SECRYPT_2019_1_CR (2).rar

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SECRYPT_2019_1_CR (2).rar
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<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/6259288892dc900e62b787bd/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/6259288892dc900e62b787bd/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">High-perf<span class="_ _0"></span>ormance<span class="_"> </span>Pipelined<span class="_"> </span>FPGA<span class="_"> </span>Implementation<span class="_"> </span>of<span class="_"> </span>the<span class="_"> </span>Elliptic<span class="_"> </span>Curv<span class="_ _0"></span>e</div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">Cryptography<span class="_"> </span>o<span class="_ _0"></span>ver<span class="_"> </span>GF<span class="_"> </span>(<span class="ff2">2</span></div><div class="t m0 x3 h3 y3 ff3 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x4 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">)</div><div class="t m0 x5 h4 y4 ff2 fs2 fc0 sc0 ls0 ws0">Salah<span class="_"> </span>Harb</div><div class="t m0 x6 h5 y5 ff2 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x7 h4 y4 ff2 fs2 fc0 sc0 ls0 ws0">,<span class="_"> </span>M.<span class="_"> </span>Omair<span class="_"> </span>Ahmad</div><div class="t m0 x8 h5 y5 ff2 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x9 h4 y4 ff2 fs2 fc0 sc0 ls0 ws0">and<span class="_"> </span>M.<span class="_"> </span>N.<span class="_"> </span>S.<span class="_"> </span>Swamy</div><div class="t m0 xa h5 y5 ff2 fs3 fc0 sc0 ls0 ws0">c</div><div class="t m0 xb h6 y6 ff3 fs4 fc0 sc0 ls0 ws0">Electrical<span class="_ _1"> </span>and<span class="_ _1"> </span>Computer<span class="_ _1"> </span>Engineering<span class="_ _1"> </span>Department,<span class="_ _1"> </span>Concor<span class="_ _0"></span>dia<span class="_ _1"> </span>University<span class="_ _0"></span>,<span class="_ _1"> </span>1440<span class="_ _1"> </span>De<span class="_ _1"> </span>maisonnue<span class="_ _0"></span>ve,<span class="_ _1"> </span>Montr<span class="_ _0"></span>eal,<span class="_ _1"> </span>Canada</div><div class="t m0 xc h7 y7 ff4 fs4 fc0 sc0 ls0 ws0">{<span class="ff3">s<span class="_ _2"> </span>rb,<span class="_ _1"> </span>omair<span class="_ _3"></span>,<span class="_ _1"> </span>swamy<span class="ff4">}</span>@ece.concor<span class="_ _0"></span>dia.ca</span></div><div class="t m0 x1 h8 y8 ff2 fs4 fc0 sc0 ls0 ws0">Ke<span class="_ _0"></span>ywords:</div><div class="t m0 xd h8 y9 ff2 fs4 fc0 sc0 ls0 ws0">Cryptography<span class="_ _4"></span>,<span class="_ _2"> </span>Elliptic<span class="_ _2"> </span>Curve<span class="_ _2"> </span>Cryptography<span class="_ _4"></span>,<span class="_ _2"> </span>FPGA,<span class="_ _2"> </span>Pipelining<span class="_ _2"> </span>Architecture,<span class="_ _5"> </span>Finite<span class="_ _2"> </span>Field<span class="_ _2"> </span>Operations,<span class="_ _2"> </span>Field</div><div class="t m0 xd h8 ya ff2 fs4 fc0 sc0 ls0 ws0">Multiplications,<span class="_"> </span>Projectiv<span class="_ _0"></span>e<span class="_"> </span>Coordination,<span class="_"> </span>Ef&#64257;cienc<span class="_ _0"></span>y<span class="_ _4"></span>.