Elliptic curve random number generation

Abstract From the Canadian patent

An elliptic curve random number generator avoids escrow keys by choosing a point Q on the elliptic curve as verifiably random. An arbitrary string is chosen and a hash of that string computed. The hash is then converted to a field element of the desired field, the field element regarded as the xcoordinate of a point Q on the elliptic curve and the x-coordinate is tested for validity on the desired elliptic curve. If valid the x-coordinate is , decompressed to the point Q wherein the choice of which is the two points is also derived from the hash value. Intentional use of escrow keys can provide for back up functionality. The relationship between P and Q is used as an escrow key and …