Elliptic curve random number generation

摘要

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 x-coordinate 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 stored by for a security domain. The administrator logs the output of the generator to reconstruct the random number with the escrow key.

主权项

1. A computer-implemented method of generating a random number for use in a cryptographic operation to be performed by a processor, the method comprising:
generating a random number by operating one or more processors on a pair of inputs, each input representing at least one coordinate of a respective one of a pair of elliptic curve points, at least one input of the pair of inputs being generated in a manner to ensure that one point of the pair of elliptic curve points is not a multiple of the other point of the pair of elliptic curve points; using a secret value to compute scalar multiples of each of the points represented by the pair of inputs; and using one of the scalar multiples to derive the random number and using the other of the scalar multiples to change the secret value for subsequent use; using the random number in cryptographic operation.