Private/Get-RandomShares.ps1
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.SYNOPSIS Generates Shamir's Secret Sharing scheme shares. .DESCRIPTION Generates Shamir's Secret Sharing scheme shares for a given secret. .PARAMETER Secret The secret to share. .PARAMETER MinShares The minimum number of shares required to recover the secret. .PARAMETER Shares The total number of shares to generate. .PARAMETER Prime The prime modulus for the finite field. .OUTPUTS An array of share objects, each containing an ID and a value. .EXAMPLE Generate Shamir's Secret Sharing scheme shares: $Secret = 12345 $MinShares = 3 $Shares = 7 $Prime = [bigint][math]::Pow(2,127) - 1 Get-RandomShares -Secret $Secret -MinShares $MinShares -Shares $Shares -Prime $Prime #> Function Get-RandomShares { Param ( [ValidateScript({ If([BigInt]::Parse($_)) { $true } })] [String]$Secret, [int]$MinShares = 3, [int]$Shares = 7, [bigint]$Prime = [bigint][math]::Pow(2,127) - 1 ) If ($MinShares -gt $Shares) { throw "Fewer shares than minimum shares to recover make the secret irrecoverable" } # Create the polynomial coefficients $Polynomial = @($Secret) + (1..($MinShares - 1) | ForEach-Object { Get-Random -Minimum 0 -Maximum $Prime }) # Generate the share points $Points = [System.Collections.ArrayList]@() for ($i = 1; $i -le $Shares; $i++) { $Value = Test-Polynomial -Polynomial $Polynomial -PointToEval $i -Prime $Prime # We output the shares as string as that will make the initial handling of the variables to recover as bigints more controllable $Points.Add( [pscustomobject]@{ id = $i value = $Value }) | Out-Null } return $Points } |