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<a name="l00355"></a>00355 <a class="code" href="class_abstract_group.html" title="Abstract Group.">AbstractGroup<ECPPoint>::SimultaneousMultiply</a>(&result, P, &k, 1);<a name="l00356"></a>00356 <span class="keywordflow">else</span><a name="l00357"></a>00357 ECP::SimultaneousMultiply(&result, P, &k, 1);<a name="l00358"></a>00358 <span class="keywordflow">return</span> result;<a name="l00359"></a>00359 }<a name="l00360"></a>00360 <a name="l00361"></a>00361 <span class="keywordtype">void</span> ECP::SimultaneousMultiply(<a class="code" href="struct_e_c_p_point.html" title="Elliptical Curve Point.">ECP::Point</a> *results, <span class="keyword">const</span> <a class="code" href="struct_e_c_p_point.html" title="Elliptical Curve Point.">ECP::Point</a> &P, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> *expBegin, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> expCount)<span class="keyword"> const</span><a name="l00362"></a>00362 <span class="keyword"></span>{<a name="l00363"></a>00363 <span class="keywordflow">if</span> (!<a class="code" href="class_e_c_p.html#e996fce212244df79b83a587317f7423">GetField</a>().IsMontgomeryRepresentation())<a name="l00364"></a>00364 {<a name="l00365"></a>00365 <a class="code" href="class_e_c_p.html" title="Elliptic Curve over GF(p), where p is prime.">ECP</a> ecpmr(*<span class="keyword">this</span>, <span class="keyword">true</span>);<a name="l00366"></a>00366 <span class="keyword">const</span> <a class="code" href="class_modular_arithmetic.html" title="ring of congruence classes modulo n">ModularArithmetic</a> &mr = ecpmr.GetField();<a name="l00367"></a>00367 ecpmr.<a class="code" href="class_abstract_group.html#00a5cd4b22aab947ec107ec93ad13122">SimultaneousMultiply</a>(results, ToMontgomery(mr, P), expBegin, expCount);<a name="l00368"></a>00368 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i<expCount; i++)<a name="l00369"></a>00369 results[i] = FromMontgomery(mr, results[i]);<a name="l00370"></a>00370 <span class="keywordflow">return</span>;<a name="l00371"></a>00371 }<a name="l00372"></a>00372 <a name="l00373"></a>00373 ProjectiveDoubling rd(<a class="code" href="class_e_c_p.html#e996fce212244df79b83a587317f7423">GetField</a>(), m_a, m_b, P);<a name="l00374"></a>00374 std::vector<ProjectivePoint> bases;<a name="l00375"></a>00375 std::vector<WindowSlider> exponents;<a name="l00376"></a>00376 exponents.reserve(expCount);<a name="l00377"></a>00377 std::vector<std::vector<word32> > baseIndices(expCount);<a name="l00378"></a>00378 std::vector<std::vector<bool> > negateBase(expCount);<a name="l00379"></a>00379 std::vector<std::vector<word32> > exponentWindows(expCount);<a name="l00380"></a>00380 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i;<a name="l00381"></a>00381 <a name="l00382"></a>00382 <span class="keywordflow">for</span> (i=0; i<expCount; i++)<a name="l00383"></a>00383 {<a name="l00384"></a>00384 assert(expBegin-><a class="code" href="class_integer.html#880ab53116f2b9f527489d86ee806896">NotNegative</a>());<a name="l00385"></a>00385 exponents.push_back(<a class="code" href="struct_window_slider.html">WindowSlider</a>(*expBegin++, <a class="code" href="class_e_c_p.html#0031a4a3a18999fda3942713da554697">InversionIsFast</a>(), 5));<a name="l00386"></a>00386 exponents[i].FindNextWindow();<a name="l00387"></a>00387 }<a name="l00388"></a>00388 <a name="l00389"></a>00389 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> expBitPosition = 0;<a name="l00390"></a>00390 <span class="keywordtype">bool</span> notDone = <span class="keyword">true</span>;<a name="l00391"></a>00391 <a