Elliptic Curve Y**2 = x**3 + a * x**2 + b
Tom Rollins
trollins at interactive.visa.com
Thu Aug 29 16:13:53 PDT 1996
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
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