  Secret sharing schemes based on the idea of hidden multipliers in encryption
are proposed. As a platform, one can use both multiplicative groups of finite
fields and groups of invertible elements of commutative rings, in particular,
multiplicative groups of residue rings. We propose two versions of the secret
sharing scheme and a version of ($k,n$)-thrested scheme. For a given $n$, the
dealer can choose any $k.$ The main feature of the proposed schemes is that the
shares of secrets are distributed once and can be used multiple times. This
property distinguishes the proposed schemes from the secret sharing schemes
known in the literature. The proposed schemes are semantically secure. The same
message can be transmitted in different forms. From the transferred secret $c$
it is impossible to determine which of the two given secrets $m_1$ or $m_2$ was
transferred. For concreteness, we give some numerical examples.
