Abstract: A method for providing a digital signature to a message, M, in accordance with a digital signature algorithm (DSA) or an elliptic curve digital signature algorithm (ECDSA) is disclosed. A secret key, x, is generated as a random secret sharing [x] among at least two parties, such as among at least three parties. Random secret sharings, [a] and [k], are generated among the at least two parties and [w]=[a][k], R=gk and W=Ra are computed and their correctness verified. [w] is verified by checking whether or not gw=W. The message, M, is signed by generating a sharing, [s], among the at least two parties, using at least M, [w], R and [x].

Abstract: A method for restoring a distributed secret key from a backup storage such that an original secret key is generated and distributed among two or more servers. A first server creates a backup containing at least the share of the original secret key which is held by the first server. The servers refresh the original secret key at least once. During each refresh the servers generate a refreshed distributed secret key and a distributed difference between the previous secret key and the refreshed secret key. The first server restores its share of the original secret key from the backup and requests the accumulated secret version of its share of the difference from the other servers and restores its share of the latest refreshed secret key from the received accumulated secret version and the restored share of the original secret key.

Abstract: A method for providing a digital signature to a message, M, in accordance with a digital signature algorithm (DSA) or an elliptic curve digital signature algorithm (ECDSA) is disclosed. A secret key, x, is generated as a random secret sharing [x] among at least two parties, such as among at least three parties. Random secret sharings, [a] and [k], are generated among the at least two parties and [w]=[a][k], R=gk and W=Ra are computed and their correctness verified. [w] is verified by checking whether or not gw=W. The message, M, is signed by generating a sharing, [s], among the at least two parties, using at least M, [w], R and [x].