A New Signature Scheme Based on Multiple Hard Number Theoretic Problems

<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">Notations</td><td align="left">Definition</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td align="left"><span style="width: 33.650002px;"><svg height="14.3875" id="M84" style="vertical-align:-3.25792pt" version="1.1" viewbox="0 0 33.650002 14.3875" width="33.650002" 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">M</tspan>
<tspan style="font-size: 8.75px; " x="7.7805281" y="0">U</tspan>
<tspan style="font-size: 8.75px; " x="14.099472" y="0">L</tspan>
</text>
</g>
</g>
</svg></span></td><td align="left">Time complexity for executing the modular multiplication</td></tr><tr><td align="left"><span style="width: 30.025px;"><svg height="14.2375" id="M85" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 30.025 14.2375" width="30.025" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<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">E</tspan>
<tspan style="font-size: 8.75px; " x="5.3474722" y="0">X</tspan>
<tspan style="font-size: 8.75px; " x="11.666416" y="0">P</tspan>
</text>
</g>
</g>
</svg></span></td><td align="left">Time complexity for executing the modular exponentiation</td></tr><tr><td align="left"><span style="width: 29.15px;"><svg height="14.3875" id="M86" style="vertical-align:-3.25792pt" version="1.1" viewbox="0 0 29.15 14.3875" width="29.15" 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">S</tspan>
<tspan style="font-size: 8.75px; " x="4.8661122" y="0">R</tspan>
<tspan style="font-size: 8.75px; " x="10.493648" y="0">T</tspan>
</text>
</g>
</g>
</svg></span></td><td align="left">Time complexity for executing the modular square<br/> root computation</td></tr><tr><td align="left"><span style="width: 28.7875px;"><svg height="14.3625" id="M87" style="vertical-align:-3.23158pt" version="1.1" viewbox="0 0 28.7875 14.3625" width="28.7875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.3625)">
<g transform="translate(72,-60.51)">
<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">I</tspan>
<tspan style="font-size: 8.75px; " x="2.9144161" y="0">N</tspan>
<tspan style="font-size: 8.75px; " x="9.2333603" y="0">V</tspan>
</text>
</g>
</g>
</svg></span></td><td align="left">Time complexity for executing the modular inverse computation</td></tr><tr><td align="left"><span style="width: 31.225px;"><svg height="14.3875" id="M88" style="vertical-align:-3.25792pt" version="1.1" viewbox="0 0 31.225 14.3875" width="31.225" 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">H</tspan>
<tspan style="font-size: 8.75px; " x="6.318944" y="0">A</tspan>
<tspan style="font-size: 8.75px; " x="12.637888" y="0">S</tspan>
</text>
</g>
</g>
</svg></span></td><td align="left">Time complexity for performing hash function</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

International Scholarly Research Notices

tab1

Table 1

Table 1: A New Signature Scheme Based on Multiple Hard Number Theoretic Problems 