Private/Resolve-Secret.ps1
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.SYNOPSIS Recovers a secret from Shamir's Secret Sharing scheme shares. .DESCRIPTION Recovers a secret from Shamir's Secret Sharing scheme by performing Lagrange interpolation over the provided shares. .PARAMETER Shares An array of share objects, each containing an ID and a value. .PARAMETER Prime The prime modulus for the finite field. Defaults to 2^127 - 1. .OUTPUTS The recovered secret value. .EXAMPLE Recover a secret from shares: $Shares = @(@{id = 1; value = "2"}, @{id = 2; value = "4"}, @{id = 3; value = "9"}) $Prime = [bigint][math]::Pow(2,127) - 1 Resolve-Secret -Shares $Shares -Prime $Prime #> Function Resolve-Secret { param ( [array[]]$Shares, [bigint]$Prime = [bigint][math]::Pow(2,127) - 1 ) if ($Shares.Length -lt 3) { # throw "Need at least three shares." } # Unzip the shares into x_s and y_s $PointNums = [System.Collections.ArrayList]@() $PointPolynomials = [System.Collections.ArrayList]@() foreach ($Share in $Shares) { $PointNums.Add($Share.id) | Out-Null # Parse the given string for more accuracy $PointPolynomials.Add([bigint]::Parse($Share.value)) | Out-Null } Return (Get-LagrangeInterpolation -x 0 -PointNums $PointNums -PointPolynomials $PointPolynomials -Prime $Prime) } |