New schemes for sharing points on an elliptic curve

A multiple secret sharing scheme can share a group of secrets in each sharing session; this scheme is deemed to be very useful in sharing important secrets. However, previously, no scheme on sharing points on an elliptic curve has been devised. In responding to the problem, this paper proposes a new (t,n)(t,n) multi-point sharing scheme using self-pairing on an elliptic curve. The security of the proposed scheme was examined. Towards the end of the study, the researchers concluded that the new scheme was computationally secure if at least n−t+1n−t+1 users in the scheme are honest, and if O(lgq)O(lgq) points at most are shared. Therefore, the threshold digital signature scheme on an elliptic curve can be designed and implemented easily.