Zipper un memorystream

Bonsoir,
Je cherche à envoyer une piece jointe zip. Le mail part bien mais le zip reste à 0 ko...
Si je ne Zippe pas le fichier.txt en pièce jointe est correcte.

Code:

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   try{
        StringBuilder MyStringBuilder = new StringBuilder("Hello World!");
        SmtpClient smtpclient = new SmtpClient("smtp.gmail.com",587);           
        smtpclient.EnableSsl = true;
 
 
// Create MailMessage
MailMessage message = new MailMessage(
    "xxxxx@gmail.com",
    "xxxxxx@gmail.com",
    "test",
    "hello");
 
 
MemoryStream memoryStream = new MemoryStream();
MemoryStream memoryStreamDest = new MemoryStream();
 
byte[] contentAsBytes = Encoding.UTF8.GetBytes(MyStringBuilder.ToString());
    memoryStream.Write(contentAsBytes, 0, contentAsBytes.Length);
 
    // Set the position to the beginning of the stream.
    memoryStream.Seek(0, SeekOrigin.Begin);
 
    GZipStream gzCompressed;
    byte[] bufferWrite = new byte[memoryStream.Length];
    gzCompressed = new GZipStream(memoryStreamDest, CompressionMode.Compress, true);
    memoryStream.Read(bufferWrite, 0, bufferWrite.Length);
    gzCompressed.Write(bufferWrite, 0, bufferWrite.Length);
    gzCompressed.Close();
 
 
    // Create attachment
    ContentType contentType = new ContentType();
    contentType.MediaType = MediaTypeNames.Application.Zip;
    contentType.Name = "test.zip";
    Attachment attachment = new Attachment(memoryStreamDest, contentType);
 
    // Add the attachment
    message.Attachments.Add(attachment);
    smtpclient.DeliveryMethod = SmtpDeliveryMethod.Network;
 
    smtpclient.Credentials = new NetworkCredential("xxxxx", "yyyyy");
 
 
    // Send Mail via SmtpClient
    smtpclient.Send(message);

Merci de votre aide