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<li class="navelem"><a class="el" href="dir_df7310d1a865926cc859bcfb1880083f.html">include</a></li> </ul>
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<a href="#define-members">Macros</a> &#124;
<a href="#func-members">Functions</a> </div>
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<div class="title">ff_2048.h File Reference</div> </div>
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<p>FF Header File.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &quot;<a class="el" href="big__1024__58_8h_source.html">big_1024_58.h</a>&quot;</code><br />
<code>#include &quot;<a class="el" href="config__ff__2048_8h_source.html">config_ff_2048.h</a>&quot;</code><br />
</div>
<p><a href="ff__2048_8h_source.html">Go to the source code of this file.</a></p>
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Macros</h2></td></tr>
<tr class="memitem:a227e21d0b00faf73e541ec680ea433cc"><td class="memItemLeft" align="right" valign="top">#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a227e21d0b00faf73e541ec680ea433cc">HFLEN_2048</a>&#160;&#160;&#160;(<a class="el" href="config__ff__2048_8h.html#a9d97b1d9ded0164b99640480ddac4f1e">FFLEN_2048</a>/2)</td></tr>
<tr class="separator:a227e21d0b00faf73e541ec680ea433cc"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad1dbd4d4757d964e79ba37b306d7e55c"><td class="memItemLeft" align="right" valign="top">#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#ad1dbd4d4757d964e79ba37b306d7e55c">P_MBITS_2048</a>&#160;&#160;&#160;(<a class="el" href="config__big__1024__58_8h.html#a9cbbac7724e17efc1d82ed6981378112">MODBYTES_1024_58</a>*8)</td></tr>
<tr class="separator:ad1dbd4d4757d964e79ba37b306d7e55c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a40c3a14228a7e89dae27ebad9d92953b"><td class="memItemLeft" align="right" valign="top">#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a40c3a14228a7e89dae27ebad9d92953b">P_TBITS_2048</a>&#160;&#160;&#160;(<a class="el" href="ff__2048_8h.html#ad1dbd4d4757d964e79ba37b306d7e55c">P_MBITS_2048</a>%<a class="el" href="config__big__1024__58_8h.html#a0fdac7cd24ebe3f1dd4d890f201cad7c">BASEBITS_1024_58</a>)</td></tr>
<tr class="separator:a40c3a14228a7e89dae27ebad9d92953b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a48cd404e88e86911f940a7f7f1048db6"><td class="memItemLeft" align="right" valign="top">#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a48cd404e88e86911f940a7f7f1048db6">P_EXCESS_2048</a>(a)&#160;&#160;&#160;(((a[<a class="el" href="big__1024__58_8h.html#a0a8882f5fa3bf70c96145d7a5a162e37">NLEN_1024_58</a>-1])&gt;&gt;(<a class="el" href="ff__2048_8h.html#a40c3a14228a7e89dae27ebad9d92953b">P_TBITS_2048</a>))+1)</td></tr>
<tr class="separator:a48cd404e88e86911f940a7f7f1048db6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:acccacd653e03a0ab4188413033799714"><td class="memItemLeft" align="right" valign="top">#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#acccacd653e03a0ab4188413033799714">P_FEXCESS_2048</a>&#160;&#160;&#160;((<a class="el" href="arch_8h.html#a0dd4b8ab353c587b22c6acb0809323aa">chunk</a>)1&lt;&lt;(<a class="el" href="config__big__1024__58_8h.html#a0fdac7cd24ebe3f1dd4d890f201cad7c">BASEBITS_1024_58</a>*<a class="el" href="big__1024__58_8h.html#a0a8882f5fa3bf70c96145d7a5a162e37">NLEN_1024_58</a>-<a class="el" href="ff__2048_8h.html#ad1dbd4d4757d964e79ba37b306d7e55c">P_MBITS_2048</a>-1))</td></tr>
<tr class="separator:acccacd653e03a0ab4188413033799714"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a100f16a442d30fae06c81b5071fbc9e6"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a100f16a442d30fae06c81b5071fbc9e6">FF_2048_copy</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *y, int n)</td></tr>
<tr class="memdesc:a100f16a442d30fae06c81b5071fbc9e6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Copy one FF element of given length to another. <a href="#a100f16a442d30fae06c81b5071fbc9e6">More...</a><br /></td></tr>
<tr class="separator:a100f16a442d30fae06c81b5071fbc9e6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:acc12c9e475768bc1a9960aa51903ffd3"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#acc12c9e475768bc1a9960aa51903ffd3">FF_2048_init</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="arch_8h.html#af31fcb3b74c4bcf6507f62d801277492">sign32</a> m, int n)</td></tr>