</div><div class="t m0 x1 h8 yb ff2 fs4 fc0 sc0 ls0 ws0">Abstract:</div><div class="t m0 xd h8 yc ff2 fs4 fc0 sc0 ls0 ws0">In<span class="_ _6"> </span>this<span class="_ _6"> </span>paper<span class="_ _0"></span>,<span class="_ _6"> </span>a<span class="_ _6"> </span>high-performance<span class="_ _6"> </span>area-ef&#64257;cient<span class="_ _6"> </span>hardware<span class="_ _6"> </span>design<span class="_ _6"> </span>for<span class="_ _6"> </span>the<span class="_ _6"> </span>Elliptic<span class="_ _6"> </span>Curv<span class="_ _0"></span>e<span class="_ _6"> </span>Cryptography<span class="_ _6"> </span>(ECC)</div><div class="t m0 xd h8 yd ff2 fs4 fc0 sc0 ls0 ws0">is<span class="_ _7"> </span>presented,<span class="_ _7"> </span>targeting<span class="_ _7"> </span>the<span class="_ _7"> </span>area-constrained<span class="_ _7"> </span>high-bandwidth<span class="_ _7"> </span>embedded<span class="_ _7"> </span>applications.<span class="_ _8"> </span>The<span class="_ _7"> </span>high-speed<span class="_ _7"> </span>design</div><div class="t m0 xd h8 ye ff2 fs4 fc0 sc0 ls0 ws0">is<span class="_ _6"> </span>implemented<span class="_ _6"> </span>using<span class="_ _6"> </span>pipelining<span class="_ _6"> </span>architecture.<span class="_ _9"> </span>The<span class="_ _6"> </span>applied<span class="_ _6"> </span>architecture<span class="_ _6"> </span>is<span class="_ _6"> </span>performed<span class="_ _6"> </span>using<span class="_ _6"> </span>n-bit<span class="_ _6"> </span>data<span class="_"> </span>path<span class="_ _6"> </span>of</div><div class="t m0 xd h8 yf ff2 fs4 fc0 sc0 ls0 ws0">the<span class="_ _7"> </span>&#64257;nite<span class="_ _2"> </span>&#64257;eld<span class="_ _2"> </span>GF(2</div><div class="t m0 xe h9 y10 ff3 fs5 fc0 sc0 ls0 ws0">n</div><div class="t m0 xf h8 yf ff2 fs4 fc0 sc0 ls0 ws0">).<span class="_ _a"> </span>For<span class="_ _7"> </span>the<span class="_ _2"> </span>&#64257;nite<span class="_ _7"> </span>&#64257;eld<span class="_ _2"> </span>operations,<span class="_ _5"> </span>the<span class="_ _7"> </span>implementation<span class="_ _2"> </span>in<span class="_ _2"> </span>the<span class="_ _7"> </span>ECC<span class="_ _2"> </span>uses<span class="_ _2"> </span>the<span class="_ _2"> </span>bit-parallel</div><div class="t m0 xd h8 y11 ff2 fs4 fc0 sc0 ls0 ws0">recursiv<span class="_ _0"></span>e<span class="_ _2"> </span>Karatsuba-Ofman<span class="_ _2"> </span>algorithm<span class="_ _2"> </span>for<span class="_ _2"> </span>multiplication<span class="_ _2"> </span>and<span class="_ _2"> </span>Itoh-Tsuji<span class="_ _2"> </span>for<span class="_ _2"> </span>in<span class="_ _0"></span>version.<span class="_ _a"> </span>A<span class="_ _2"> </span>modi&#64257;ed<span class="_ _2"> </span>ef&#64257;cient</div><div class="t m0 xd h8 y12 ff2 fs4 fc0 sc0 ls0 ws0">montgomery<span class="_ _6"> </span>ladder<span class="_ _6"> </span>algorithm<span class="_ _6"> </span>is<span class="_ _6"> </span>utilized<span class="_ _7"> </span>for<span class="_ _6"> </span>the<span class="_ _6"> </span>scalar<span class="_ _6"> </span>multiplication<span class="_ _6"> </span>of<span class="_ _7"> </span>a<span class="_ _6"> </span>point.<span class="_ _b"> </span>The<span class="_ _6"> </span>pipelined<span class="_ _6"> </span>registers<span class="_ _6"> </span>are</div><div class="t m0 xd h8 y13 ff2 fs4 fc0 sc0 ls0 ws0">inserted<span class="_"> </span>in<span class="_ _6"> </span>ideal<span class="_"> </span>locations,<span class="_"> </span>where<span class="_ _6"> </span>balanced-e<span class="_ _0"></span>xecution<span class="_"> </span>paths<span class="_"> </span>among<span class="_ _6"> </span>computing<span class="_"> </span>components<span class="_"> </span>are<span class="_ _6"> </span>guaranteed.