From b52bc60b3e475ee57ed731d8e177eda6f6c0214f Mon Sep 17 00:00:00 2001 From: AtHeartEngineer Date: Sun, 9 Oct 2022 02:58:52 +0000 Subject: [PATCH] deploy: 5238d154d34473f89c1dd26ef314a865bfbf61bb --- print.html | 24 ++++++++++++------------ searchindex.js | 2 +- searchindex.json | 2 +- sss.html | 24 ++++++++++++------------ 4 files changed, 26 insertions(+), 26 deletions(-) diff --git a/print.html b/print.html index e69cee5..1558587 100644 --- a/print.html +++ b/print.html @@ -422,21 +422,21 @@ component main {public [x, epoch, rln_identifier ]} = RLN(15);
  • Shamir's Secret Sharing

    • Shamir's Secret Sharing Scheme

    -

    This topic is an explanation of Shamir's Secret Sharing scheme (SSS) also known as \((k, n)\) threshold secret sharing scheme. SSS is one of the key parts of RLN due to which we can share and restore the secret.

    +

    This topic is an explanation of Shamir's Secret Sharing scheme (SSS), also known as \((k, n)\) threshold secret sharing scheme. SSS is one of the critical parts of RLN.

    Overview

    -

    Imagine, if you have some important secret (secret key) and you don't want to store it anywhere. For that you can use SSS scheme. It allows you to split this secret into \(n\) parts (each individual part doesn't give any information about the secret) and restore this secret upon presentation of \(k\) \((k <= n)\) parts.

    -

    For example, you have a secret and you want to split it into \(n\) parts/shares. You can divide these shares between your friends (1 share to 1 friend). Now when \(k\) of your friends reveal their share you can restore the secret.

    +

    Imagine if you have some important secret (secret key) and you don't want to store it anywhere. For that, you can use the SSS scheme. It allows you to split this secret into \(n\) parts (each individual part doesn't give any information about the secret) and restore this secret upon presentation of \(k\) \((k <= n)\) parts.

    +

    For example, you have a secret that you want to split into \(n\) parts/shares. You can divide these shares between your friends (1 share to 1 friend). Now when \(k\) of your friends reveal their share, you can restore the secret.

    This scheme is also called \((k, n)\) threshold secret sharing scheme.

    -

    This scheme is possible due to polynomial interpolation (especially Lagrange interpolation). Let's describe how Lagrange interpolation works and then how it's used in SSS scheme.

    +

    This scheme is possible due to polynomial interpolation (especially Lagrange interpolation). Let's describe how Lagrange interpolation works and how it's used in a SSS scheme.

    Polynomial (Lagrange) interpolation

    -

    Interpolation is a method of constructing (or restoring) new points/values (or function) based on the range of a set of known points/values (f.e. we can restore the line (linear function) from two points, that are from this line). Previous example actually describes how that works.

    +

    Interpolation is a method of constructing (or restoring) new points/values (or function) based on the range of a set of known points/values (f.e. we can restore the line (linear function) from two points that are from this line). The previous example describes how that works.

    - An unlimited number of parabolas (second degree polynomials) can be drawn through two points. To choose the only one, you need a third point. + An unlimited number of parabolas (second-degree polynomials) can be drawn through two points. To choose the only one, you need a third point.

    -

    Thus, if we have a polynomial \(f(x) = 3x + 2\) we only need two points from this polynomial to restore it. Let's peek two random \(x\) values and calculate \(f(x)\):

    +

    Thus, if we have a polynomial \(f(x) = 3x + 2\), we only need two points from this polynomial to restore it. Let's peek two random \(x\) values and calculate \(f(x)\):