<tr class="memdesc:acc12c9e475768bc1a9960aa51903ffd3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Initialize an FF element of given length from a 32-bit integer m. <a href="#acc12c9e475768bc1a9960aa51903ffd3">More...</a><br /></td></tr>
<tr class="separator:acc12c9e475768bc1a9960aa51903ffd3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9a3486518d9dcf2ef743a6dd2aa56336"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a9a3486518d9dcf2ef743a6dd2aa56336">FF_2048_zero</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, int n)</td></tr>
<tr class="memdesc:a9a3486518d9dcf2ef743a6dd2aa56336"><td class="mdescLeft">&#160;</td><td class="mdescRight">Set FF element of given size to zero. <a href="#a9a3486518d9dcf2ef743a6dd2aa56336">More...</a><br /></td></tr>
<tr class="separator:a9a3486518d9dcf2ef743a6dd2aa56336"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab79fd4f6686b2fe714c3d33f20f4c48a"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#ab79fd4f6686b2fe714c3d33f20f4c48a">FF_2048_iszilch</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, int n)</td></tr>
<tr class="memdesc:ab79fd4f6686b2fe714c3d33f20f4c48a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Tests for FF element equal to zero. <a href="#ab79fd4f6686b2fe714c3d33f20f4c48a">More...</a><br /></td></tr>
<tr class="separator:ab79fd4f6686b2fe714c3d33f20f4c48a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0445b77f49dbfb68babf95a6cd2ecbea"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a0445b77f49dbfb68babf95a6cd2ecbea">FF_2048_parity</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x)</td></tr>
<tr class="memdesc:a0445b77f49dbfb68babf95a6cd2ecbea"><td class="mdescLeft">&#160;</td><td class="mdescRight">return parity of an FF, that is the least significant bit <a href="#a0445b77f49dbfb68babf95a6cd2ecbea">More...</a><br /></td></tr>
<tr class="separator:a0445b77f49dbfb68babf95a6cd2ecbea"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5e75fed78290b43d0b440031b12ebf89"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a5e75fed78290b43d0b440031b12ebf89">FF_2048_lastbits</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, int m)</td></tr>
<tr class="memdesc:a5e75fed78290b43d0b440031b12ebf89"><td class="mdescLeft">&#160;</td><td class="mdescRight">return least significant m bits of an FF <a href="#a5e75fed78290b43d0b440031b12ebf89">More...</a><br /></td></tr>
<tr class="separator:a5e75fed78290b43d0b440031b12ebf89"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af59e05d4afd7575e07300199a60a1484"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#af59e05d4afd7575e07300199a60a1484">FF_2048_one</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, int n)</td></tr>
<tr class="memdesc:af59e05d4afd7575e07300199a60a1484"><td class="mdescLeft">&#160;</td><td class="mdescRight">Set FF element of given size to unity. <a href="#af59e05d4afd7575e07300199a60a1484">More...</a><br /></td></tr>
<tr class="separator:af59e05d4afd7575e07300199a60a1484"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a7375ad720811c0f9678492ea4da08549"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a7375ad720811c0f9678492ea4da08549">FF_2048_comp</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *y, int n)</td></tr>
<tr class="memdesc:a7375ad720811c0f9678492ea4da08549"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compares two FF numbers. Inputs must be normalised externally. <a href="#a7375ad720811c0f9678492ea4da08549">More...</a><br /></td></tr>
<tr class="separator:a7375ad720811c0f9678492ea4da08549"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a99bc0c23aa9bf3a1d8356cd1dcd838e1"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a99bc0c23aa9bf3a1d8356cd1dcd838e1">FF_2048_add</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *y, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *z, int n)</td></tr>
<tr class="memdesc:a99bc0c23aa9bf3a1d8356cd1dcd838e1"><td class="mdescLeft">&#160;</td><td class="mdescRight">addition of two FFs <a href="#a99bc0c23aa9bf3a1d8356cd1dcd838e1">More...</a><br /></td></tr>
