{i} \\ \end{aligned}$$

where $\nu$ is a $k$-subset of the correct $w_{i}$’s and $\lambda_{i}$’s are the corresponding Lagrange interpolation coefficients. For more background information, see the following: [7, 14, 16, 19, 22].