<span class="_ _7"> </span>A</div><div class="t m0 xd h8 y14 ff2 fs4 fc0 sc0 ls0 ws0">Memory-less<span class="_ _6"> </span>&#64257;nite<span class="_"> </span>state<span class="_ _6"> </span>machine<span class="_ _6"> </span>model<span class="_"> </span>is<span class="_ _6"> </span>dev<span class="_ _0"></span>eloped<span class="_ _6"> </span>to<span class="_ _6"> </span>control<span class="_"> </span>the<span class="_ _6"> </span>instructions<span class="_ _6"> </span>of<span class="_"> </span>computing<span class="_ _6"> </span>the<span class="_ _6"> </span>&#64257;nite<span class="_"> </span>&#64257;eld</div><div class="t m0 xd h8 y15 ff2 fs4 fc0 sc0 ls0 ws0">operations<span class="_ _6"> </span>ef&#64257;ciently<span class="_ _4"></span>.<span class="_ _b"> </span>The<span class="_ _6"> </span>high-performance<span class="_ _7"> </span>design<span class="_ _6"> </span>has<span class="_ _7"> </span>been<span class="_ _6"> </span>implemented<span class="_ _7"> </span>using<span class="_ _6"> </span>Xilinx<span class="_ _7"> </span>V<span class="_ _4"></span>irtex,<span class="_ _6"> </span>Kintex<span class="_ _6"> </span>and</div><div class="t m0 xd h8 y16 ff2 fs4 fc0 sc0 ls0 ws0">Artix<span class="_ _7"> </span>FPGA<span class="_ _7"> </span>devices.<span class="_ _8"> </span>It<span class="_ _6"> </span>can<span class="_ _7"> </span>perform<span class="_ _7"> </span>a<span class="_ _7"> </span>single<span class="_ _7"> </span>scalar<span class="_ _2"> </span>multiplication<span class="_ _7"> </span>in<span class="_ _7"> </span>226<span class="_ _7"> </span>clock<span class="_ _7"> </span>cycles<span class="_ _7"> </span>within<span class="_ _7"> </span>0.63<span class="ff3">&#181;</span>s<span class="_ _7"> </span>using</div><div class="t m0 xd h8 y17 ff2 fs4 fc0 sc0 ls0 ws0">2780<span class="_"> </span>slices<span class="_ _6"> </span>and<span class="_"> </span>360Mhz<span class="_"> </span>working<span class="_"> </span>frequency<span class="_"> </span>on<span class="_"> </span>V<span class="_ _0"></span>irtex-7<span class="_"> </span>ov<span class="_ _0"></span>er<span class="_"> </span>GF<span class="_ _6"> </span>(2</div><div class="t m0 x10 ha y18 ff2 fs5 fc0 sc0 ls0 ws0">163</div><div class="t m0 x11 h8 y17 ff2 fs4 fc0 sc0 ls0 ws0">).<span class="_ _7"> </span>In<span class="_ _6"> </span>GF<span class="_"> </span>(2</div><div class="t m0 x12 ha y18 ff2 fs5 fc0 sc0 ls0 ws0">233</div><div class="t m0 x13 h8 y17 ff2 fs4 fc0 sc0 ls0 ws0">)<span class="_"> </span>and<span class="_ _6"> </span>GF<span class="_"> </span>(2</div><div class="t m0 x14 ha y18 ff2 fs5 fc0 sc0 ls0 ws0">571</div><div class="t m0 x15 h8 y17 ff2 fs4 fc0 sc0 ls0 ws0">),<span class="_"> </span>a<span class="_ _6"> </span>scalar</div><div class="t m0 xd h8 y19 ff2 fs4 fc0 sc0 ls0 ws0">multiplication<span class="_ _c"> </span>can<span class="_ _c"> </span>be<span class="_ _c"> </span>computed<span class="_ _c"> </span>in<span class="_ _c"> </span>327<span class="_ _c"> </span>and<span class="_ _c"> </span>674<span class="_ _c"> </span>clock<span class="_ _c"> </span>cycles<span class="_ _c"> </span>within<span class="_ _c"> </span>1.05<span class="ff3">&#181;</span>s<span class="_ _c"> </span>and<span class="_ _c"> </span>2.32<span class="ff3">&#181;</span>s,<span class="_ _c"> </span>respecti<span class="_ _0"></span>vely<span class="_ _4"></span>.