The arrival of indistinguishability obfuscation (iO) has transformed the cryptographic landscape by enabling several security goals that were previously beyond our reach. Consequently, one of the pressing goals currently is to construct iO from well-studied standard cryptographic assumptions. In this work, we make progress in this direction by presenting a reduction from iO to a natural form of...

An n-ary operation q : Σn → Σ is called an n-ary quasigroup of order |Σ| if in x0 = q(x1, . . . , xn) knowledge of any n elements of x0, . . . , xn uniquely specifies the remaining one. An n-ary quasigroup q is permutably reducible if q(x1, . . . , xn) = p(r(xσ(1), . . . , xσ(k)), xσ(k+1), . . . , xσ(n)) where p and r are (n− k + 1)-ary and k-ary quasigroups, σ is a permutation, and 1 < k < n. ...

The main tools in the theory of n-ary hyperstructures are the fundamental relations. The fundamental relation on an n-ary hypersemigroup is defined as the smallest equivalence relation so that the quotient would be the n-ary semigroup. In this paper we study neutral elements in n-ary hypersemigroups and introduce a new strongly compatible equivalence relation on an n-ary hypersemigroup so that ...

This paper introduces new type of m-ary systolic arrays called m-ary reversible systolic arrays which extends the new concept of two-valued reversible systolic arrays that was introduced in the first part of my article. The m-ary quantum systolic architectures’ computations of the new type of systolic arrays are also introduced. The new m-ary systolic arrays maintain the high level of regularit...

A parallel algorithm for generating t-ary tree sequences in reverse B-order is presented. The algorithm generates t-ary trees by 0-1 sequences, and each 0-1 sequences is generated in constant average time O(1). The algorithm is executed on a CREW SM SIMD model, and is adaptive and cost-optimal. Prior to the discussion of the parallel algorithm a new sequential generation with O(1) average time ...

This paper focuses on multi-ary α-semantic resolution automated reasoning method based on multi-ary α-resolution principle for lattice-valued propositional logic LP(X) with truth-value in lattice implication algebras. The definitions of the multi-ary α-semantic resolution and multi-ary α-semantic resolution deduction in lattice-valued propositional logic LP(X) are given, respectively, and the s...

n-ary transit functions are introduced as a generalization of binary (2-ary) transit functions. We show that they can be associated with convexities in natural way and discuss the Steiner convexity as a natural n-ary generalization of geodesicaly convexity. Furthermore, we generalize the betweenness axioms to n-ary transit functions and discuss the connectivity conditions for underlying hypergr...

a parallel algorithm for generating t-ary tree sequences in reverse b-order is presented. the algorithm generates t-ary trees by 0-1 sequences, and each 0-1 sequences is generated in constant average time o(1). the algorithm is executed on a crew sm simd model, and is adaptive and cost-optimal. prior to the discussion of the parallel algorithm a new sequential generation with o(1) average time ...

We classify a type of language called a reflectable language. We then develop a generic algorithm that can be used to list all strings of length n for any reflectable language in Gray code order. The algorithm generalizes Gray code algorithms developed independently for k-ary strings, restricted growth strings, and k-ary trees, as each of these objects can be represented by a reflectable langua...