Production of cryptographic signatures

A method for producing a cryptographic signature on a message, under a key, at a user computer of a data processing system wherein the key is shared between the user computer, which stores a first key-share, and an authentication computer of said system, the authentication computer storing a second key-share and a first authentication value which encodes a secret value of the user computer and a predetermined user password, the method comprising:

• at the user computer, in response to provision of the message and input of said user password, encoding the message to produce a blinded message, producing said first authentication value from the user password and said secret value and producing a second authentication value which encodes the first authentication value and a nonce, and sending the second authentication value and the blinded message to the authentication computer;
• at the authentication computer, in response to receipt of the blinded message and the second authentication value, using said nonce and the first authentication value stored in the authentication computer 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 sending the partial signature to the user computer;
• and
• at the user computer, producing a signature on the message under said key 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.