A new multiple secrets sharing scheme

based on the intractability of the discrete logarithm (DL) and the RSA encryption algorithm is presented

in which the participants' shadows remain secret and can be reused

even if all subshadows are made public.Meanwhile

by using a zero-knowledge proof protocol

the validity verification of shadow and subshadow is also provided to prevent both dealer cheating and other participant cheating

and any freely given secrets without pre-computation by dealer can be reconstructed.The scheme can be applied to many areas such as conference key distribution

secure multi-part-computation

threshold signature etc.