Secure communication system

1. A computer-implemented method of rendering data transmitted via a communications system accessible solely to a predefined group of users of the communications system, comprising:

a) making available solely to each user of said group

i) a user secret s i , wherein s i equals f 1 (R, ui), and f 1 is a first one-way function operating on a root key R and a unique public identifier for that user (ui); and

ii) a public identifier (uj) for each other user in said group;

b) wherein a deriving user, employing a computer,

i) derives a group key by operating a second one-way function (f 2 ) on parameters comprising:

a) the deriving user's secret s i ; and

b) the public identifier(s) for each of said one or more other user of said group (u 1 , u 2 , . . . u j−1 , u j+1 , . . . , un- 1 , u n );

f 2 being selected so that:

f 2 ( f 1 ( R,u 1 ), u 2 , . . . ,u n )= f 2 ( f 1 ( R,u 2 ), u 1 ,u 3 ,u 4 . . . ,u n )= . . . = f 2 ( f 1 ( R,u n ), u 1 ,u 2 ,u 4 . . . ,u n −1);

and

ii) encrypts said data using the group key as input to an encryption algorithm; and

c) transferring said encrypted data to each other user in said group via said communications system.

2. A method as claimed in claim 1 , further comprising changing the composition of the group authorized to access the data, by carrying out steps (b) to (d) in respect of the users of the changed group.

3. A method as claimed in claim 1 , in which the root key is held at a remote central facility.

4. A method as claimed in claim 1 , in which the encrypted data is tagged with the public user identities of the users of the group.

5. A method as claimed in claim 1 , in which the parameters on which the first one-way function operates include a parameter indicating a validity period for the user secret.

6. A method as claimed in claim 1 , in which the parameters on which the second one-way function operates include a random or pseudorandom element.

7. A method as claimed in claim 1 , in which the parameters on which the second one-way function operates include parameters indicating the identities of a plurality of distribution authorities, each distribution authority having calculated the secret identities of a different portion of the users in the group.

8. A method as claimed in claim 1 , comprising the steps:

(i) receiving a second user secret, the second user secret having been created by operating the first one-way function on parameters comprising a second root key and a second public identifier for the user;

(ii) receiving a second public identifier for each of the other users in the group;

(iii) obtaining the group key by operating the second one-way function on parameters comprising the user secret and the second user secret and the public identifiers and the second public identifiers, for the other users in the group.

9. A method as claimed in claim 8 , in which the user secret and the public identifier are received from a first distribution authority and the second user secret and the second public identifier are received from a second, different, distribution authority.

10. A method as claimed in claim 8 , in which a third one-way function is used to calculate a derived user secret, by operation on the user secret and the second user secret, and that the group key is calculated by operating the second one-way function on parameters including the derived user secret.

11. A method as claimed in claim 10 , in which a fourth one-way function is used to calculate a derived user identity, by operation on the public user identity and the second public user identity, and that the group key is calculated by operating the second one-way function on parameters including the derived user identity.

12. A method as claimed in claim 1 , in which each user in the group is provided with the user secret via a discrete data carrying object comprising one of: CD-ROM, DVD, USB stick, or a cryptographic token.

13. A method as claimed in claim 1 , in which the one-way functions are commutative one-way function.

14. A method as claimed in claim 13 , in which solution of the functions is NP-hard.

15. A method as claimed in claim 1 , in which the method is a method of authenticating users.

16. A computer program product configured to perform the method in claim 1 .

17. A communications system including apparatus adapted to perform the method in claim 1 .

18. A computer-implemented method of decrypting data accessible only by a predefined group of users, the method comprising making available solely to a user of said group who has received encrypted data via a communications system from another user of said group:

(a) a user secret s i =ƒ l (R, u i ), the user secret having been created by operating a first one-way function ƒ 1 on parameters comprising a root key R and a public identifier u i for the user;

(b) a public identifier u j for each of the other users in the group;

(c) wherein a decrypting user, employing a computer, derives a group key by operating a second one-way function ƒ 2 on parameters comprising the decrypting user's secret s i and the public identifiers for the other users in the group u 1 , u 2 , . . . , u j−1 , u j+1 . . . u n−1 , u n , wherein said second one-way function ƒ 2 and said first one-way function ƒ 1 satisfy:

ƒ 2 (ƒ 1 ( R,u 1 ) u 2 , . . . ,u n )=ƒ 2 (ƒ 1 ( R,u 2 ), u 1 ,u 3 ,u 4 . . . ,u n )= . . . =ƒ 2 (ƒ 1 ( R,u n ), u 1 u 2 , . . . ,u n−1 ); and

 and decrypts the encrypted data using the group key as input to a decription algorithm.

19. A method as claimed in claim 18 , in which the root key is held at a remote central facility.

20. A method as claimed in claim 18 , in which the encrypted data is tagged with the public user identities of the users of the group.

21. A method as claimed in claim 18 , in which the parameters on which the first one-way function operates include a parameter indicating a validity period for the user secret.

22. A method as claimed in claim 18 , in which the parameters on which the second one-way function operates include a random or pseudorandom element.

23. A method as claimed in claim 18 , in which the parameters on which the second one-way function operates include parameters indicating the identities of a plurality of distribution authorities, each distribution authority having calculated the secret identities of a different portion of the users in the group.

24. A method as claimed in claim 18 , comprising the steps

(iv) receiving a second user secret, the second user secret having been created by operating the first one-way function on parameters comprising a second root key and a second public identifier for the user;

(v) receiving a second public identifier for each of the other users in the group;

(vi) obtaining the group key by operating the second one-way function on parameters comprising the user secret and the second user secret and the public identifiers and the second public identifiers, for the other users in the group.

25. A method as claimed in claim 24 , in which the user secret and the public identifier are received from a first distribution authority and the second user secret and the second public identifier are received from a second, different, distribution authority.

26. A method as claimed in claim 24 , in which a third one-way function is used to calculate a derived user secret, by operation on the user secret and the second user secret, and that the group key is calculated by operating the second one-way function on parameters including the derived user secret.

27. A method as claimed in claim 26 , in which a fourth one-way function is used to calculate a derived user identity, by operation on the public user identity and the second public user identity, and that the group key is calculated by operating the second one-way function on parameters including the derived user identity.

28. A method as claimed in claim 18 , in which each user in the group is provided with the user secret via a discrete data carrying object comprising one of: CD-ROM, DVD, USB stick, or a cryptographic token.

29. A method as claimed in claim 18 , in which the one-way functions are commutative one-way functions.

30. A method as claimed in claim 29 , in which solution of the functions is NP-hard.

31. A method as claimed in claim 18 , in which the method is a method of authenticating users.

32. A computer program product configured to perform the method in claim 18 .

33. A communications system including apparatus adapted to perform the method in claim 18 .