Windowed backward key rotation

1. A method of windowed backward key generation, comprising:

providing, by a computer system, information to a user that allows determining a limited number of previous keys in a series of keys from a later key in the series;

generating, by the computer system, a key in the series, based at least in part on said information provided to said user;

providing, by the computer system, said generated key in the series to the user to allow a determination of

at least one key in the limited number of previous keys in the series by applying said information to said generated key in the series.

2. The method of claim 1 , wherein providing the information comprises providing a key rotation element that is forward rotatable by said user but is not backward rotatable.

3. The method of claim 1 , wherein providing the information comprises providing to the user a key rotation exponent that is used to determine a previous key in the series from a later key in the series by exponentiating said later key by said key rotation exponent.

4. The method of claim 2 , further comprising:

generating, from the key rotation element, a new key rotation element;

generating a new key based, in part, on said new key rotation element; and

distributing said new key to non-revoked users.

5. The method of claim 1 , wherein providing the information comprises providing a secret share and a key rotation catalyst to said user, wherein said secret share and said key rotation catalyst allow said user to generate a next key in the series provided sufficient public information is available.

6. The method of claim 5 , further comprising:

publishing at least one public share, wherein the next key in the series is determinable based on the key rotation catalyst, the secret share, and the at least one public share.

7. The method of claim 5 , further comprising revoking a user by publishing a version of the revoked user's secret share.

8. A method of windowed backward key rotation, comprising:

providing, by a computer system, to a user a key rotation element and a key (K i ), wherein later versions of the key rotation element are determinable using a predetermined function but previous versions of the key rotation element are not determinable using the predetermined function;

generating, by the computer system, a later version of the key (K i+n ) based on a later version of the key rotation element, wherein “n” is a positive integer;

providing, by the computer system, to the user the later version of the key (K i+n ) to allow a determination of

a particular version of the key from (K i -K i+n−1 ), inclusive, by applying one of the later versions of the key rotation element to a given version of the key from (K i+1 -K i+n ), inclusive, wherein the given version of the key is a later version than the particular version of the key.

9. The method of claim 8 , further comprising:

determining a later version of said key rotation element from said provided key rotation element.

10. The method of claim 9 , wherein

determining the version of the key K i+n−1 is performed by applying the one of the later versions of the key rotation element to the version of the key K i+n .

11. The method of claim 8 , further comprising:

generating a new key rotation element;

generating a new key based, in part, on said new key rotation element; and

distributing said new key to non-revoked users.

12. The method of claim 8 , wherein the predetermined function is a one-way hash function.

13. A method of windowed backward file key generation, comprising:

generating, by a computer system, a file key;

generating, by the computer system, a key rotation exponent, wherein said key rotation exponent allows previous versions of the file key to be determined, wherein a first previous version of the file key is computable from the generated file key and the generated key rotation exponent, and a second previous version of the file key earlier than the first version is computable from the first previous version of the key file and a previous version of the key rotation exponent.

14. The method of claim 13 , further comprising:

joining a new user by distributing said generated file key and said generated key rotation exponent to said new user.

15. The method of claim 13 , further comprising:

generating a new key rotation exponent;

generating a new file key based, in part, on said new key rotation exponent; and

distributing said new file key to non-revoked users.

16. The method of claim 13 , further comprising:

generating a key rotation catalyst; and

providing a secret share and said key rotation catalyst, wherein said secret share and said key rotation catalyst allow generation of a new version of the file key provided sufficient public information is available.

17. The method of claim 16 , further comprising:

publishing a public share, wherein users are able to determine a new version of the file key using their own secret shares, the public shares, the key rotation catalyst, and a previous file key.

18. The method of claim 16 , further comprising:

generating a new key rotation catalyst;

publishing said new key rotation catalyst;

generating a new file key based, in part, on said new key rotation catalyst; and

publishing a revoked user's private share.