Huge cryptographically secure random numbers

Just a tiny implementation example on how to use .NET crypto-package to create really huge pseudo random numbers.
Add approprite controls and rock.
(in my example I just kicked out the number on a webpage - feel free to do it where ever you like)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Web;
using System.Web.UI;
using System.Web.UI.WebControls;
using System.Numerics;
using System.Security.Cryptography;

namespace numbers
{
    public partial class WebForm1 : System.Web.UI.Page
    {
        protected void Page_Load(object sender, EventArgs e)
        {

        }

        private static BigInteger GetRandom()
        {
            RandomNumberGenerator ran = RNGCryptoServiceProvider.Create();
            byte[] ranbytes = new Byte[256];
            //ex: Byte[20] gives 8 bit * 20 = 160 bit ~  50 digits
            //ex: Byte[2] gives 8 bit * 2 = 16 bit  = +- 32768
            //ex: Byte[128] gives 8 bit * 128 = 1024 bit ~ 300 digits
    
            //fill the byte array with cryptographically strong random bytes
            ran.GetBytes(ranbytes);

            //put the random bytes into a bigInteger
            BigInteger mynum = new BigInteger(ranbytes);
            return mynum;
        }

        protected void Button1_Click(object sender, EventArgs e)
            {

            //Roll the really really big dice :)
            BigInteger roll = GetRandom();
            result.Text= roll.ToString();
 
        }
    }
}

random curve with point

If you just need any short form weierstrass curve at random with a random point the easiest way is to create the point first, then the curve.
suitable for lenstra.
Given a composite you would like to factor.
toy example:
given N= 1289
random point P=(x,y)=(235,156)
random A= 21
calculate B as
B=y^2 -x^3 - A*x mod N
156^2-235^3-21*235 mod 1289 gives B=-157
then you got your random curve:
Y^2=X^3 + 21X-157 with a point P that by construction is on the curve.

the solution for B ofcourse can be plus/minus any multiplication of N. equivalence class: B + Z/ZN
More about lenstra later