Verifiable threshold cryptosystems based on elliptic curve

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.