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Low Complexity BitParallel Square Root Computation over GF(2^m) for all Trinomials
, 2006
"... In this contribution we introduce a lowcomplexity bitparallel algorithm for computing square roots over binary extension fields. Our proposed method can be applied for any type of irreducible polynomials. We derive explicit formulae for the space and time complexities associated to the square root ..."
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Cited by 4 (2 self)
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In this contribution we introduce a lowcomplexity bitparallel algorithm for computing square roots over binary extension fields. Our proposed method can be applied for any type of irreducible polynomials. We derive explicit formulae for the space and time complexities associated to the square
On the time course of perceptual choice: the leaky competing accumulator model
 PSYCHOLOGICAL REVIEW
, 2001
"... The time course of perceptual choice is discussed in a model based on gradual and stochastic accumulation of information in nonlinear decision units with leakage (or decay of activation) and competition through lateral inhibition. In special cases, the model becomes equivalent to a classical diffus ..."
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Cited by 457 (20 self)
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The time course of perceptual choice is discussed in a model based on gradual and stochastic accumulation of information in nonlinear decision units with leakage (or decay of activation) and competition through lateral inhibition. In special cases, the model becomes equivalent to a classical diffusion process, but leakage and mutual inhibition work together to address several challenges to existing diffusion, randomwalk, and accumulator models. The model provides a good account of data from choice tasks using both timecontrolled (e.g., deadline or response signal) and standard reaction time paradigms and its overall adequacy compares favorably with that of other approaches. An experimental paradigm that explicitly controls the timing of information supporting different choice alternatives provides further support. The model captures flexible choice behavior regardless of the number of alternatives, accounting for the linear slowing of reaction time as a function of the log of the number of alternatives (Hick’s law) and explains a complex pattern of visual and contextual priming effects in visual word identification. Perceptual Choice 2 When an experience presents itself to the senses, the need often arises to determine its identity or to make some other judgment about it. In experimental paradigms, the time course of this judgment process is
1A Chinese Remainder Theorem Approach to BitParallel GF (2n) Polynomial Basis Multipliers for Irreducible Trinomials
, 2015
"... We show that the step “modulo the degreen field generating irreducible polynomial ” in the classical definition of the GF (2n) multiplication operation can be avoided. This leads to an alternative representation of the finite field multiplication operation. Combining this representation and the Ch ..."
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Cited by 1 (1 self)
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and the Chinese Remainder Theorem, we design bitparallel GF (2n) multipliers for irreducible trinomials un + uk + 1 on GF (2). For some values of n, our architectures have the same time complexity as the fastest bitparallel multipliers – the quadratic multipliers, but their space complexities are reduced. Take
Limits of instructionlevel parallelism
, 1991
"... research relevant to the design and application of high performance scientific computers. We test our ideas by designing, building, and using real systems. The systems we build are research prototypes; they are not intended to become products. There two other research laboratories located in Palo Al ..."
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Cited by 406 (7 self)
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research relevant to the design and application of high performance scientific computers. We test our ideas by designing, building, and using real systems. The systems we build are research prototypes; they are not intended to become products. There two other research laboratories located in Palo Alto, the Network Systems
KARATSUBA ALGORITHM
, 2005
"... The Karatsuba algorithm (KA) for multiplying two polynomials was introduced in 1962 [3]. It saves coefficient multiplications at the cost of extra additions compared to the schoolbook or ordinary multiplication method. The basic KA is performed as follows. Consider two degree1 polynomials A(x) and ..."
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The Karatsuba algorithm (KA) for multiplying two polynomials was introduced in 1962 [3]. It saves coefficient multiplications at the cost of extra additions compared to the schoolbook or ordinary multiplication method. The basic KA is performed as follows. Consider two degree1 polynomials A
ControlFlow Analysis of HigherOrder Languages
, 1991
"... representing the official policies, either expressed or implied, of ONR or the U.S. Government. Keywords: dataflow analysis, Scheme, LISP, ML, CPS, type recovery, higherorder functions, functional programming, optimising compilers, denotational semantics, nonstandard Programs written in powerful, ..."
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Cited by 362 (10 self)
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representing the official policies, either expressed or implied, of ONR or the U.S. Government. Keywords: dataflow analysis, Scheme, LISP, ML, CPS, type recovery, higherorder functions, functional programming, optimising compilers, denotational semantics, nonstandard Programs written in powerful, higherorder languages like Scheme, ML, and Common Lisp should run as fast as their FORTRAN and C counterparts. They should, but they don’t. A major reason is the level of optimisation applied to these two classes of languages. Many FORTRAN and C compilers employ an arsenal of sophisticated global optimisations that depend upon dataflow analysis: commonsubexpression elimination, loopinvariant detection, inductionvariable elimination, and many, many more. Compilers for higherorder languages do not provide these optimisations. Without them, Scheme, LISP and ML compilers are doomed to produce code that runs slower than their FORTRAN and C counterparts. The problem is the lack of an explicit controlflow graph at compile time, something which traditional dataflow analysis techniques require. In this dissertation, I present a technique for recovering the controlflow graph of a Scheme program at compile time. I give examples of how this information can be used to perform several dataflow analysis optimisations, including copy propagation, inductionvariable elimination, uselessvariable elimination, and type recovery. The analysis is defined in terms of a nonstandard semantic interpretation. The denotational semantics is carefully developed, and several theorems establishing the correctness of the semantics and the implementing algorithms are proven. iii ivTo my parents, Julia and Olin. v viContents
Low complexity bitparallel GF (2 m) multiplier for allone polynomials
"... Abstract. This paper presents a new bitparallel multiplier for the finite field GF (2 m) generated with an irreducible allone polynomial. Redundant representation is used to reduce the time delay of the proposed multiplier, while a threeterm Karatsubalike formula is combined with this representa ..."
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Abstract. This paper presents a new bitparallel multiplier for the finite field GF (2 m) generated with an irreducible allone polynomial. Redundant representation is used to reduce the time delay of the proposed multiplier, while a threeterm Karatsubalike formula is combined
Hardware Accelerator for the Tate Pairing in Characteristic Three Based on KaratsubaOfman Multipliers
 CHES 2009
, 2009
"... This paper is devoted to the design of fast parallel accelerators for the cryptographic Tate pairing in characteristic three over supersingular elliptic curves. We propose here a novel hardware implementation of Miller’s loop based on a pipelined KaratsubaOfman multiplier. Thanks to a careful sel ..."
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Cited by 3 (2 self)
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This paper is devoted to the design of fast parallel accelerators for the cryptographic Tate pairing in characteristic three over supersingular elliptic curves. We propose here a novel hardware implementation of Miller’s loop based on a pipelined KaratsubaOfman multiplier. Thanks to a careful
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