name="l00392"></a>00392 <span class="keywordflow">while</span> (notDone)<a name="l00393"></a>00393 {<a name="l00394"></a>00394 notDone = <span class="keyword">false</span>;<a name="l00395"></a>00395 <span class="keywordtype">bool</span> baseAdded = <span class="keyword">false</span>;<a name="l00396"></a>00396 <span class="keywordflow">for</span> (i=0; i<expCount; i++)<a name="l00397"></a>00397 {<a name="l00398"></a>00398 <span class="keywordflow">if</span> (!exponents[i].finished && expBitPosition == exponents[i].windowBegin)<a name="l00399"></a>00399 {<a name="l00400"></a>00400 <span class="keywordflow">if</span> (!baseAdded)<a name="l00401"></a>00401 {<a name="l00402"></a>00402 bases.push_back(rd.P);<a name="l00403"></a>00403 baseAdded =<span class="keyword">true</span>;<a name="l00404"></a>00404 }<a name="l00405"></a>00405 <a name="l00406"></a>00406 exponentWindows[i].push_back(exponents[i].expWindow);<a name="l00407"></a>00407 baseIndices[i].push_back((word32)bases.size()-1);<a name="l00408"></a>00408 negateBase[i].push_back(exponents[i].negateNext);<a name="l00409"></a>00409 <a name="l00410"></a>00410 exponents[i].FindNextWindow();<a name="l00411"></a>00411 }<a name="l00412"></a>00412 notDone = notDone || !exponents[i].finished;<a name="l00413"></a>00413 }<a name="l00414"></a>00414 <a name="l00415"></a>00415 <span class="keywordflow">if</span> (notDone)<a name="l00416"></a>00416 {<a name="l00417"></a>00417 rd.Double();<a name="l00418"></a>00418 expBitPosition++;<a name="l00419"></a>00419 }<a name="l00420"></a>00420 }<a name="l00421"></a>00421 <a name="l00422"></a>00422 <span class="comment">// convert from projective to affine coordinates</span><a name="l00423"></a>00423 ParallelInvert(<a class="code" href="class_e_c_p.html#e996fce212244df79b83a587317f7423">GetField</a>(), ZIterator(bases.begin()), ZIterator(bases.end()));<a name="l00424"></a>00424 <span class="keywordflow">for</span> (i=0; i<bases.size(); i++)<a name="l00425"></a>00425 {<a name="l00426"></a>00426 <span class="keywordflow">if</span> (bases[i].z.NotZero())<a name="l00427"></a>00427 {<a name="l00428"></a>00428 bases[i].y = <a class="code" href="class_e_c_p.html#e996fce212244df79b83a587317f7423">GetField</a>().<a class="code" href="class_modular_arithmetic.html#3b88a85b11eb1a826d26d01bdaafbf0a">Multiply</a>(bases[i].y, bases[i].z);<a name="l00429"></a>00429 bases[i].z = <a class="code" href="class_e_c_p.html#e996fce212244df79b83a587317f7423">GetField</a>().<a class="code" href="class_modular_arithmetic.html#c378a2527fe2107d3379bc35d7cd0487">Square</a>(bases[i].z);<a name="l00430"></a>00430 bases[i].x = <a class="code" href="class_e_c_p.html#e996fce212244df79b83a587317f7423">GetField</a>().<a class="code" href="class_modular_arithmetic.html#3b88a85b11eb1a826d26d01bdaafbf0a">Multiply</a>(bases[i].x, bases[i].z);<a name="l00431"></a>00431 bases[i].y = <a class="code" href="class_e_c_p.html#e996fce212244df79b83a587317f7423">GetField</a>().<a class="code" href="class_modular_arithmetic.html#3b88a85b11eb1a826d26d01bdaafbf0a">Multiply</a>(bases[i].y, bases[i].z);<a name="l00432"></a>00432 }<a name="l00433"></a>00433 }<a name="l00434"></a>00434 <a name="l00435"></a>00435 std::vector<BaseAndExponent<Point, Integer> > finalCascade;<a name="l00436"></a>00436 <span class="keywordflow">for</span> (i=0; i<expCount; i++)<a name="l00437"></a>00437 {<a name="l00438"></a>00438 finalCascade.resize(baseIndices[i].size());<a name="l00439"></a>00439 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j=0; j<baseIndices[i].size(); j++)<a name="l00440"></a>00440 {<a name="l00441"></a>00441 ProjectivePoint &base = bases[baseIndices[i][j]];<a