Fast Parallel Molecular Algorithms for  DNA-Based Computation: Solving the Elliptic Curve  Discrete Logarithm Problem over <svg style="vertical-align:-3.186pt;width:64.987503px;" id="M1" height="20.275" version="1.1" viewBox="0 0 64.987503 20.275" width="64.987503" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(1.25,0,0,-1.25,0,20.275)"><g transform="translate(72,-55.78)"><text transform="matrix(1,0,0,-1,-71.95,59)"><tspan style="font-size: 17.93px; " x="0" y="0">𝐺</tspan><tspan style="font-size: 17.93px; " x="13.162822" y="0">𝐹</tspan><tspan style="font-size: 17.93px; " x="24.245417" y="0">(</tspan><tspan style="font-size: 17.93px; " x="30.217106" y="0">2</tspan></text><text transform="matrix(1,0,0,-1,-32.77,66.41)"><tspan style="font-size: 12.55px; " x="0" y="0">𝑛</tspan></text><text transform="matrix(1,0,0,-1,-26.03,59)"><tspan style="font-size: 17.93px; " x="0" y="0">)</tspan></text></g></g></svg>

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td align="left">Tube</td><td align="center">The result is generated by ParallelAdder</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td align="left"><span style="width: 14.8125px;"><svg height="14.3875" id="M143" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 14.8125 14.3875" width="14.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.3875)">
<g transform="translate(72,-60.49)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑇</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">0</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center">110001111, 010101111, 001111110, 100011111</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Result of tube <svg height="14.3875" id="M142" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 14.8125 14.3875" width="14.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.3875)">
<g transform="translate(72,-60.49)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑇</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">0</tspan>
</text>
</g>
</g>
</svg>.

BioMed Research International

tab1

Table 1

Table 1: Fast Parallel Molecular Algorithms for  DNA-Based Computation: Solving the Elliptic Curve  Discrete Logarithm Problem over <svg style="vertical-align:-3.186pt;width:64.987503px;" id="M1" height="20.275" version="1.1" viewBox="0 0 64.987503 20.275" width="64.987503" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(1.25,0,0,-1.25,0,20.275)"><g transform="translate(72,-55.78)"><text transform="matrix(1,0,0,-1,-71.95,59)"><tspan style="font-size: 17.93px; " x="0" y="0">𝐺</tspan><tspan style="font-size: 17.93px; " x="13.162822" y="0">𝐹</tspan><tspan style="font-size: 17.93px; " x="24.245417" y="0">(</tspan><tspan style="font-size: 17.93px; " x="30.217106" y="0">2</tspan></text><text transform="matrix(1,0,0,-1,-32.77,66.41)"><tspan style="font-size: 12.55px; " x="0" y="0">𝑛</tspan></text><text transform="matrix(1,0,0,-1,-26.03,59)"><tspan style="font-size: 17.93px; " x="0" y="0">)</tspan></text></g></g></svg> 

BioMed Research International

Fast Parallel Molecular Algorithms for DNA-Based Computation: Solving the Elliptic Curve Discrete Logarithm Problem over 𝐺𝐹(2𝑛)

Table 1

Fast Parallel Molecular Algorithms for DNA-Based Computation: Solving the Elliptic Curve Discrete Logarithm Problem over