We propose an optimization and generalization of OT extension of Ishai et al. of Crypto 2003. For computational security parameter k, our OT extension for short secrets offers O(log k) factor performance improvement in communication and computation, compared to prior work. In concrete terms, for today’s security parameters, this means approx. factor 2-3 improvement. This results in correspondin...

An extension of the Bojanić–Stanojević type inequality [1] is made by considering the r-th derivate of the Dirichlet kernel D k instead of Dk. Namely, the following inequality is proved ∥∥∥∥ n ∑ k=1 αkD (r) k (x) ∥∥∥∥ 1 ≤Mpn ( 1 n n ∑ k=1 |αk| )1/p , where ‖ · ‖1 is the L-norm, {αk} is a sequence of real numbers, 1 < p ≤ 2, r = 0, 1, 2, . . . and Mp is an absolute constant dependent only on p. ...

Let H be a connected graph and G be a supergraph of H . It is trivial that for any k-flow (D, f ) of G, the restriction of (D, f ) on the edge subset E(G/H) is a k-flow of the contracted graph G/H . However, the other direction of the question is neither trivial nor straightforward at all: for any k-flow (D′, f ′) of the contracted graph G/H , whether or not the supergraph G admits a k-flow (D,...

Given a valuation v on field K, an extension v¯ to algebraic closure K¯ and w K(X). In this paper, we study common extensions w¯ of both the K¯(X). We describe set valuations using last key polynomial for its roots.

We study the fermionic extension of the E10/K(E10) coset model and its relation to eleven-dimensional supergravity. Finite-dimensional spinor representations of the compact subgroup K(E10) of E10(R) are studied and the supergravity equations are rewritten using the resulting algebraic variables. The canonical bosonic and fermionic constraints are also analysed in this way, and the compatibility...

The GHS attack is known to solve discrete logarithm problems (DLP) in the Jacobian of a curve C0 defined over the d degree extension field kd of k := Fq by mapping it to the DLP in the Jacobian of a covering curve C of C0 over k. Recently, classifications for all elliptic curves and hyperelliptic curves C0/kd of genus 2,3 which possess (2, ..., 2)-covering C/k of P were shown under an isogeny c...

We propose an optimization and generalization of OT extension of Ishai et al. of Crypto 2003. For computational security parameter k, our OT extension for short secrets o↵ers O(log k) factor performance improvement in communication and computation, compared to prior work. In concrete terms, for today’s security parameters, this means approx. factor 2-3 improvement. This results in corresponding...

Lemma 2.1. Let F be a field, let E = F (α) be a simple extension of F , where α is algebraic over F and f = irr(α, F, x), let ψ : F → K be a homomorphism from F to a field K, and let L be an extension of K. If β ∈ L is a root of ψ(f), then there is a unique extension of ψ to a homomorphism φ : E → L such that φ(α) = β. Hence there is a bijection from the set of homomorphisms φ : E → L such that...

In Part I of this paper, we introduced a method of making two isomorphic intervals of a bounded lattice congruence equivalent. In this paper, we make one interval dominate another one. Let L be a bounded lattice, let [a, b] and [c, d] be intervals of L, and let φ be a homomorphism of [a, b] onto [c, d]. We construct a bounded (convex) extension K of L such that a congruence Θ of L has an extens...

Close reduction by extension-block K-wire fixation for acute mallet fracture is a relatively novel mode of treatment which is based on two sound orthopedic principles - stable arc splinting and early protected motion. Distal interphalangeal joint splinting is still the technique commonly used for mallet fractures with significant morbidity and only moderate functional outcome. We have demonstra...