C# Export Private/Public RSA key from RSACryptoServiceProvider to PEM string

I have an instance of System.Security.Cryptography.RSACryptoServiceProvider, i need to export it's key to a PEM string - like this:

-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----

But there is no such option according to the MSDN documentation, there is only some kind of XML export. I can't use any third party libraries like BouncyCastle. Is there any way to generate this string?

Please note: The code below is for exporting a private key. If you are looking to export the public key, please refer to my answer given here.

The PEM format is simply the ASN.1 DER encoding of the key (per PKCS#1) converted to Base64. Given the limited number of fields needed to represent the key, it's pretty straightforward to create quick-and-dirty DER encoder to output the appropriate format then Base64 encode it. As such, the code that follows is not particularly elegant, but does the job:

private static void ExportPrivateKey(RSACryptoServiceProvider csp, TextWriter outputStream)
{
    if (csp.PublicOnly) throw new ArgumentException("CSP does not contain a private key", "csp");
    var parameters = csp.ExportParameters(true);
    using (var stream = new MemoryStream())
    {
        var writer = new BinaryWriter(stream);
        writer.Write((byte)0x30); // SEQUENCE
        using (var innerStream = new MemoryStream())
        {
            var innerWriter = new BinaryWriter(innerStream);
            EncodeIntegerBigEndian(innerWriter, new byte[] { 0x00 }); // Version
            EncodeIntegerBigEndian(innerWriter, parameters.Modulus);
            EncodeIntegerBigEndian(innerWriter, parameters.Exponent);
            EncodeIntegerBigEndian(innerWriter, parameters.D);
            EncodeIntegerBigEndian(innerWriter, parameters.P);
            EncodeIntegerBigEndian(innerWriter, parameters.Q);
            EncodeIntegerBigEndian(innerWriter, parameters.DP);
            EncodeIntegerBigEndian(innerWriter, parameters.DQ);
            EncodeIntegerBigEndian(innerWriter, parameters.InverseQ);
            var length = (int)innerStream.Length;
            EncodeLength(writer, length);
            writer.Write(innerStream.GetBuffer(), 0, length);
        }

        var base64 = Convert.ToBase64String(stream.GetBuffer(), 0, (int)stream.Length).ToCharArray();
        outputStream.WriteLine("-----BEGIN RSA PRIVATE KEY-----");
        // Output as Base64 with lines chopped at 64 characters
        for (var i = 0; i < base64.Length; i += 64)
        {
            outputStream.WriteLine(base64, i, Math.Min(64, base64.Length - i));
        }
        outputStream.WriteLine("-----END RSA PRIVATE KEY-----");
    }
}

private static void EncodeLength(BinaryWriter stream, int length)
{
    if (length < 0) throw new ArgumentOutOfRangeException("length", "Length must be non-negative");
    if (length < 0x80)
    {
        // Short form
        stream.Write((byte)length);
    }
    else
    {
        // Long form
        var temp = length;
        var bytesRequired = 0;
        while (temp > 0)
        {
            temp >>= 8;
            bytesRequired++;
        }
        stream.Write((byte)(bytesRequired | 0x80));
        for (var i = bytesRequired - 1; i >= 0; i--)
        {
            stream.Write((byte)(length >> (8 * i) & 0xff));
        }
    }
}

private static void EncodeIntegerBigEndian(BinaryWriter stream, byte[] value, bool forceUnsigned = true)
{
    stream.Write((byte)0x02); // INTEGER
    var prefixZeros = 0;
    for (var i = 0; i < value.Length; i++)
    {
        if (value[i] != 0) break;
        prefixZeros++;
    }
    if (value.Length - prefixZeros == 0)
    {
        EncodeLength(stream, 1);
        stream.Write((byte)0);
    }
    else
    {
        if (forceUnsigned && value[prefixZeros] > 0x7f)
        {
            // Add a prefix zero to force unsigned if the MSB is 1
            EncodeLength(stream, value.Length - prefixZeros + 1);
            stream.Write((byte)0);
        }
        else
        {
            EncodeLength(stream, value.Length - prefixZeros);
        }
        for (var i = prefixZeros; i < value.Length; i++)
        {
            stream.Write(value[i]);
        }
    }
}

