Motivated by recent constructions and barriers in secret sharing, we study multislice functions. These functions, parametrized by a width parameter $w$, take the value 0 on inputs of Hamming weight below a base value $k$, 1 on inputs of weight above $k+w$, and are monotone in between.
We first investigate ... more >>>

A secret-sharing scheme allows a dealer to distribute a secret $s$ among $n$ parties such that only predefined “authorized” sets of parties can reconstruct the secret, and all other “unauthorized” sets learn nothing about $s$. Families of authorized sets are called access structures, and a scheme is called linear if ... more >>>

A secret-sharing scheme allows the distribution of a secret $s$ among $n$ parties, such that only certain predefined “authorized” sets of parties can reconstruct the secret, while all other “unauthorized” sets learn nothing about $s$. The collection of authorized/unauthorized sets is defined by a monotone function $f: \{0,1\}^n \rightarrow \{0,1\}$. ... more >>>

A major open problem in information-theoretic cryptography is to obtain a super-polynomial lower bound for the communication complexity of basic cryptographic tasks. This question is wide open even for very powerful non-interactive primitives such as private information retrieval (or locally-decodable codes), general secret sharing schemes, conditional disclosure of secrets, and ... more >>>

Threshold cryptography is typically based on the idea of secret-sharing a private-key $s\in F$ ``in the exponent'' of some cryptographic group $G$, or more generally, encoding $s$ in some linearly homomorphic domain. In each invocation of the threshold system (e.g., for signing or decrypting) an ``encoding'' of the secret is ... more >>>

A secret-sharing scheme allows to distribute a secret $s$ among $n$ parties such that only some predefined ``authorized'' sets of parties can reconstruct the secret, and all other ``unauthorized'' sets learn nothing about $s$. For over 30 years, it was known that any (monotone) collection of authorized sets can be ... more >>>

A secret-sharing scheme allows to distribute a secret $s$ among $n$ parties such that only some predefined ``authorized'' sets of parties can reconstruct the secret, and all other ``unauthorized'' sets learn nothing about $s$.
The collection of authorized/unauthorized sets can be captured by a monotone function $f:\{0,1\}^n\rightarrow \{0,1\}$.
more >>>

A secret-sharing scheme allows to distribute a secret $s$ among $n$ parties such that only some predefined ``authorized'' sets of parties can reconstruct the secret, and all other ``unauthorized'' sets learn nothing about $s$. The collection of authorized sets is called the access structure. For over 30 years, it was ... more >>>