```
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```

```
#!html
<h1>modexp</h1>

<p>Modular exponentiation core for implementing public key algorithms such
as RSA, DH, ElGamal etc.</p>

<p>The core calculates the following function:</p>

<p>C = M ** e mod N</p>

<p>M is a message with a length of n bits
  e is the exponent with a length of m bits
  N is the modulus  with a length of n bits</p>

<p>The size n be one and up to and including 8192 bits in steps of 32
bits.</p>

<p>The size m be one and up to and including 8192 bits in steps of 32
bits.</p>

<p>The core has a 32-bit memory like interface, but provides status signals
to inform the system that a given operation has is done. Additionally,
any errors will also be asserted.</p>

<p>The core is written in Verilog 2001 and suitable for implementation in
FPGA and ASIC devices. No vendor specific macros are used in the code.</p>

<h2>Implementation details</h2>

<p>The core is iterative with 32-bit operands and not the fastest core on
the planet.</p>

<h2>Future developments</h2>

<ul>
<li><p>The core will perform blinding to protect against side channel
attacks.</p></li>
<li><p>Increased operands to 64-, 128-, or possibly even 256 bits for
increased performance.</p></li>
</ul>

<h2>FPGA-results</h2>

<h2>Altera Cyclone-V</h2>

<ul>
<li>203 registers</li>
<li>387 ALMs</li>
<li>106496 block memory bits</li>
<li>107 MHz</li>
</ul>

<h3>Xilinx Artix-7 100T</h3>

<ul>
<li>160 registers</li>
<li>565 LUTs</li>
<li>13 RAMB18E1 block memories</li>
<li>160 MHz</li>
</ul>

<h3>Xilinx Spartan-6 LX45</h3>

<ul>
<li>169 registers</li>
<li>589 LUTs</li>
<li>13 RAMB8BWER block memories</li>
<li>136 MHz</li>
</ul>

<h2>Status</h2>

<p><strong><em>(2015-04-27)</em></strong></p>

<p>Modexp simulation with exponent and modolus with up to 1280 bits
simulates. The auto test generation system works. Implementation in
different FPGA types and vendors works.</p>

<p><strong><em>(2015-04-23)</em></strong></p>

<p>The Montgomery multiplication module works. The Residue calculation
module works. Top level integration and debugging is onging. The core
does not yet work and there are dragons to be found.</p>

<p><strong><em>(2014-12-07)</em></strong></p>

<p>Renamed the core tom modexp from rsa to make it more clear that it
provides generic modular exponentiation, not RSA.</p>

<p><strong><em>(2014-10-01)</em></strong></p>

<p>Very early phase. Started to collect information and drawing some rough
ideas on paper.</p>
```

[[RepositoryIndex(format=table,glob=core/math/modexp)]]

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