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  1. \documentclass{article}
  2. \usepackage[utf8]{inputenc}
  3.  
  4. \title{Generalised Schnorr}
  5. \author{kennonero}
  6. \date{July 2019}
  7.  
  8. \usepackage{natbib}
  9. \usepackage{graphicx}
  10.  
  11. \begin{document}
  12.  
  13. \maketitle
  14.  
  15. \section{Introduction}
  16. In this draft, we show that the Schnorr identification scheme can be generalised using polynomial interpolation.
  17.  
  18. \section{Draft proof}
  19.  
  20. The following proof will follow in a similar format to Schnorr.
  21. \newline
  22. \newline
  23. - Prover owns $`n`$ public keys: $P_1, P_2, ..., P_n$
  24. \newline
  25. \newline
  26. - He wants to prove that he owns the private keys to all of these public keys with respect to some generator $G$
  27. \newline
  28. \newline
  29. 1) Prover generates a random scalar `r`
  30. \newline
  31. \newline
  32. 2) Prover sends $R = rG$ to verifer
  33. \newline
  34. \newline
  35. 3) Verifier sends a challenge scalar `c`
  36. \newline
  37. \newline
  38. 4) Prover sends scalar $d = c * p_1 + c^2 * p_2 + ... + c^n * p_n + r $
  39. \newline
  40. \newline
  41. 5) Verifier accepts iff $d * G = c * P_1 + c^2 * P_2 + ... + c^n * P_n + R$
  42.  
  43.  
  44. \section{Conclusion}
  45. When n =1, this is a special case of the Schnorr identification protocol
  46.  
  47. \end{document}
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