<tr class="separator:a99bc0c23aa9bf3a1d8356cd1dcd838e1"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aebafa634bb7c45532f0cc30b005fece7"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#aebafa634bb7c45532f0cc30b005fece7">FF_2048_sub</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *y, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *z, int n)</td></tr>
<tr class="memdesc:aebafa634bb7c45532f0cc30b005fece7"><td class="mdescLeft">&#160;</td><td class="mdescRight">subtraction of two FFs <a href="#aebafa634bb7c45532f0cc30b005fece7">More...</a><br /></td></tr>
<tr class="separator:aebafa634bb7c45532f0cc30b005fece7"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a45a6fb55cb8695885e92427b95d93b0f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a45a6fb55cb8695885e92427b95d93b0f">FF_2048_inc</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, int m, int n)</td></tr>
<tr class="memdesc:a45a6fb55cb8695885e92427b95d93b0f"><td class="mdescLeft">&#160;</td><td class="mdescRight">increment an FF by an integer,and normalise <a href="#a45a6fb55cb8695885e92427b95d93b0f">More...</a><br /></td></tr>
<tr class="separator:a45a6fb55cb8695885e92427b95d93b0f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a08c90508ecc6c2229143ec0de481888f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a08c90508ecc6c2229143ec0de481888f">FF_2048_dec</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, int m, int n)</td></tr>
<tr class="memdesc:a08c90508ecc6c2229143ec0de481888f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Decrement an FF by an integer,and normalise. <a href="#a08c90508ecc6c2229143ec0de481888f">More...</a><br /></td></tr>
<tr class="separator:a08c90508ecc6c2229143ec0de481888f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a84c276a9cb2fb6b8c88677c8a5241174"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a84c276a9cb2fb6b8c88677c8a5241174">FF_2048_norm</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, int n)</td></tr>
<tr class="memdesc:a84c276a9cb2fb6b8c88677c8a5241174"><td class="mdescLeft">&#160;</td><td class="mdescRight">Normalises the components of an FF. <a href="#a84c276a9cb2fb6b8c88677c8a5241174">More...</a><br /></td></tr>
<tr class="separator:a84c276a9cb2fb6b8c88677c8a5241174"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a175d8db0f1789c940961189bb00dc009"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a175d8db0f1789c940961189bb00dc009">FF_2048_shl</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, int n)</td></tr>
<tr class="memdesc:a175d8db0f1789c940961189bb00dc009"><td class="mdescLeft">&#160;</td><td class="mdescRight">Shift left an FF by 1 bit. <a href="#a175d8db0f1789c940961189bb00dc009">More...</a><br /></td></tr>
<tr class="separator:a175d8db0f1789c940961189bb00dc009"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a85f56b1a48a3867295e4af39275ca836"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a85f56b1a48a3867295e4af39275ca836">FF_2048_shr</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, int n)</td></tr>
<tr class="memdesc:a85f56b1a48a3867295e4af39275ca836"><td class="mdescLeft">&#160;</td><td class="mdescRight">Shift right an FF by 1 bit. <a href="#a85f56b1a48a3867295e4af39275ca836">More...</a><br /></td></tr>
<tr class="separator:a85f56b1a48a3867295e4af39275ca836"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8011729411cf198d0a19a0a1ffa17ae1"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a8011729411cf198d0a19a0a1ffa17ae1">FF_2048_output</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, int n)</td></tr>
<tr class="memdesc:a8011729411cf198d0a19a0a1ffa17ae1"><td class="mdescLeft">&#160;</td><td class="mdescRight">Formats and outputs an FF to the console. <a href="#a8011729411cf198d0a19a0a1ffa17ae1">More...</a><br /></td></tr>
<tr class="separator:a8011729411cf198d0a19a0a1ffa17ae1"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0fa3a98953b3f941c4a1d77811c663da"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a0fa3a98953b3f941c4a1d77811c663da">FF_2048_rawoutput</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, int n)</td></tr>
<tr class="memdesc:a0fa3a98953b3f941c4a1d77811c663da"><td class="mdescLeft">&#160;</td><td class="mdescRight">Formats and outputs an FF to the console, in raw form. <a href="#a0fa3a98953b3f941c4a1d77811c663da">More...</a><br /></td></tr>