For exporting PublicKey use this code:

public static String ExportPublicKeyToPEMFormat(RSACryptoServiceProvider csp)
{
    TextWriter outputStream = new StringWriter();

    var parameters = csp.ExportParameters(false);
    using (var stream = new MemoryStream())
    {
        var writer = new BinaryWriter(stream);
        writer.Write((byte)0x30); // SEQUENCE
        using (var innerStream = new MemoryStream())
        {
            var innerWriter = new BinaryWriter(innerStream);
            EncodeIntegerBigEndian(innerWriter, new byte[] { 0x00 }); // Version
            EncodeIntegerBigEndian(innerWriter, parameters.Modulus);
            EncodeIntegerBigEndian(innerWriter, parameters.Exponent);

            //All Parameter Must Have Value so Set Other Parameter Value Whit Invalid Data  (for keeping Key Structure  use "parameters.Exponent" value for invalid data)
            EncodeIntegerBigEndian(innerWriter, parameters.Exponent); // instead of parameters.D
            EncodeIntegerBigEndian(innerWriter, parameters.Exponent); // instead of parameters.P
            EncodeIntegerBigEndian(innerWriter, parameters.Exponent); // instead of parameters.Q
            EncodeIntegerBigEndian(innerWriter, parameters.Exponent); // instead of parameters.DP
            EncodeIntegerBigEndian(innerWriter, parameters.Exponent); // instead of parameters.DQ
            EncodeIntegerBigEndian(innerWriter, parameters.Exponent); // instead of parameters.InverseQ

            var length = (int)innerStream.Length;
            EncodeLength(writer, length);
            writer.Write(innerStream.GetBuffer(), 0, length);
        }

        var base64 = Convert.ToBase64String(stream.GetBuffer(), 0, (int)stream.Length).ToCharArray();
        outputStream.WriteLine("-----BEGIN PUBLIC KEY-----");
        // Output as Base64 with lines chopped at 64 characters
        for (var i = 0; i < base64.Length; i += 64)
        {
            outputStream.WriteLine(base64, i, Math.Min(64, base64.Length - i));
        }
        outputStream.WriteLine("-----END PUBLIC KEY-----");

        return outputStream.ToString();

    }
}

private static void EncodeIntegerBigEndian(BinaryWriter stream, byte[] value, bool forceUnsigned = true)
{
    stream.Write((byte)0x02); // INTEGER
    var prefixZeros = 0;
    for (var i = 0; i < value.Length; i++)
    {
        if (value[i] != 0) break;
        prefixZeros++;
    }
    if (value.Length - prefixZeros == 0)
    {
        EncodeLength(stream, 1);
        stream.Write((byte)0);
    }
    else
    {
        if (forceUnsigned && value[prefixZeros] > 0x7f)
        {
            // Add a prefix zero to force unsigned if the MSB is 1
            EncodeLength(stream, value.Length - prefixZeros + 1);
            stream.Write((byte)0);
        }
        else
        {
            EncodeLength(stream, value.Length - prefixZeros);
        }
        for (var i = prefixZeros; i < value.Length; i++)
        {
            stream.Write(value[i]);
        }
    }
}

private static void EncodeLength(BinaryWriter stream, int length)
{
    if (length < 0) throw new ArgumentOutOfRangeException("length", "Length must be non-negative");
    if (length < 0x80)
    {
        // Short form
        stream.Write((byte)length);
    }
    else
    {
        // Long form
        var temp = length;
        var bytesRequired = 0;
        while (temp > 0)
        {
            temp >>= 8;
            bytesRequired++;
        }
        stream.Write((byte)(bytesRequired | 0x80));
        for (var i = bytesRequired - 1; i >= 0; i--)
        {
            stream.Write((byte)(length >> (8 * i) & 0xff));
        }
    }
}

If you're using .NET Core 3.0 and you don't need the Windows platform dependent RSACryptoServiceProvider this is already implemented out of the box

    public string ExportPrivateKey(RSA rsa)
    {
        var privateKeyBytes = rsa.ExportRSAPrivateKey();
        var builder = new StringBuilder("-----BEGIN RSA PRIVATE KEY");
        builder.AppendLine("-----");

        var base64PrivateKeyString = Convert.ToBase64String(privateKeyBytes);
        var offset = 0;
        const int LINE_LENGTH = 64;

        while (offset < base64PrivateKeyString.Length)
        {
            var lineEnd = Math.Min(offset + LINE_LENGTH, base64PrivateKeyString.Length);
            builder.AppendLine(base64PrivateKeyString.Substring(offset, lineEnd - offset));
            offset = lineEnd;
        }

        builder.Append("-----END RSA PRIVATE KEY");
        builder.AppendLine("-----");
        return builder.ToString();
    }

Note: In .NET Core you wouldn't use RSACryptoServiceProvider as it's more Windows specific.