<span class="_ _6"> </span>Comparing</div><div class="t m0 xd h8 y1a ff2 fs4 fc0 sc0 ls0 ws0">with<span class="_"> </span>pre<span class="_ _4"></span>vious<span class="_"> </span>works,<span class="_"> </span>our<span class="_ _c"> </span>design<span class="_"> </span>requires<span class="_ _c"> </span>less<span class="_"> </span>number<span class="_"> </span>of<span class="_ _c"> </span>clock<span class="_"> </span>cycles,<span class="_ _c"> </span>and<span class="_"> </span>operates<span class="_ _c"> </span>using<span class="_"> </span>less<span class="_"> </span>FPGA<span class="_ _c"> </span>resources</div><div class="t m0 xd h8 y1b ff2 fs4 fc0 sc0 ls0 ws0">with<span class="_ _6"> </span>competitive<span class="_ _6"> </span>high<span class="_ _6"> </span>working<span class="_ _7"> </span>frequencies.<span class="_ _8"> </span>Therefore,<span class="_ _6"> </span>the<span class="_ _7"> </span>proposed<span class="_ _7"> </span>design<span class="_ _6"> </span>is<span class="_ _7"> </span>well<span class="_ _7"> </span>suited<span class="_ _7"> </span>in<span class="_ _6"> </span>the<span class="_ _7"> </span>resources-</div><div class="t m0 xd h8 y1c ff2 fs4 fc0 sc0 ls0 ws0">constrained<span class="_ _c"> </span>real<span class="_"> </span>time<span class="_ _c"> </span>cryptosystems<span class="_"> </span>like<span class="_ _c"> </span>those<span class="_"> </span>i<span class="_ _0"></span>n<span class="_"> </span>online<span class="_ _c"> </span>banking<span class="_"> </span>services,<span class="_ _c"> </span>wearable<span class="_"> </span>smart<span class="_ _c"> </span>devices<span class="_ _c"> </span>and<span class="_ _d"> </span>network</div><div class="t m0 xd h8 y1d ff2 fs4 fc0 sc0 ls0 ws0">attached<span class="_"> </span>storages.</div><div class="t m0 x1 hb y1e ff1 fs6 fc0 sc0 ls0 ws0">1<span class="_ _e"> </span>INTR<span class="_ _4"></span>ODUCTION</div><div class="t m0 x1 hc y1f ff2 fs7 fc0 sc0 ls0 ws0">Elliptic<span class="_ _8"> </span>curv<span class="_ _4"></span>e<span class="_ _8"> </span>cryptosystem<span class="_ _8"> </span>(ECC)<span class="_ _b"> </span>is<span class="_ _8"> </span>a<span class="_ _b"> </span>public-key</div><div class="t m0 x1 hc y20 ff2 fs7 fc0 sc0 ls0 ws0">cryptography<span class="_ _4"></span>,<span class="_ _f"> </span>which<span class="_ _10"> </span>was<span class="_ _10"> </span>&#64257;rst<span class="_ _10"> </span>proposed<span class="_ _10"> </span>by<span class="_ _10"> </span>Neal</div><div class="t m0 x1 hc y21 ff2 fs7 fc0 sc0 ls0 ws0">K<span class="_ _0"></span>oblitz<span class="_"> </span>and<span class="_ _6"> </span>V<span class="_ _4"></span>ictor<span class="_"> </span>Miller<span class="_ _6"> </span>in<span class="_"> </span>the<span class="_ _6"> </span>1980s<span class="_"> </span>(Kocher<span class="_"> </span>et<span class="_"> </span>al.,</div><div class="t m0 x1 hc y22 ff2 fs7 fc0 sc0 ls0 ws0">1999)<span class="_"> </span>,<span class="_"> </span>(Miller<span class="_ _0"></span>,<span class="_"> </span>1985).