\documentclass{article}
\usepackage[utf8]{inputenc}

\title{Generalised Schnorr}
\author{kennonero}
\date{July 2019}

\usepackage{natbib}
\usepackage{graphicx}

\begin{document}

\maketitle

\section{Introduction}
In this draft, we show that the Schnorr identification scheme can be generalised using polynomial interpolation.

\section{Draft proof}

The following proof will follow in a similar format to Schnorr.
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- Prover owns $`n`$ public keys: $P_1, P_2, ..., P_n$
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- He wants to prove that he owns the private keys to all of these public keys with respect to some generator $G$
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1) Prover generates a random scalar `r`
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2) Prover sends $R = rG$ to verifer
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3) Verifier sends a challenge scalar `c`
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4) Prover sends scalar $d = c * p_1 + c^2 * p_2 + ... + c^n * p_n + r $
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5) Verifier accepts iff $d * G = c * P_1 + c^2 * P_2 + ... + c^n * P_n + R$


\section{Conclusion}
When n =1, this is a special case of the Schnorr identification protocol

\end{document}