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Faster DoubleSize Modular Multiplication from Euclidean Multipliers
, 2003
"... A novel technique for computing a 2nbit modular multiplication using nbit arithmetic was introduced at CHES 2002 by Fischer and Seifert. Their technique makes use of an Euclidean division based instruction returning not only the remainder but also the integer quotient resulting from a modular ..."
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A novel technique for computing a 2nbit modular multiplication using nbit arithmetic was introduced at CHES 2002 by Fischer and Seifert. Their technique makes use of an Euclidean division based instruction returning not only the remainder but also the integer quotient resulting from a modular
Faster interleaved modular multiplication based on Barrett and Montgomery reduction methods
 1715–1721, 2010, [Online] Available: http://dx.doi.org/10.1109/TC.2010.93
"... IEEE Abstract—This paper proposes two improved interleaved modular multiplication algorithms based on Barrett and Montgomery modular reduction. The algorithms are simple and especially suitable for hardware implementations. Four large sets of moduli for which the proposed methods apply are given and ..."
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and analyzed from a security point of view. By considering stateoftheart attacks on publickey cryptosystems, we show that the proposed sets are safe to use, in practice, for both elliptic curve cryptography and RSA cryptosystems. We propose a hardware architecture for the modular multiplier that is based
Low Complexity and Hardwarefriendly Spectral Modular Multiplication
"... Abstract—The SchönhageStrassen Algorithm (SSA) is an asymptotically fast multiplication algorithm with the complexity of O(l log l log log l) where l is the operand size. It outperforms other multiplication algorithms when l is large enough. One possible usage of such long integer multiplication is ..."
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is for cryptography. Innovated from SSA, the Interleaved Spectral Montgomery Modular Multiplication (ISM 3) algorithm is proposed to accelerate the modular multiplication. ISM 3 algorithm primarily interleaves the Montgomery modular multiplication algorithm between time and spectral (frequency) domain. We show
A GEMM interface and implementation on NVIDIA GPUs for multiple small matrices
"... We present an interface and an implementation of the General Matrix Multiply (GEMM) routine for multiple small matrices processed simultaneously on NVIDIA graphics processing units (GPUs). We focus on matrix sizes under 16. The implementation can be easily extended to larger sizes. For single preci ..."
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We present an interface and an implementation of the General Matrix Multiply (GEMM) routine for multiple small matrices processed simultaneously on NVIDIA graphics processing units (GPUs). We focus on matrix sizes under 16. The implementation can be easily extended to larger sizes. For single
A GEMM interface and implementation on NVIDIA GPUs for multiple small matrices
"... We present an interface and an implementation of the General Matrix Multiply (GEMM) routine for multiple small matrices processed simultaneously on NVIDIA graphics processing units (GPUs). We focus on matrix sizes under 16. The implementation can be easily extended to larger sizes. For single precis ..."
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We present an interface and an implementation of the General Matrix Multiply (GEMM) routine for multiple small matrices processed simultaneously on NVIDIA graphics processing units (GPUs). We focus on matrix sizes under 16. The implementation can be easily extended to larger sizes. For single
n, Systolic Montgomery multiplication version 19920225
"... Abstract. Montgomery multiplication is a divisionfree and memoryefficient algorithm for modular multipli cation. We describe a fast systolic version of Montgomery multiplication. Our version is particularly useful to turn a short sequence of moderately fast processing elements, that operate in SIM ..."
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Abstract. Montgomery multiplication is a divisionfree and memoryefficient algorithm for modular multipli cation. We describe a fast systolic version of Montgomery multiplication. Our version is particularly useful to turn a short sequence of moderately fast processing elements, that operate
FPGA Accelerator for FloatingPoint Matrix Multiplication
 IET COMPUTERS & DIGITAL TECHNIQUES
, 2012
"... This study treats architecture and implementation of a FPGA accelerator for doubleprecision floatingpoint matrix multiplication. The architecture is oriented towards minimising resource utilisation and maximising clock frequency. It employs the block matrix multiplication algorithm which returns t ..."
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This study treats architecture and implementation of a FPGA accelerator for doubleprecision floatingpoint matrix multiplication. The architecture is oriented towards minimising resource utilisation and maximising clock frequency. It employs the block matrix multiplication algorithm which returns
ACM Sigplan Notices 27,1 (Jan. 1992),9598. COMPUTING A*B (MOD N)
"... Let W be the word size of the ANSI C "long integer " implementation. Then W1 is the largest unsigned long integer, and W/21 is the largest signed long integer. Since we assume that N is a positive (but signed) integer, 0<N<W/2. Let A,B be nonnegative integers such that 0≤A, ..."
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,B<N. Let P=A*B; i.e., P requires double precision, and can be as large as W 2 /42W+4. Let R=mod(P,N)=mod(A*B,N). In other words, there exists an integer Q such that R=PQ*N=A*BQ*N, and 0≤R<N. If we could calculate Q, then we could calculate R using two double precision multiplies and a double
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"... The kinematic analyses, of manipulators and other robotic devices composed of mechanical links, usually depend on the solution of sets of nonlinear equations. There are a variety of both numerical and algebraic techniques available to solve such systems of equations and to give bounds on the number ..."
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of solutions. These solution methods have also led to an understanding of how special choices of the various structural parameters of a mechanism influence the number of solutions inherent to the kinematic geometry of a given structure. In this paper, results from studying the kinematic geometry
On Equivalences and Fair Comparisons Among Residue Number Systems with Special Moduli
"... Properties and applications of residue number systems (RNS) with special moduli of the form 2 k ± 1, with a single powerof2 modulus often also included, have been studied extensively. We show that lack of systematic studies has led to rediscovery of “new ” moduli sets that are really equivalent to ..."
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addition that leads to faster tree multipliers. However, modular multioperand addition is rather costly and slow for an arbitrary modulus m. 1.
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