Совершенные схемы разделения секрета и конечные универсальные алгебры

Предложен метод построения совершенных схем разделения секрета по конгруэнциям конечных универсальных алгебр, обобщающий известные способы синтеза линейных схем разделения секрета над конечными полями или коммутативными кольцами.Запропоновано метод побудови досконалих схем розділення секрету за конгруенціями скінчених універсальних алгебр, який узагальнює відомі способи синтезу лінійних схем розділення секрету над скінченими полями або комутативними кільцями.A method of constructing perfect secret sharing schemes which are obtained from congruences of finite universal algebras is provided. This method extends well-known constructions of linear secret sharing schemes over finite fields or commutative rings

Linear threshold multisecret sharing schemes

In a multisecret sharing scheme, several secret values are distributed among a set of n users, and each secret may have a differ- ent associated access structure. We consider here unconditionally secure schemes with multithreshold access structures. Namely, for every subset P of k users there is a secret key that can only be computed when at least t of them put together their secret information. Coalitions with at most w users with less than t of them in P cannot obtain any information about the secret associated to P. The main parameters to optimize are the length of the shares and the amount of random bits that are needed to set up the distribution of shares, both in relation to the length of the secret. In this paper, we provide lower bounds on this parameters. Moreover, we present an optimal construction for t = 2 and k = 3, and a construction that is valid for all w, t, k and n. The models presented use linear algebraic techniques.Peer ReviewedPostprint (author’s final draft