Production of cryptographic signatures

1. A method for producing a cryptographic signature on a message with a first key-share and second key-share, the method comprising:

generating a second authentication value encoding a nonce and a first authentication value, the first authentication value being produced from a user password;

encoding a message to produce a blinded message;

authenticating, with an authentication computer, the first authentication value using the nonce and a stored first authentication value to determine if the first authentication value encoded in the second authentication value is correct and, if so, encoding the blinded message using the second key-share to produce a partial signature; and

producing a signature on the message by encoding the partial signature and the message using the first key-share and an unblinding function for unblinding the blinded message in the partial signature.

2. The method as claimed in claim 1 , wherein the first authentication value encodes a secret value of the user computer and the predetermined user password, said secret value comprising the first key-share of a key shared between the user computer and the authentication computer.

3. The method as claimed in claim 2 , wherein the key comprises a sum of the first and second key-shares.

4. The method as claimed in claim 1 , wherein the first authentication value encodes a secret value and the user password, said secret value differing from the first key share.

5. The method as claimed in claim 1 , further comprising, requesting the nonce from the authentication computer prior to producing the second authentication value.

6. The method as claimed claim 1 , further comprising selecting a random value and using the random value in said encoding to produce the blinded message.

7. The method as claimed in claim 1 , wherein said signature comprises a BLS signature.

8. A method for producing a cryptographic signature on a message with a first key-share and second key-share, the method comprising:

generating a first authentication value from a user password;

generating a second authentication value encoding a nonce and the first authentication value;

encoding a message to produce a blinded message;

encoding the blinded message using the second key-share to produce a partial signature upon an authentication computer authenticating the first authentication value using the nonce and a stored first authentication value stored at the authentication computer to determine if the first authentication value encoded in the second authentication value is correct; and

producing a signature on the message by encoding the partial signature and the message using the first key-share and an unblinding function for unblinding the blinded message in the partial signature.

9. The method as claimed in claim 7 , wherein the first authentication value encodes a secret value and the user password, said secret value comprising the first key-share of a key shared with the authentication computer.

10. The method as claimed in claim 9 , wherein the key comprises a SUM of the first and second key-shares.

11. The method as claimed in claim 8 , wherein the first authentication value encodes a secret value and the user password, said secret value differing from the first key share.

12. The method as claimed in claim 8 , further comprising requesting the nonce from the authentication computer prior to producing the second authentication value.

13. The method as claimed in claim 8 , further comprising selecting a random value and using the random value in said encoding to produce the blinded message.

14. The method as claimed in claim 8 , wherein said signature comprises a BLS signature.

15. A method for generating a partial signature to produce a cryptographic signature on a message, the method comprising:

decoding a second authentication value using a nonce to reveal a received first authentication value;

authenticating the received first authentication value with a stored authentication value;

encoding a blinded message corresponding to a message using a second key-share to produce a partial signature; and producing, at a user computer, a signature on the message by encoding the partial signature and the message using a first key-share and an unblinding function for unblinding the blinded message in the partial signature.

16. The method as claimed in claim 15 , wherein the received first authentication value encodes a secret value of the user computer and a predetermined user password, said secret value comprising the first key-share of a key shared with the user computer.

17. The method as claimed in claim 16 , wherein the key comprises a sum of the first and second key-shares.

18. The method as claimed in claim 15 , wherein the received first authentication value encodes a secret value of the user computer and a predetermined user password, said secret value differing from the first key share and wherein the user computer stores the secret value.

19. The method as claimed in claim 15 , further comprising receiving a nonce request from the user computer and sending said nonce to the user computer.

20. The method as claimed in claim 15 , wherein the blinded message is encoded by a random value selected by the user computer.