Starting from a general operator representation in the time-frequency domain, this paper addresses the problem of approximating linear operators by operators that are diagonal or band-diagonal with respect to Gabor frames. A characterization of operators that can be realized as Gabor multipliers is given and necessary conditions for the existence of (Hilbert-Schmidt) optimal Gabor multiplier ap...

This article is concerned with the question of whether Marcinkiewicz multipliers on R2n give rise to bilinear multipliers on R×R. We show that this is not always the case. Moreover, we find necessary and sufficient conditions for such bilinear multipliers to be bounded. These conditions in particular imply that a slight logarithmic modification of the Marcinkiewicz condition gives multipliers f...

This paper presents a system for the automatic generation of Galois-field (GF) arithmetic circuits, named the GF Arithmetic Module Generator (GF-AMG). The proposed system employs a graph-based circuit description called the GF Arithmetic Circuit Graph (GF-ACG). First, we present an extension of the GF-ACG to handle GF(pm) (p ≥ 3) arithmetic circuits, which can be efficiently implemented by mult...

Multiplication is the dominant operation for many applications implemented on field-programmable gate arrays (FPGAs). Although most current FPGA families have embedded hard multipliers, soft multipliers using lookup tables (LUTs) in the logic fabric remain important. This paper presents a novel two-operand addition circuit (patent pending) that combines radix-4 partial-product generation with a...

This paper proposes novel algorithms for computing doublesize modular multiplications with few modulus-dependent precomputations. Low-end devices such as smartcards are usually equipped with hardware Montgomery multipliers. However, due to progresses of mathematical attacks, security institutions such as NIST have steadily demanded longer bit-lengths for public-key cryptography, making the mult...

In the article, we find new dilatation results on non-commutative $$L^p$$ spaces. We prove that any self-adjoint, unital, positive measurable Schur multiplier some $$B(L^2(\Sigma ))$$ admits, for all $$1\leqslant p<\infty $$ , an invertible isometric dilation -space. obtain a similar result completely Fourier VN(G), when G is unimodular locally compact group. Furthermore, establish multivariabl...

This Paper presents an efficient implementation of high speed multiplier using the shift and add method, Radix_2, Radix_4 modified Booth multiplier algorithm. In This paper we compare the working of the three multipliers by implementing each of them separately in FIR filter. The parallel multipliers like radix2 and radix4 modified booth multiplier does the computations using lesser adders and l...

This paper propose an efficient algorithm for multipliers modulo . To achieve high speed, the Wallace tree is adopted for the multipliers. The proposed Wallace tree multipliers exhibit much more resular structure than binary Wallace tree cultipliers. Comparison with a previous counterpart shows favorable to our multiplier in both speed and hardware..

We present a novel approach for computing 2n-bit Montgomery multiplications with n-bit hardware Montgomery multipliers. Smartcards are usually equipped with such hardware Montgomery multipliers; however, due to progresses in factoring algorithms, the recommended bit length of public-key schemes such as RSA is steadily increasing, making the hardware quickly obsolete. Thanks to our doublesize te...