How to pass an exception or show an error in a suitable ASP.NET web service

I am developing a web service using ASP.NET. I am not using WCF. I am using legacy web service technologies. But I have a big problem. I want clients to pass credentials in the soap header for every request in order to validate them. I have created an authentication function. I don't want to call this function in every function of my service class. So I call this function inside the constructor of my service class. If the check fails. I want to throw an exception. But I know this is not good for throwing exceptions in a webservice. So please tell me the most efficient way to throw exceptions in a .NET webservice and any suggestions for improving my code. Below is my code.

My service code

public class math : System.Web.Services.WebService
{
    public AuthHeader Authentication;

    public math()
    {
        if(Authentication==null || Authentication.Username!="username" || Authentication.Password!="mypassword")
        {
            throw new Exception("Authentication failed");
        }
    }

    [WebMethod]
    [SoapHeader("Authentication",Required=true)]
    public int Sum(int num1,int num2)
    {
            return num1 + num2;

    }
}

      

        
        
        
      

    

My Authentication Header Class

public class AuthHeader : SoapHeader
{
    public string Username { get; set; }
    public string Password { get; set; }
}