How to (Really) Share a Secret

Abstract

JntroductionIn information based systems, the integrity of the information (from unauthorized scrutiny or disclosure, manipulation or alteration, forgery, false dating, etc.) is commonly provided for by requiring operation(s) on the information that one or more of the participants, who know some private piece(s) of information not known to all of the other participants, can carry out but which (probably) can't be carried out by anyone who doesn't know the private information. Encryption/decryption in a single key cryptoalgorithm is a paradigm of such an operation, with the key being the private (secret) piece of information. Although it is implicit, it is almost never stated explicitly that in a single-key cryptographic communications link, the transmitter and the receiver must unconditionally trust each other since either can do anything that the other can. a system are trustworthy, so long as there exists at least one identified unconditionally trustworthy element (individual or device), it is generally possible to devise protocols to transfer trust from this element to other elements of Unknown trustworthiness to make it possible for users to trust the integrity of the information in the system even though they may not trust all of the elements. A paradigm for such a protocol is the cryptographic key distribution system described in ANSI X9.17 which makes it possible for Even if it can't be assumed that all of the elements in S. Goldwasser (Ed.): Advances in Cryptology

Key-Policy Attribute-Based Encryption for Boolean Circuits from Bilinear Maps

“…We will show in this section that the Boolean circuits representing multilevel access structures [12,14] fulfill this property. For a compact representation of multilevel access structures we need Boolean circuits with threshold gates (as in [7]).…”

Some Ideal Secret Sharing Schemes

“…Simmons [5] has described an access structure that arises in a practical application of secret sharing. A multileueI access structure is one in which each participant is assigned a level which is a positive integer and the access structure consists of those subsets which contain at least r participants all of level at most T .…”

“…For example, if the secret is a random element of GF(q), and all shares are elements of GF(q), then the information rate is 1. Simmons [5] defined a related notion. He called a secret sharing scheme eztrinsic if the set T of possible shares is the same for all participants.…”

Weightedness and structural characterization of hierarchical simple games

“…The access structure in secret a sharing scheme (e.g., Simmons, 1990;Stinson, 1992) can also be modeled by a simple game, but in this theory a different approach to defining seniority is often used. To this end Simmons (1990) introduced the concept of a hierarchical access structure.…”

“…To this end Simmons (1990) introduced the concept of a hierarchical access structure. Such an access structure stipulates that agents are partitioned into m levels, and a sequence of thresholds k 1 < k 2 < .…”