Secure Computation of Shared Secrets and Its Applications
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
There has been renewed attention to threshold signature in recent years as the threshold version of the ECDSA and SM2 Elliptic Curve Cryptographic Algorithm (SM2) could be used in Bitcoin as an underlying digital signature scheme to protect users’ private keys that guarantees transactions. A (t, n) threshold signature scheme means in a set of n parties, at least t players can exercise the right of generating signatures on behalf of the group, and any less than t of the players’ cooperation cannot generate a valid signature for the message nor obtain any information about the shared secret key. Thus, it is meaningful to construct a purely (t, n) threshold SM2 signature scheme (purely (t, n) means in the whole signature scheme, the threshold value is fixed to t). We propose a robust multiplication protocol of shared secrets to resolve the “multiplication of shared secrets” problem in existing threshold signature schemes. Using the proposed multiplication protocol, we improve the existing secret reciprocal computation protocol and show how to get a purely (t, n) threshold SM2 signature scheme.
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