Problems generating a self-signed 1024-bit X509Certificate2 using the RSA AES provider

I am trying to generate an X509Certificate2 object using the Microsoft AES Cryptographic Provider:

CALG_AES_256 (0x00006610) 256 bit AES. This algorithm is supported by the Microsoft AES Cryptographic Provider.

My problem is that my call to CryptGenKey(providerContext, 0x6610, 0x4000001, out cryptKey) fails with the following error:

An unhandled exception of type 'System.Runtime.InteropServices.COMException' occurred in mscorlib.dll

Additional information: Invalid flags specified. (Exception from HRESULT: 0x80090009)

The flags I am using are (1024 << 16) | 1). Unless I am mistaken, should this not produce a 1024-bit exportable key according to the documentation on MSDN? What is the problem with my approach here?

My code is as follows:

using System;
using System.Security;
using System.Runtime.InteropServices;
using System.Runtime.CompilerServices;
using System.Security.Cryptography.X509Certificates;

namespace WebSockets
{
    public struct SystemTime
    {
        public short Year;
        public short Month;
        public short DayOfWeek;
        public short Day;
        public short Hour;
        public short Minute;
        public short Second;
        public short Milliseconds;
    }

    public static class MarshalHelper
    {
        public static void CheckReturnValue(bool nativeCallSucceeded)
        {
            if (!nativeCallSucceeded)
                Marshal.ThrowExceptionForHR(Marshal.GetHRForLastWin32Error());
        }
    }

    public static class DateTimeExtensions
    {

        [DllImport("kernel32.dll", SetLastError = true)]
        static extern bool FileTimeToSystemTime(ref long fileTime, out SystemTime systemTime);

        public static SystemTime ToSystemTime(this DateTime dateTime)
        {
            long fileTime = dateTime.ToFileTime();
            SystemTime systemTime;
            MarshalHelper.CheckReturnValue(FileTimeToSystemTime(ref fileTime, out systemTime));
            return systemTime;
        }
    }

    class X509Certificate2Helper
    {

        [DllImport("advapi32.dll", SetLastError = true, CharSet = CharSet.Unicode)]
        static extern bool CryptAcquireContextW(out IntPtr providerContext, string container, string provider, uint providerType, uint flags);

        [DllImport("advapi32.dll", SetLastError = true)]
        static extern bool CryptReleaseContext(IntPtr providerContext, int flags);

        [DllImport("advapi32.dll", SetLastError = true)]
        static extern bool CryptGenKey(IntPtr providerContext, int algorithmId, int flags, out IntPtr cryptKeyHandle);

        [DllImport("advapi32.dll", SetLastError = true)]
        static extern bool CryptDestroyKey(IntPtr cryptKeyHandle);

        [DllImport("crypt32.dll", SetLastError = true)]
        static extern bool CertStrToNameW(int certificateEncodingType, IntPtr x500, int strType, IntPtr reserved, byte[] encoded, ref int encodedLength, out IntPtr errorString);

        [DllImport("crypt32.dll", SetLastError = true)]
        static extern IntPtr CertCreateSelfSignCertificate(IntPtr providerHandle, ref CryptoApiBlob subjectIssuerBlob, int flags, ref CryptKeyProviderInformation keyProviderInformation, IntPtr signatureAlgorithm, ref SystemTime startTime, ref SystemTime endTime, IntPtr extensions);

        [DllImport("crypt32.dll", SetLastError = true)]
        static extern bool CertFreeCertificateContext(IntPtr certificateContext);

        [DllImport("crypt32.dll", SetLastError = true)]
        static extern bool CertSetCertificateContextProperty(IntPtr certificateContext, int propertyId, int flags, ref CryptKeyProviderInformation data);