<span class="_ _2"> </span>Since<span class="_"> </span>then,<span class="_"> </span>many<span class="_"> </span>studies<span class="_"> </span>hav<span class="_ _0"></span>e</div><div class="t m0 x1 hc y23 ff2 fs7 fc0 sc0 ls0 ws0">been<span class="_ _2"> </span>conducted<span class="_ _2"> </span>to<span class="_ _5"> </span>explore<span class="_ _7"> </span>its<span class="_ _5"> </span>security<span class="_ _2"> </span>lev<span class="_ _0"></span>els<span class="_ _2"> </span>against</div><div class="t m0 x1 hc y24 ff2 fs7 fc0 sc0 ls0 ws0">other<span class="_ _8"> </span>public-ke<span class="_ _0"></span>y<span class="_ _8"> </span>cryptosystems<span class="_ _8"> </span>such<span class="_ _8"> </span>as<span class="_ _8"> </span>El-Gamal,</div><div class="t m0 x1 hc y25 ff2 fs7 fc0 sc0 ls0 ws0">RSA<span class="_ _7"> </span>and<span class="_ _6"> </span>Digital<span class="_ _7"> </span>Signature<span class="_ _7"> </span>Algorithm<span class="_ _7"> </span>(DSA)<span class="_ _7"> </span>(ElGa-</div><div class="t m0 x1 hc y26 ff2 fs7 fc0 sc0 ls0 ws0">mal,<span class="_ _7"> </span>1985),<span class="_ _7"> </span>(Riv<span class="_ _0"></span>est<span class="_ _7"> </span>et<span class="_ _6"> </span>al.,<span class="_ _2"> </span>1978),<span class="_ _7"> </span>which<span class="_ _7"> </span>are<span class="_ _7"> </span>based<span class="_ _6"> </span>on</div><div class="t m0 x1 hc y27 ff2 fs7 fc0 sc0 ls0 ws0">either<span class="_ _5"> </span>the<span class="_ _5"> </span>integer<span class="_ _5"> </span>factorization<span class="_ _5"> </span>or<span class="_ _5"> </span>discrete<span class="_ _9"> </span>logarithm</div><div class="t m0 x1 hc y28 ff2 fs7 fc0 sc0 ls0 ws0">problems<span class="_ _9"> </span>(McGrew<span class="_ _9"> </span>et<span class="_ _9"> </span>al.,<span class="_ _b"> </span>2011).<span class="_ _11"> </span>Equiv<span class="_ _4"></span>alent<span class="_ _9"> </span>secu-</div><div class="t m0 x1 hc y29 ff2 fs7 fc0 sc0 ls0 ws0">rity<span class="_ _2"> </span>lev<span class="_ _0"></span>els<span class="_ _2"> </span>with<span class="_ _2"> </span>smaller<span class="_ _2"> </span>sizes<span class="_ _5"> </span>of<span class="_ _7"> </span>keys,<span class="_ _2"> </span>ease<span class="_ _5"> </span>to<span class="_ _2"> </span>imple-</div><div class="t m0 x1 hc y2a ff2 fs7 fc0 sc0 ls0 ws0">ment,<span class="_ _7"> </span>and<span class="_ _7"> </span>resource<span class="_ _7"> </span>savings,<span class="_ _7"> </span>are<span class="_ _6"> </span>reasons<span class="_ _7"> </span>that<span class="_ _7"> </span>give<span class="_ _6"> </span>the</div><div class="t m0 x1 hc y2b ff2 fs7 fc0 sc0 ls0 ws0">ECC<span class="_ _b"> </span>to<span class="_ _9"> </span>be<span class="_ _b"> </span>very<span class="_ _b"> </span>appealing<span class="_ _9"> </span>and<span class="_ _b"> </span>more<span class="_ _b"> </span>dominant<span class="_ _b"> </span>be-</div><div class="t m0 x1 hc y2c ff2 fs7 fc0 sc0 ls0 ws0">tween<span class="_ _2"> </span>the<span class="_ _2"> </span>hardware<span class="_ _2"> </span>recon&#64257;gurable<span class="_ _2"> </span>implementations.</div><div class="t m0 x1 hc y2d ff2 fs7 fc0 sc0 ls0 ws0">Moreov<span class="_ _0"></span>er<span class="_ _0"></span>,<span class="_ _5"> </span>ECC<span class="_ _5"> </span>is<span class="_ _2"> </span>well<span class="_ _5"> </span>suited<span class="_ _2"> </span>to<span class="_ _5"> </span>be<span class="_ _2"> </span>implemented<span class="_ _5"> </span>in</div><div class="t m0 x1 hc y2e ff2 fs7 fc0 sc0 ls0 ws0">such<span class="_ _d"> </span>resource-constrained<span class="_ _d"> </span>embedded<span class="_ _d"> </span>systems,<span class="_"> </span>since<span class="_ _c"> </span>it</div><div class="t m0 x16 ha y2f ff2 fs5 fc0 sc0 ls0 ws0">a</div><div class="t m0 x17 h8 y30 ff2 fs4 fc0 sc0 ls0 ws0">https://orcid.org/0000-0002-5975-6537</div><div class="t m0 x16 ha y31 ff2 fs5 fc0 sc0 ls0 ws0">b</div><div class="t m0 x17 h8 y32 ff2 fs4 fc0 sc0 ls0 ws0">https://orcid.org/0000-0002-2924-6659</div><div class="t m0 x16 ha y33 ff2 fs5 fc0 sc0 ls0 ws0">c</div><div class="t m0 x17 h8 y34 ff2 fs4 fc0 sc0 ls0 ws0">https://orcid.org/0000-0002-3989-5476</div><div class="t m0 x18 hc y1e ff2 fs7 fc0 sc0 ls0 ws0">provides<span class="_ _7"> </span>same<span class="_ _7"> </span>security<span class="_ _2"> </span>lev<span class="_ _0"></span>els<span class="_ _7"> </span>as<span class="_ _2"> </span>in<span class="_ _7"> </span>RSA<span class="_ _2"> </span>using<span class="_ _7"> </span>small</div><div class="t m0 x18 hc y35 ff2 fs7 fc0 sc0 ls0 ws0">keys.<span class="_ _12"> </span>ECC<span class="_ _5"> </span>has<span class="_ _5"> </span>been<span class="_ _5"> </span>standardized<span class="_ _9"> </span>by<span class="_ _5"> </span>IEEE<span class="_ _5"> </span>and<span class="_ _5"> </span>the</div><div class="t m0 x18 hc y36 ff2 fs7 fc0 sc0 ls0 ws0">National<span class="_ _d"> </span>Institute<span class="_ _c"> </span>of<span class="_ _d"> </span>Standard<span class="_ _d"> </span>and<span class="_ _d"> </span>T<span class="_ _4"></span>echnology<span class="_ _d"> </span>(NIST)</div><div class="t m0 x18 hc y37 ff2 fs7 fc0 sc0 ls0 ws0">as<span class="_ _5"> </span>a<span class="_ _9"> </span>scheme<span class="_ _5"> </span>in<span class="_ _9"> </span>digital<span class="_ _5"> </span>signature<span class="_ _9"> </span>and<span class="_ _5"> </span>key<span class="_ _5"> </span>agreement</div><div class="t m0 x18 hc y38 ff2 fs7 fc0 sc0 ls0 ws0">protocols<span class="_"> </span>(for<span class="_"> </span>Standardization<span class="_"> </span>(ISO),<span class="_"> </span>2000).</div><div class="t m0 x19 hc y39 ff2 fs7 fc0 sc0 ls0 ws0">Generally<span class="_ _4"></span>,<span class="_ _9"> </span>most<span class="_ _9"> </span>of<span class="_ _9"> </span>cryptographic<span class="_ _5"> </span>algorithms<span class="_ _9"> </span>are</div><div class="t m0 x18 hc y3a ff2 fs7 fc0 sc0 ls0 ws0">implemented<span class="_ _9"> </span>in<span class="_ _9"> </span>software<span class="_ _5"> </span>platforms.<span class="_ _11"> </span>Performing<span class="_ _9"> </span>an</div><div class="t m0 x18 hc y3b ff2 fs7 fc0 sc0 ls0 ws0">algorithm<span class="_"> </span>on<span class="_ _6"> </span>a<span class="_ _6"> </span>general<span class="_ _6"> </span>purpose<span class="_ _6"> </span>processor<span class="_ _6"> </span>(e.g.<span class="_ _9"> </span>CPU)</div><div class="t m0 x18 hc y3c ff2 fs7 fc0 sc0 ls0 ws0">will<span class="_ _2"> </span>require<span class="_ _2"> </span>most<span class="_ _2"> </span>of<span class="_ _2"> </span>its<span class="_ _2"> </span>resources<span class="_ _2"> </span>to<span class="_ _5"> </span>compute<span class="_ _7"> </span>results</div><div class="t m0 x18 hc y3d ff2 fs7 fc0 sc0 ls0 ws0">of<span class="_ _6"> </span>intensiv<span class="_ _0"></span>e<span class="_ _6"> </span>operations<span class="_ _6"> </span>because<span class="_ _7"> </span>of<span class="_ _6"> </span>the<span class="_ _6"> </span>large<span class="_ _6"> </span>operands</div><div class="t m0 x18 hc y3e ff2 fs7 fc0 sc0 ls0 ws0">used<span class="_ _8"> </span>in<span class="_ _b"> </span>these<span class="_ _8"> </span>very<span class="_ _13"> </span>accurate<span class="_ _13"> </span>computations.