Multilinear maps serve as a basis for a wide range of cryptographic applications. The first candidate construction of multilinear maps was proposed by Garg, Gentry, and Halevi in 2013, and soon afterwards, another construction was suggested by Coron, Lepoint, and Tibouchi (CLT13), which works over the integers. However, both of these were found to be insecure in the face of so-called zeroizing ...

Let h and g be polynomials of bounded Euclidean norm in the ring Z[X]/⟨X+1⟩. Given polynomial [h/g]q ∈ Zq[X]/⟨X+1⟩, the NTRU problem is to find a, b ∈ Z[X]/⟨X + 1⟩ with small Euclidean norm such that [a/b]q = [h/g]q. We propose an algorithm to solve the NTRU problem which runs in 2 2 q) time when ∥g∥, ∥h∥ and ∥g−1∥ are in some range. The main technique of our algorithm is to reduce a problem on...

Present constructions of indistinguishability obfuscation (iO) create obfuscated programs where the size of the obfuscated program is at least a factor of a security parameter larger than the size of the original program. In this work, we construct the first iO scheme that achieves only a constant multiplicative overhead (in fact, the constant is 2) in the size of the program. The security of o...

The design of a robust nonlinear H∞ static output feedback controller for parameter dependent polynomial systems is a hard problem. This paper presents a computational relaxation in form of an iterative design approach. The proposed controller guarantees the L2-gain of the mapping from exogenous input noise to the controlled output is less than or equal to a prescribed value. The sufficient con...

Results on polynomial fixed order controller design are extended to SISO gainscheduling with guaranteed stability andH∞ performance over the whole scheduling parameter range. Salient features of the approach are (a) the use of polynomials as modeling objects; (b) the use of flexible LMI conditions allowing polynomial dependence of the open-loop system and controller transfer functions in the sc...

the effect of partial slip and temperature dependent fluid properties on the mhd mixed convection flow from a heated, non-linearly stretching surface in the presence of radiation and non-uniform internal heat generation/absorption is investigated. the velocity of the stretching surface was assumed to vary according to power-law form. thermal transport is analyzed for two types of non-isothermal...