How to generate a large prime via cryptography provider? - powershell

Question

I want to generate a 2048-bit prime number via the buildin cryptography provider in Powershell. This is the code I have so far, but testing the result via Rabin-Miller Test is telling me, that the number is NOT prime. What is wrong here?
$rsa = [System.Security.Cryptography.RSA]::Create(2048)
$format = [System.Security.Cryptography.CngKeyBlobFormat]::GenericPrivateBlob
$bytes = $rsa.Key.Export($format)
[bigint]$prime = 0
foreach($b in $bytes) {$prime = ($prime -shl 8) + $b}
$prime
This link tells me, that the BLOB should contain both RSA primes, but for any reason I am not able to get that info as expected: https://learn.microsoft.com/en-us/windows/win32/seccrypto/rsa-schannel-key-blobs#private-key-blobs

Answer 1

Finally I solved it after digging a bit deeper into the generic BLOB-format. The learning point here is the fact, that a 4096 RSA key includes two 2048-bit primes. One is on the last 256 bytes in the BLOB and the other prime is in the 256 bytes in front of that.
Here is the working code:
# generating two random 2048-bit PRIME numbers:
cls
$rsa = [System.Security.Cryptography.RSA]::Create(4096)
$key = $rsa.Key.Export('PRIVATEBLOB')
$len = $key.Length
$Pb = [byte[]]::new(256+1)
[array]::Copy($key, $len-512, $Pb, 1, 256)
[array]::Reverse($Pb)
$P = [bigint]$Pb
write-host $P
# optionally same for the second prime in the BLOB:
$Qb = [byte[]]::new(256+1)
[array]::Copy($key, $len-256, $Qb, 1, 256)
[array]::Reverse($Qb)
$Q = [bigint]$Qb
write-host $Q
# optionally here the Test-Function:
function Is-PrimeRabinMiller ([BigInt] $Source, [int] $Iterate) {
if ($source -eq 2 -or $source -eq 3) {return $true}
if (($source -band 1) -eq 0) {return $false}
[BigInt]$d = $source - 1;
$s = 0;
while (($d -band 1) -eq 0) {$d = $d -shr 1; $s++;}
if ($source.ToByteArray().Length -gt 255) {
$sourceLength = 255
}
else {
$sourceLength = $source.ToByteArray().Length
}
$rngProv = [System.Security.Cryptography.RNGCryptoServiceProvider]::Create()
[Byte[]] $bytes = $sourceLength
[BigInt]$a = 0
foreach ($i in 1..$iterate) {
do {
$rngProv.GetBytes($bytes)
$a = [BigInt]$bytes
} while (($a -lt 2) -or ($a -ge ($source - 2)))
[BigInt]$x = ([BigInt]::ModPow($a,$d,$source))
if ($x -eq 1 -or ($x -eq $source-1)) {continue}
foreach ($j in 1..($s-1)) {
$x = [BigInt]::ModPow($x, 2, $source)
if ($x -eq 1) {return $false}
if ($x -eq $source-1) {break}
}
return $false
}
return $true
}
if (Is-PrimeRabinMiller $P 42) {"P is prime!"}
if (Is-PrimeRabinMiller $Q 42) {"Q is prime!"}
Also I created a small function based on the above findings, that generates a random large prime numer:
function get-RandomPrime {
Param (
[parameter(Mandatory=$true)]
[ValidateRange(256, 8192)]
[ValidateScript({$_ % 8 -eq 0})]
[int]$bitLength
)
$rsa = [System.Security.Cryptography.RSA]::Create($bitLength*2)
$key = $rsa.Key.Export('PRIVATEBLOB')
$len = $key.Length
$byteLength = [int]$bitLength/8
$bytes = [byte[]]::new($byteLength+1)
[array]::Copy($key, $len-$byteLength, $bytes, 1, $byteLength)
[array]::Reverse($bytes)
[bigint]$bytes
}
$prime = get-RandomPrime -bitLength 2048
write-host "`nprime (DEC):" $prime
write-host "`nprime (HEX):" $prime.ToString('X2').SubString(1)