<tr class="separator:a0fa3a98953b3f941c4a1d77811c663da"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a7cea17d94848af54dc71659f4aa78121"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a7cea17d94848af54dc71659f4aa78121">FF_2048_toOctet</a> (<a class="el" href="structoctet.html">octet</a> *S, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, int n)</td></tr>
<tr class="memdesc:a7cea17d94848af54dc71659f4aa78121"><td class="mdescLeft">&#160;</td><td class="mdescRight">Formats and outputs an FF instance to an octet string. <a href="#a7cea17d94848af54dc71659f4aa78121">More...</a><br /></td></tr>
<tr class="separator:a7cea17d94848af54dc71659f4aa78121"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:acf36351fa465903335db78c4d1539fc6"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#acf36351fa465903335db78c4d1539fc6">FF_2048_fromOctet</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="structoctet.html">octet</a> *S, int n)</td></tr>
<tr class="memdesc:acf36351fa465903335db78c4d1539fc6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Populates an FF instance from an octet string. <a href="#acf36351fa465903335db78c4d1539fc6">More...</a><br /></td></tr>
<tr class="separator:acf36351fa465903335db78c4d1539fc6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ac5970b0360b38a0c3bde877abac7fe90"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#ac5970b0360b38a0c3bde877abac7fe90">FF_2048_mul</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *y, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *z, int n)</td></tr>
<tr class="memdesc:ac5970b0360b38a0c3bde877abac7fe90"><td class="mdescLeft">&#160;</td><td class="mdescRight">Multiplication of two FFs. <a href="#ac5970b0360b38a0c3bde877abac7fe90">More...</a><br /></td></tr>
<tr class="separator:ac5970b0360b38a0c3bde877abac7fe90"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a7ed651a772be1e7c644d4153e67574f3"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a7ed651a772be1e7c644d4153e67574f3">FF_2048_mod</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *m, int n)</td></tr>
<tr class="memdesc:a7ed651a772be1e7c644d4153e67574f3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Reduce FF mod a modulus. <a href="#a7ed651a772be1e7c644d4153e67574f3">More...</a><br /></td></tr>
<tr class="separator:a7ed651a772be1e7c644d4153e67574f3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a2ba04edfe1eb1b4e925598bebf135b8f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a2ba04edfe1eb1b4e925598bebf135b8f">FF_2048_sqr</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *y, int n)</td></tr>
<tr class="memdesc:a2ba04edfe1eb1b4e925598bebf135b8f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Square an FF. <a href="#a2ba04edfe1eb1b4e925598bebf135b8f">More...</a><br /></td></tr>
<tr class="separator:a2ba04edfe1eb1b4e925598bebf135b8f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8b287a310c335b1e3a8693381d112eaf"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a8b287a310c335b1e3a8693381d112eaf">FF_2048_dmod</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *y, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *z, int n)</td></tr>
<tr class="memdesc:a8b287a310c335b1e3a8693381d112eaf"><td class="mdescLeft">&#160;</td><td class="mdescRight">Reduces a double-length FF with respect to a given modulus. <a href="#a8b287a310c335b1e3a8693381d112eaf">More...</a><br /></td></tr>
<tr class="separator:a8b287a310c335b1e3a8693381d112eaf"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa4e3c92baa3179198a3cdefc5b61eac9"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#aa4e3c92baa3179198a3cdefc5b61eac9">FF_2048_invmodp</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *y, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *z, int n)</td></tr>
<tr class="memdesc:aa4e3c92baa3179198a3cdefc5b61eac9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Invert an FF mod a prime modulus. <a href="#aa4e3c92baa3179198a3cdefc5b61eac9">More...</a><br /></td></tr>
<tr class="separator:aa4e3c92baa3179198a3cdefc5b61eac9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:abda74d9b71138e17a7fbe7086426c3e7"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#abda74d9b71138e17a7fbe7086426c3e7">FF_2048_random</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="structcsprng.html">csprng</a> *R, int n)</td></tr>
