Multiplication-addition modulaire: algorithmes itératifs et implantations sur FPGA

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(1)Multiplication-addition modulaire: algorithmes itératifs et implantations sur FPGA Jean-Luc Beuchat. To cite this version: Jean-Luc Beuchat. Multiplication-addition modulaire: algorithmes itératifs et implantations sur FPGA. RR-4840, INRIA. 2003. �inria-00071745�. HAL Id: inria-00071745 https://hal.inria.fr/inria-00071745 Submitted on 23 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Multiplication-addition modulaire: algorithmes itératifs et implantations sur FPGA Jean-Luc Beuchat et Jean-Michel Muller. No 4840 Juin 2003. ISSN 0249-6399. ISRN INRIA/RR--4840--FR+ENG. ` THEME 2. apport de recherche.

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(163) ¯ hM³d±-l

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(166) T[s−i] n+2 0 1. LUT. T[s−i] n+1. P[n−i+1]n 0 1. 0 ϕ(1)n−1 ϕ(2)n−1 ϕ(3)n−1 ϕ(4)n−1. 000. T[s−i] n+1. 001. 011 100. ϕ(.)m1. T[s−i] n+1. ϕ(.)m2. Select. 3. T[s−i] n. T[s−i] n. 010. T[s−i] n. P[n−i+1]n−1 P[s−i] n x n−i y n−1 P[n−i+1]n−2. 0 1. x n−i y1 P[n−i+1]0. 0 1. x n−i y0 wn−i. P[s−i] n. 0 1. T[s−i] n−1. ϕ(.). T[s−i] 1. ϕ(.). 0 1. P[s−i] n−1. T[s−i] n−1. ϕ(.). T[s−i] 1. ϕ(.). P[s−i] n−1. 0 1. 0 1. P[s−i] 1. 0 1. P[s−i] 1. 0 1. T[s−i] 0. ϕ(.). 0 1. P[s−i] 0. T[s−i] 0. ϕ(.) Select. (a). P[s−i] 0. (b). v ãK[F^ Knkãl []mZgpqnodGm{m{XZnobmuhMeiyuhkY-d[F \] qZ)d0rubqZm{y%nkgjk \noy lXZ em{efmub\yl n+mum{qefhMyud\)rqZ\y¤g qZhMd0Kb-»"y{x¤nomu`\q~¬y-¥ \Sgpnnk[Feig f\ªÁSeiym{\

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(210) %p

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(245) !f (+*-, (+*-, % m E #&%

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(263) hMyuy{\-l

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(266) ®Ê\-l

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(270) '(%L$&L

(271)

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(276) b

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(392) Unité de recherche INRIA Lorraine, Technopôle de Nancy-Brabois, Campus scientifique, ` NANCY 615 rue du Jardin Botanique, BP 101, 54600 VILLERS LES Unité de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unité de recherche INRIA Rhône-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST MARTIN Unité de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unité de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP 93, 06902 SOPHIA-ANTIPOLIS Cedex. ´ Editeur INRIA, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France)

(393) ISSN 0249-6399.

(394)