Elliptic curve random number generation
An elliptic curve random number generator avoids escrow keys by choosing a point 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 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 , 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 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.
1. A computer-implemented method of establishing an escrow key for a security domain within a network, comprising:
establishing a pair of points (P, ) as respective inputs to an elliptic curve random number generator (ECRNG), wherein P=e , and e is a relationship between the pair of points (P, );
storing the relationship e as an escrow key with an administrator;
generating from the ECRNG a random number for use in cryptographic operations within the security domain;
using the random number in a cryptographic operation; and
logging an output of the ECRNG to reconstruct the random number with the escrow key by the administrator.
2. The computer-implemented method of claim 1 , wherein the pair of points (P, ) is a pair of elliptic curve points.
3. The computer-implemented method of claim 1 , wherein one point of the pair of points (P, ) is obtained from an output of a one way function.
4. The computer-implemented method of claim 3 , wherein the one way function is a hash function.
5. The computer-implemented method of claim 3 , wherein the other point of the pair of points (P, ) is utilized as an input to the one way function.
6. The computer-implemented method of claim 5 , wherein the one point of the pair of points (P, ) is , and the other point of the pair of points (P, ) is P.
7. A device, comprising:
a memory; and
at least one processor communicatively coupled with the memory and configured to:
establish a pair of points (P, ) as respective inputs to an elliptic curve random number generator (ECRNG), wherein P=e , and e is a relationship between the pair of points (P, );
store the relationship e as an escrow key with an administrator;
generate from the ECRNG a random number for use in cryptographic operations within a security domain;
using the random number in a cryptographic operation; and
logging an output of the ECRNG to reconstruct the random number with the escrow key by the administrator.
8. The device of claim 7 , wherein the pair of points (P, ) is a pair of elliptic curve points.
9. The device of claim 7 , wherein one point of the pair of points (P, ) is obtained from an output of a one way function.
10. The device of claim 9 , wherein the one way function is a hash function.
11. The device of claim 9 , wherein the other point of the pair of points (P, ) is utilized as an input to the one way function.
12. The device of claim 11 , wherein the one point of the pair of points (P, ) is , and the other point of the pair of points (P, ) is P.
13. A non-transitory computer readable medium storing instructions which, when executed, cause a computing device to perform operations comprising:
establishing a pair of points (P, ) as respective inputs to an elliptic curve random number generator (ECRNG), wherein P=e , and e is a relationship between the pair of points (P, );
storing the relationship e as an escrow key with an administrator;
generating from the ECRNG a random number for use in cryptographic operations within a security domain;
using the random number in a cryptographic operation; and
logging an output of the ECRNG to reconstruct the random number with the escrow key by the administrator.
14. The non-transitory computer readable medium of claim 13 , wherein the pair of points (P, ) is a pair of elliptic curve points.
15. The non-transitory computer readable medium of claim 13 , wherein one point of the pair of points (P, ) is obtained from an output of a one way function.
16. The non-transitory computer readable medium of claim 15 , wherein the one way function is a hash function.
17. The non-transitory computer readable medium of claim 15 , wherein the other point of the pair of points (P, ) is utilized as an input to the one way function.
18. The non-transitory computer readable medium of claim 17 , wherein the one point of the pair of points (P, ) is , and the other point of the pair of points (P, ) is P.