Key-dependent message (KDM) security identity-based encryption (IBE) schemes aim to solve the risks caused by dependency between plaintext and secret keys in traditional IBE schemes. However, current KDM-IBE are only secure with respect affine functions, which limits their level when a is derived from evaluation of polynomial function using key. To address this issue, study, we propose novel ap...

We show that for any constant d ∈ N, there exists a public-key encryption scheme that can securely encrypt any function f of its own secret-key, assuming f can be expressed as a polynomial of total degree-d. Such a scheme is said to be key-dependent message (KDM) secure w.r.t. degree-d polynomials. We also show that there exists a public-key encryption scheme that is KDM secure w.r.t. all Turin...

‎let $v$ be a vector space over a field $f$ of characteristic $pgeq 0$ and let‎ ‎$t$ be a regular subgroup of the affine group $agl(v)$‎. ‎in the finite dimensional case we show that‎, ‎if $t$ is abelian or $p>0$‎, ‎then $t$ is unipotent‎. ‎for $t$ abelian‎, ‎pushing forward some ideas used in [a‎. ‎caranti‎, ‎f‎. ‎dalla volta and m‎. ‎sala‎, ‎abelian regular subgroups of the affine group and r...

Explicit expressions are presented for general branching functions for cosets of affine Lie algebras ĝ with respect to subalgebras ĝ′ for the cases where the corresponding finite dimensional algebras g and g′ are such that g is simple and g′ is either simple or sums of u(1) terms. A special case of the latter yields the string functions. Our derivation is purely algebraical and has its origin i...

We study some classes of generalized a¢ ne functions, using a generalized di¤erential. We study some properties and characterizations of these classes and we devise some characterizations of solution sets of optimization problems involving such functions or functions of related classes. Key words: colinvex, colin…ne, generalized di¤erential, optimization problem, protoconvex function, pseudocon...

In this paper we derive two bosonic (alternating sign) formulas for branching functions for general affine Kac-Moody Lie algebra g. Both formulas are given in terms of Weyl group and string functions of g.

Affine-invariant properties are an abstract class of properties that generalize some central algebraic ones, such as linearity and low-degree-ness, that have been studied extensively in the context of property testing. Affine invariant properties consider functions mapping a big field Fqn to the subfield Fq and include all properties that form an Fq-vector space and are invariant under affine t...