        public static X509Certificate2 GenerateSelfSignedCertificate(String name = "", DateTime? startTime = null, DateTime? endTime = null)
        {
            if (startTime == null || (DateTime)startTime < DateTime.FromFileTimeUtc(0))
                startTime = DateTime.FromFileTimeUtc(0);
            var startSystemTime = ((DateTime)startTime).ToSystemTime();
            if (endTime == null)
                endTime = DateTime.MaxValue;
            var endSystemTime = ((DateTime)endTime).ToSystemTime();
            string containerName = Guid.NewGuid().ToString();
            GCHandle dataHandle = new GCHandle();
            IntPtr providerContext = IntPtr.Zero;
            IntPtr cryptKey = IntPtr.Zero;
            IntPtr certificateContext = IntPtr.Zero;
            IntPtr algorithmPointer = IntPtr.Zero;
            RuntimeHelpers.PrepareConstrainedRegions();
            try
            {
                MarshalHelper.CheckReturnValue(CryptAcquireContextW(out providerContext, containerName, null, 0x18, 0x8));
                MarshalHelper.CheckReturnValue(CryptGenKey(providerContext, 0x6610, 0x4000001, out cryptKey));
                IntPtr errorStringPtr;
                int nameDataLength = 0;
                byte[] nameData;
                dataHandle = GCHandle.Alloc(name, GCHandleType.Pinned);
                if (!CertStrToNameW(0x10001, dataHandle.AddrOfPinnedObject(), 3, IntPtr.Zero, null, ref nameDataLength, out errorStringPtr))
                {
                    string error = Marshal.PtrToStringUni(errorStringPtr);
                    throw new ArgumentException(error);
                }
                nameData = new byte[nameDataLength];
                if (!CertStrToNameW(0x10001, dataHandle.AddrOfPinnedObject(), 3, IntPtr.Zero, nameData, ref nameDataLength, out errorStringPtr))
                {
                    string error = Marshal.PtrToStringUni(errorStringPtr);
                    throw new ArgumentException(error);
                }
                dataHandle.Free();
                dataHandle = GCHandle.Alloc(nameData, GCHandleType.Pinned);
                CryptoApiBlob nameBlob = new CryptoApiBlob { cbData = (uint)nameData.Length, pbData = dataHandle.AddrOfPinnedObject() };
                dataHandle.Free();
                CryptKeyProviderInformation keyProvider = new CryptKeyProviderInformation { pwszContainerName = containerName, dwProvType = 1, dwKeySpec = 1 };
                CryptAlgorithmIdentifier algorithm = new CryptAlgorithmIdentifier { pszObjId = "1.2.840.113549.1.1.13", Parameters = new CryptoApiBlob() };
                algorithmPointer = Marshal.AllocHGlobal(Marshal.SizeOf(algorithm));
                Marshal.StructureToPtr(algorithm, algorithmPointer, false);
                certificateContext = CertCreateSelfSignCertificate(providerContext, ref nameBlob, 0, ref keyProvider, algorithmPointer, ref startSystemTime, ref endSystemTime, IntPtr.Zero);
                MarshalHelper.CheckReturnValue(certificateContext != IntPtr.Zero);
                return new X509Certificate2(certificateContext);
            }
            finally
            {
                if (dataHandle.IsAllocated)
                    dataHandle.Free();
                if (certificateContext != IntPtr.Zero)
                    CertFreeCertificateContext(certificateContext);
                if (cryptKey != IntPtr.Zero)
                    CryptDestroyKey(cryptKey);
                if (providerContext != IntPtr.Zero)
                    CryptReleaseContext(providerContext, 0);
                if (algorithmPointer != IntPtr.Zero)
                {
                    Marshal.DestroyStructure(algorithmPointer, typeof(CryptAlgorithmIdentifier));
                    Marshal.FreeHGlobal(algorithmPointer);
                }
            }
        }

        struct CryptoApiBlob
        {
            public uint cbData;
            public IntPtr pbData;
        }

        struct CryptAlgorithmIdentifier {
            [MarshalAs(UnmanagedType.LPStr)]
            public String pszObjId;
            public CryptoApiBlob Parameters;
        }

        struct CryptKeyProviderInformation
        {
            [MarshalAs(UnmanagedType.LPWStr)]
            public String pwszContainerName;
            [MarshalAs(UnmanagedType.LPWStr)]
            public String pwszProvName;
            public uint dwProvType;
            public uint dwFlags;
            public uint cProvParam;
            public IntPtr rgProvParam;
            public uint dwKeySpec;
        }
    }
}

To call it, you may use: X509Certificate2Helper.GenerateSelfSignedCertificate("CN = Example");.

Update:

If I use 0x1 for the flags:

CryptAcquireContextW(out providerContext, containerName, "Microsoft Enhanced RSA and AES Cryptographic Provider", 0x18, 0x8);
CryptGenKey(providerContext, 0x6610, 0x1, out cryptKey);

It gets past CryptGenKey, but then fails on CertCreateSelfSignCertificate with:

An unhandled exception of type 'System.Runtime.InteropServices.COMException' occurred in mscorlib.dll

Additional information: Key does not exist. (Exception from HRESULT: 0x8009000D)

Must this key-set be passed in differently? What is wrong with the way I have created it above?

The problem is with CryptGenKey function call. In the Algid parameter, you should pass either 0x1 (for RSA key exchange) or 0x2 (RSA digital signature). You don't need other values. And key length value should be 0x4000001 (with exportable key). Also, I noticed that you pass incorrect provider type when you instantiate CryptKeyProviderInformation object. Replace this line:

CryptKeyProviderInformation keyProvider = new CryptKeyProviderInformation {
    pwszContainerName = containerName,
    dwProvType = 1,
    dwKeySpec = 1
};

with this line:

CryptKeyProviderInformation keyProvider = new CryptKeyProviderInformation {
    pwszContainerName = containerName,
    dwProvType = 0x18,
    dwKeySpec = 1
};