Abstract
Verifiable (t, n) threshold ECSA (elliptic curve signature verification) signature algorithm and verifiable (t, n) threshold ECES (elliptic curve encrypt scheme) encryption algorithm are presented according to a secret sharing scheme for elliptic curve using Lagrange polynomial interpolation as access structure. A group of n players share an ECC (elliptic curve cryptosystem) secret key. Every qualified subset of the group, including t out of n players, could recover the secret key, so that they can sign and decrypt as well as the whole group, while no subset of t-1 players can accomplish it. The algorithms are perfect and secure verifiable secret shared schemes and their complexity is less than the same schemes based on DLP.
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