<span class="_ _14"> </span>More-</div><div class="t m0 x18 hc y3f ff2 fs7 fc0 sc0 ls0 ws0">ov<span class="_ _0"></span>er<span class="_ _0"></span>,<span class="_ _b"> </span>CPU<span class="_ _9"> </span>is<span class="_ _9"> </span>not<span class="_ _9"> </span>suitable<span class="_ _5"> </span>in<span class="_ _9"> </span>performing<span class="_ _9"> </span>such<span class="_ _9"> </span>these</div><div class="t m0 x18 hc y40 ff2 fs7 fc0 sc0 ls0 ws0">algorithms<span class="_"> </span>that<span class="_ _6"> </span>having<span class="_"> </span>the<span class="_"> </span>parallel<span class="_ _6"> </span>architecture<span class="_ _6"> </span>in<span class="_ _6"> </span>na-</div><div class="t m0 x18 hc y41 ff2 fs7 fc0 sc0 ls0 ws0">ture.<span class="_ _f"> </span>These<span class="_ _5"> </span>issues<span class="_ _5"> </span>prove<span class="_ _2"> </span>that<span class="_ _9"> </span>software<span class="_ _5"> </span>implementa-</div><div class="t m0 x18 hc y42 ff2 fs7 fc0 sc0 ls0 ws0">tion<span class="_ _b"> </span>of<span class="_ _9"> </span>encryption<span class="_ _b"> </span>algorithms<span class="_ _b"> </span>does<span class="_ _b"> </span>not<span class="_ _9"> </span>provide<span class="_ _b"> </span>the</div><div class="t m0 x18 hc y43 ff2 fs7 fc0 sc0 ls0 ws0">required<span class="_ _b"> </span>performance.<span class="_ _15"> </span>Due<span class="_ _b"> </span>to<span class="_ _b"> </span>the<span class="_ _b"> </span>div<span class="_ _0"></span>ersity<span class="_ _b"> </span>in<span class="_ _b"> </span>the</div><div class="t m0 x18 hc y44 ff2 fs7 fc0 sc0 ls0 ws0">applications,<span class="_ _b"> </span>the<span class="_ _b"> </span>trade-of<span class="_ _0"></span>f<span class="_ _9"> </span>between<span class="_ _b"> </span>area,<span class="_ _b"> </span>speed<span class="_ _b"> </span>and</div><div class="t m0 x18 hc y45 ff2 fs7 fc0 sc0 ls0 ws0">power<span class="_ _6"> </span>is<span class="_ _7"> </span>required.<span class="_ _13"> </span>Some<span class="_ _7"> </span>applications,<span class="_ _2"> </span>such<span class="_ _7"> </span>as<span class="_ _7"> </span>RFID</div><div class="t m0 x18 hc y46 ff2 fs7 fc0 sc0 ls0 ws0">cards,<span class="_ _a"> </span>nodes<span class="_ _b"> </span>of<span class="_ _8"> </span>wireless<span class="_ _13"> </span>sensor<span class="_ _13"> </span>networks<span class="_ _13"> </span>and<span class="_ _8"> </span>cell</div><div class="t m0 x18 hc y47 ff2 fs7 fc0 sc0 ls0 ws0">phones,<span class="_ _7"> </span>need<span class="_ _6"> </span>a<span class="_ _7"> </span>small<span class="_ _7"> </span>area<span class="_ _7"> </span>and<span class="_ _6"> </span>power<span class="_ _4"></span>.<span class="_ _b"> </span>Other<span class="_ _6"> </span>applica-</div><div class="t m0 x18 hc y48 ff2 fs7 fc0 sc0 ls0 ws0">tions,<span class="_"> </span>such<span class="_ _6"> </span>as<span class="_ _6"> </span>web<span class="_ _6"> </span>servers,<span class="_"> </span>large<span class="_"> </span>bandwidth<span class="_ _6"> </span>networks</div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div> </body> </html>
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