Q:

How to encrypt data using a certificate? 

How do i encrypt data using a "certificate" in the Microsoft Crypto API? 

i know how to encrypt data with the Microsoft Crypto API using AES encryption:
keyBlob.hdr.bType := PLAINTEXTKEYBLOB;
keyBlob.hdr.bVersion := CUR_BLOB_VERSION;
keyBlob.hdr.reserved := 0;
keyBlob.hdr.aiKeyAlg := CALG_AES_128;
keyBlob.cbKeySize := 16;
Move(data[0], keyBlob.key[0], 16);

/*
   Set ProviderName to either
   providerName = "Microsoft Enhanced RSA and AES Cryptographic Provider"
   providerName = "Microsoft Enhanced RSA and AES Cryptographic Provider (Prototype)"  //Windows XP and earlier
*/
MS_ENH_RSA_AES_PROV_W: WideString = 'Microsoft Enhanced RSA and AES Cryptographic Provider';
providerName := MS_ENH_RSA_AES_PROV_W;

CryptAcquireContextW(provider, nil, PWideChar(providerName), PROV_RSA_AES, CRYPT_VERIFYCONTEXT);
CryptImportKey(provider, PByte(@keyBlob), sizeof(keyBlob), 0, 0, importedKey);

mode := CRYPT_MODE_CBC;
CryptSetKeyParam(importedKey, KP_MODE, @mode, 0);

//CryptEncrypt encrypts in-place.  Copy stuff to be encrypted into new byte buffer
utf8PlainText := TCrypt. WideStringToUTF8(szPlainText);
dataLen := Length(utf8PlainText);
bufferLen := dataLen+16; //allocate a buffer larger than we need to hold the data we want to encrypt
SetLength(data, bufferLen);
Move(utf8PlainText[1], data[0], dataLen);

if not CryptEncrypt(importedKey, 0, True, 0, @data[0], {var}dataLen, bufferLen) then
begin
   le := GetLastError;
   if le = ERROR_MORE_DATA  then
   begin
      /*
         If the buffer allocated for pbData is not large enough to hold the encrypted data,
         GetLastError returns ERROR_MORE_DATA and stores the required buffer size,
         in bytes, in the DWORD value pointed to by pdwDataLen. 
      */
      bufferLen := dataLen;
      SetLength(data, bufferLen);
      CryptEncrypt(importedKey, 0, True, 0, @data[0], {var}dataLen, bufferLen);
   end;
   CryptDestroyKey(importedKey);
   CryptReleaseContext(provider, 0);
end;

Now i need to do the same thing, except rather than symmetric encryption i need to use a public-key to encrypt, and a private key to decrypt. 

Note: It took 3 days to come up with those 15 lines of code for symmetric encryption.  i'm hoping someone can same me from a week of banging my head against a wall, and i end up going down the wrong path thinking that i have to install OpenSSL.  Even worse, if i try to call COM Objects from native code
Note: i only included the code example as a way to fill-up the question with irrelavent junk.  Some people vote to close a question if it only contains one line. 

A:

Microsoft Crypto API contain high-level functions for asymmetric encryption and decryption with certificates.  Look at CryptEncryptessage and CryptDecryptMessage. 
In decryption case your CERT_CONTEXT must have a CERT_KEY_PROV_INFO_PROP_ID property. 
I can give you an examples of usage:
const wchar_t message[] = L"This is a simple test message."; 
PCCERT_CONTEXT hCert = NULL;
HCERTSTORE hStore = NULL;

static bool openCertStoreMY(CDialog *parent)
{
    if(!hStore)
    {
        hStore = CertOpenSystemStore(NULL, L"MY");

        if(!hStore)
        {
            parent->MessageBox(L"Cannot open \"MY\"", L"Error", MB_ICONERROR);
            return false;
        }
    }

    return true;
}

void CTestDlg::OnEncryptClicked()
{
    if(!hCert)
    {
        if(!openCertStoreMY(this))
            return;

        hCert = CryptUIDlgSelectCertificateFromStore(hStore, GetSafeHwnd(), NULL, NULL, 0, 0, 0);

        if(!hCert)
            return;
    }

    CRYPT_ENCRYPT_MESSAGE_PARA params;
    memset(&params, 0, sizeof(CRYPT_ENCRYPT_MESSAGE_PARA));
    params.cbSize = sizeof(CRYPT_ENCRYPT_MESSAGE_PARA);
    params.dwMsgEncodingType = X509_ASN_ENCODING | PKCS_7_ASN_ENCODING;
    params. ContentEncryptionAlgorithm.pszObjId = "2.16.840.1.101.3.4.1.2"; //AES128

    DWORD msz;
    DWORD cbMsg = sizeof(message);
    const BYTE *pbMsg = (PBYTE)message;
    if(!CryptEncryptMessage(&params, 1, &hCert, pbMsg, cbMsg, NULL, &msz))
        return;

    PBYTE outBuf = new BYTE[msz];
    if(CryptEncryptMessage(&params, 1, &hCert, pbMsg, cbMsg, outBuf, &msz))
    {
        FILE *fil = _wfopen(filename, L"wb");
        if(fil)
        {
            fwrite(outBuf, 1, msz, fil);
            fclose(fil);
            MessageBox(L"Complete");
        }
        else
            MessageBox(L"Cannot open file", L"Error", MB_ICONERROR);
    }

    delete [] outBuf;
}

void CTestDlg::OnDecryptClicked()
{
    if(!openCertStoreMY(this))
        return;

    CRYPT_DECRYPT_MESSAGE_PARA params;
    params.cbSize = sizeof(CRYPT_DECRYPT_MESSAGE_PARA);
    params.dwMsgAndCertEncodingType = X509_ASN_ENCODING | PKCS_7_ASN_ENCODING;
    params.cCertStore = 1;
    params.rghCertStore = &hStore;
    params.dwFlags = 0;

    DWORD cbMsg;
    PBYTE pbMsg;

    FILE *fil = _wfopen(filename, L"rb");
    if(fil)
    {
        fseek(fil, 0 ,2);
        cbMsg = ftell(fil);
        fseek(fil, 0, 0);
        pbMsg = new BYTE[cbMsg];

        fread(pbMsg, 1, cbMsg, fil);
        fclose(fil);
    } else {
        MessageBox(L"Cannot open file", L"Error", MB_ICONERROR);
        return;
    }

    DWORD msz;
    if(!CryptDecryptMessage(&params, pbMsg, cbMsg, NULL, &msz, NULL))
    {
        delete [] pbMsg;
        return;
    }

    PBYTE outBuf = new BYTE[msz];
    if(CryptDecryptMessage(&params, pbMsg, cbMsg, outBuf, &msz, NULL))
        MessageBox((LPCWSTR)outBuf);

    delete [] pbMsg;
    delete [] outBuf;
}

