System and method for deterministic signing of a message using a multi-party computation (MPC) process

A method for signing a message, comprising:

• performing a first Multi-Party Computation (MPC) process by multiple parties to compute a pseudorandom function, an input of the first MPC process comprises shares of a private signing key, each share is held by a party of the multiple parties, wherein the message to be signed is an input value to the pseudorandom function,
• wherein an output of the first MPC process to compute the pseudorandom function comprises producing multiple pairs of shares of the output of the pseudorandom function, each party of the multiple parties holding a pair of shares, and
• wherein each pair of the multiple pairs comprises a first value used for the MPC signing process and a second verifying value used for verifying correctness of the values provided by the multiple parties for the MPC signing process;
• verifying correctness of the shares of the private signing key inputted by the multiple parties to the MPC signing process using the verifying values,
• wherein verifying correctness of the shares of the private signing key comprises performing an arithmetic manipulation on the verifying values, and
• wherein each party of the multiple parties provides one of the values in the pair of shares based on a random mechanism executed multiple times, to verify that at least once the value used for the MPC signing process is provided by the multiple parties and at least once the second verifying value is provided by the multiple parties;
• and
• computing the signature on the message by performing an MPC signing protocol on the message, wherein the MPC signing protocol receives as input shares of the output of the pseudorandom function from the multiple parties for the signature randomness, and the message to be signed.

A method for signing a message, comprising:

• performing a first Multi-Party Computation (MPC) process by multiple parties to compute a pseudorandom function, an input of the first MPC process comprises shares of a private signing key, each share is held by a party of the multiple parties,
• wherein the message to be signed is an input value to the pseudorandom function,
• wherein an output of the first MPC process to compute the pseudorandom function comprises producing multiple pairs of shares of the output of the pseudorandom function, each party of the multiple parties holding a pair of shares, and
• wherein each pair of the multiple pairs comprises a first value used for the MPC signing process and a second verifying value used for verifying correctness of the values provided by the multiple parties for the MPC signing process;
• verifying correctness of the shares of the private signing key inputted by the multiple parties to the MPC signing process using the verifying values, wherein the values provided by the multiple parties to the MPC signing process are used after verifying correctness of the shares of the private signing key, wherein each party of the multiple parties provides one of the values in the pair of shares based on a random mechanism executed multiple times, to verify that at least once the value used for the MPC signing process is provided by the multiple parties and at least once the second verifying value is provided by the multiple parties;
• and
• computing the signature on the message by performing an MPC signing protocol on the message, wherein the MPC signing protocol receives as input shares of the output of the pseudorandom function from the multiple parties for the signature randomness, and the message to be signed.