Secret Sharing Homomorphisms: Keeping Shares of a Secret Secret

In 1979, Blackley and Shamir independently proposed schemes by which a secret can be divided into many shares which can be distributed to mutually suspicious agents. This paper describes a homomorphism property attained by these and several other secret sharing schemes which allows multiple secrets to be combined by direct computation on shares. This property reduces the need for trust among agents and allows secret sharing to be applied to many new problems. One application described gives a method of verifiable secret sharing which is much simpler and more efficient than previous schemes. A second application is described which gives a fault-tolerant method of holding verifiable secret-ballot elections.