I'm having a problem using a machine level RSA key container when storing only the public key of a public/private key pair.

The following code creates a public/private pair and extracts the public key from that pair. The pair and the public key are stored in separate key containers. The keys are then obtained from those key containers at which point they should be the same as the keys going into the containers.

The code works when CspProviderFlags.UseDefaultKeyContainer is specified for CspParameters.Flags (i.e. the key read back out from the PublicKey container is the same), but when CspProviderFlags.UseMachineKeyStore is specified for CspParameters.Flags the key read back from PublicKey is different.

Why is the behaviour different, and what do I need to do differently to retrieve the public key from a machine-level RSA key container?

var publicPrivateRsa = new RSACryptoServiceProvider(new CspParameters()
{
    KeyContainerName = "PublicPrivateKey",
    Flags = CspProviderFlags.UseMachineKeyStore
    //Flags = CspProviderFlags.UseDefaultKeyContainer
}
    )
{
    PersistKeyInCsp = true,

};

var publicRsa = new RSACryptoServiceProvider(new CspParameters()
{
    KeyContainerName = "PublicKey",
    Flags = CspProviderFlags.UseMachineKeyStore
    //Flags = CspProviderFlags.UseDefaultKeyContainer
}
    )
{
    PersistKeyInCsp = true
};


//Export the key.
publicRsa.ImportParameters(publicPrivateRsa.ExportParameters(false));


Console.WriteLine(publicRsa.ToXmlString(false));
Console.WriteLine(publicPrivateRsa.ToXmlString(false));

//Dispose those two CSPs.
using (publicRsa)
{
    publicRsa.Clear();
}
using (publicPrivateRsa)
{
    publicRsa.Clear();
}

publicPrivateRsa = new RSACryptoServiceProvider(new CspParameters()
{
    KeyContainerName = "PublicPrivateKey",
    Flags = CspProviderFlags.UseMachineKeyStore
    //Flags = CspProviderFlags.UseDefaultKeyContainer
}
    );


publicRsa = new RSACryptoServiceProvider(new CspParameters()
{
    KeyContainerName = "PublicKey",
    Flags = CspProviderFlags.UseMachineKeyStore
    //Flags = CspProviderFlags.UseDefaultKeyContainer
}
    );

Console.WriteLine(publicRsa.ToXmlString(false));
Console.WriteLine(publicPrivateRsa.ToXmlString(false));


using (publicRsa)
{
    publicRsa.Clear();
}
using (publicPrivateRsa)
{
    publicRsa.Clear();
}