Reading the BitBucket API with Authentication for a Private Repository in C#.net

I had the same problem recently, and I found two different solutions.

First, vanilla .net with HttpWebRequest and HttpWebResponse:
(this came from an answer here at Stack Overflow, but unfortunately I can't find the link anymore)

string url = "https://api.bitbucket.org/1.0/repositories/your_username/your_repo/issues/1";
var request = WebRequest.Create(url) as HttpWebRequest;

string credentials = Convert.ToBase64String(ASCIIEncoding.ASCII.GetBytes("your_username" + ":" + "your_password"));
request.Headers.Add("Authorization", "Basic " + credentials);

using (var response = request.GetResponse() as HttpWebResponse)
{
    var reader = new StreamReader(response.GetResponseStream());
    string json = reader.ReadToEnd();
}  

Or, if you want to do the same with less code, you can use RestSharp:

var client = new RestClient("https://api.bitbucket.org/1.0/");
client.Authenticator =
    new HttpBasicAuthenticator("your_username", "your_password");
var request = new RestRequest("repositories/your_username/your_repo/issues/1");
RestResponse response = client.Execute(request);
string json = response.Content;   

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By the way, I decided to use the HttpWebRequest solution for my own application.
I'm writing a small tool to clone all my Bitbucket repositories (including the private ones) to my local machine. So I just make one single call to the Bitbucket API to get the list of repositories.
And I didn't want to include another library in my project just to save a few lines of code for this one single call.