Hello all, I have a math question concerning implementation of elliptic curve systems. In coding some elliptic curve source, I need to pick a random point on the following elliptic curve in field F_p where p is a prime number. Y**2 = x**3 + a * x**2 + b where 4a**3 + 27b**2 is not equal to 0 mod p In selecting a random point, I pick a random value for x in the range 0 < x < p, compute the right hand side of the equation and find myself needing to take the square root for the two solutions. Questions are: 1: How can I take the suqare root mod p ? 2: How to determine if a solution exists for a selected value of x ? 3: Is the a simpler method than find a square root ? Thanks for any ideas you may have about this... -tom