name="l00442"></a>00442 <span class="keywordflow">if</span> (base.z.IsZero())<a name="l00443"></a>00443 finalCascade[j].base.identity = <span class="keyword">true</span>;<a name="l00444"></a>00444 <span class="keywordflow">else</span><a name="l00445"></a>00445 {<a name="l00446"></a>00446 finalCascade[j].base.identity = <span class="keyword">false</span>;<a name="l00447"></a>00447 finalCascade[j].base.x = base.x;<a name="l00448"></a>00448 if (negateBase[i][j])<a name="l00449"></a>00449 finalCascade[j].base.y = <a class="code" href="class_e_c_p.html#e996fce212244df79b83a587317f7423">GetField</a>().<a class="code" href="class_modular_arithmetic.html#7e3a9d9ae5e151fdd75f00f7c22bdda3">Inverse</a>(base.y);<a name="l00450"></a>00450 <span class="keywordflow">else</span><a name="l00451"></a>00451 finalCascade[j].base.y = base.y;<a name="l00452"></a>00452 }<a name="l00453"></a>00453 finalCascade[j].exponent = <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a>(<a class="code" href="class_integer.html#e0d4d9975fb6ab7667aab6f7ab8612d2d10299fe0b190d3de927db776b8dc42d">Integer::POSITIVE</a>, 0, exponentWindows[i][j]);<a name="l00454"></a>00454 }<a name="l00455"></a>00455 results[i] = GeneralCascadeMultiplication(*<span class="keyword">this</span>, finalCascade.begin(), finalCascade.end());<a name="l00456"></a>00456 }<a name="l00457"></a>00457 }<a name="l00458"></a>00458 <a name="l00459"></a>00459 <a class="code" href="struct_e_c_p_point.html" title="Elliptical Curve Point.">ECP::Point</a> ECP::CascadeScalarMultiply(<span class="keyword">const</span> <a class="code" href="class_e_c_p.html#99c34a437007f32af4e6c4ae275358ea">Point</a> &P, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &k1, <span class="keyword">const</span> <a class="code" href="class_e_c_p.html#99c34a437007f32af4e6c4ae275358ea">Point</a> &Q, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &k2)<span class="keyword"> const</span><a name="l00460"></a>00460 <span class="keyword"></span>{<a name="l00461"></a>00461 <span class="keywordflow">if</span> (!<a class="code" href="class_e_c_p.html#e996fce212244df79b83a587317f7423">GetField</a>().IsMontgomeryRepresentation())<a name="l00462"></a>00462 {<a name="l00463"></a>00463 <a class="code" href="class_e_c_p.html" title="Elliptic Curve over GF(p), where p is prime.">ECP</a> ecpmr(*<span class="keyword">this</span>, <span class="keyword">true</span>);<a name="l00464"></a>00464 <span class="keyword">const</span> <a class="code" href="class_modular_arithmetic.html" title="ring of congruence classes modulo n">ModularArithmetic</a> &mr = ecpmr.GetField();<a name="l00465"></a>00465 <span class="keywordflow">return</span> FromMontgomery(mr, ecpmr.<a class="code" href="class_abstract_group.html#ca3e1ca578003aff2595cc8d73522894">CascadeScalarMultiply</a>(ToMontgomery(mr, P), k1, ToMontgomery(mr, Q), k2));<a name="l00466"></a>00466 }<a name="l00467"></a>00467 <span class="keywordflow">else</span><a name="l00468"></a>00468 <span class="keywordflow">return</span> <a class="code" href="class_abstract_group.html#ca3e1ca578003aff2595cc8d73522894">AbstractGroup<Point>::CascadeScalarMultiply</a>(P, k1, Q, k2);<a name="l00469"></a>00469 }<a name="l00470"></a>00470 <a name="l00471"></a>00471 NAMESPACE_END<a name="l00472"></a>00472 <a name="l00473"></a>00473 <span class="preprocessor">#endif</span></pre></div><hr size="1"><address style="text-align: right;"><small>Generated on Fri Jun 1 11:11:20 2007 for Crypto++ by <a href="http://www.doxygen.org/index.html"><img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.2 </small></address></body></html>⌨️ 快捷键说明
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