<tr class="memdesc:abda74d9b71138e17a7fbe7086426c3e7"><td class="mdescLeft">&#160;</td><td class="mdescRight">Create an FF from a random number generator. <a href="#abda74d9b71138e17a7fbe7086426c3e7">More...</a><br /></td></tr>
<tr class="separator:abda74d9b71138e17a7fbe7086426c3e7"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a7cfdc4c363575059d802b91713b03737"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a7cfdc4c363575059d802b91713b03737">FF_2048_randomnum</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *y, <a class="el" href="structcsprng.html">csprng</a> *R, int n)</td></tr>
<tr class="memdesc:a7cfdc4c363575059d802b91713b03737"><td class="mdescLeft">&#160;</td><td class="mdescRight">Create a random FF less than a given modulus from a random number generator. <a href="#a7cfdc4c363575059d802b91713b03737">More...</a><br /></td></tr>
<tr class="separator:a7cfdc4c363575059d802b91713b03737"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a2789a44182bc8d1fb91fd048a23361b9"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a2789a44182bc8d1fb91fd048a23361b9">FF_2048_skpow</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *r, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *e, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *m, int n)</td></tr>
<tr class="memdesc:a2789a44182bc8d1fb91fd048a23361b9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculate r=x^e mod m, side channel resistant. <a href="#a2789a44182bc8d1fb91fd048a23361b9">More...</a><br /></td></tr>
<tr class="separator:a2789a44182bc8d1fb91fd048a23361b9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:acadc23a6f6c053b971d7afaf121d7196"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#acadc23a6f6c053b971d7afaf121d7196">FF_2048_skspow</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *r, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> e, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *m, int n)</td></tr>
<tr class="memdesc:acadc23a6f6c053b971d7afaf121d7196"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculate r=x^e mod m, side channel resistant. <a href="#acadc23a6f6c053b971d7afaf121d7196">More...</a><br /></td></tr>
<tr class="separator:acadc23a6f6c053b971d7afaf121d7196"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8b87d4ad585cbfaaeadca3d586ffb05a"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a8b87d4ad585cbfaaeadca3d586ffb05a">FF_2048_power</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *r, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, int e, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *m, int n)</td></tr>
<tr class="memdesc:a8b87d4ad585cbfaaeadca3d586ffb05a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculate r=x^e mod m. <a href="#a8b87d4ad585cbfaaeadca3d586ffb05a">More...</a><br /></td></tr>
<tr class="separator:a8b87d4ad585cbfaaeadca3d586ffb05a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a7764e294274140465a4676717677f6b6"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a7764e294274140465a4676717677f6b6">FF_2048_pow</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *r, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *e, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *m, int n)</td></tr>
<tr class="memdesc:a7764e294274140465a4676717677f6b6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculate r=x^e mod m. <a href="#a7764e294274140465a4676717677f6b6">More...</a><br /></td></tr>
<tr class="separator:a7764e294274140465a4676717677f6b6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a261bad7b5b39fd6eb3d98e3c9ae292de"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a261bad7b5b39fd6eb3d98e3c9ae292de">FF_2048_cfactor</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="arch_8h.html#af31fcb3b74c4bcf6507f62d801277492">sign32</a> s, int n)</td></tr>
<tr class="memdesc:a261bad7b5b39fd6eb3d98e3c9ae292de"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test if an FF has factor in common with integer s. <a href="#a261bad7b5b39fd6eb3d98e3c9ae292de">More...</a><br /></td></tr>
<tr class="separator:a261bad7b5b39fd6eb3d98e3c9ae292de"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9ede4163e174ca5564b724d5d50c3242"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#a9ede4163e174ca5564b724d5d50c3242">FF_2048_prime</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="structcsprng.html">csprng</a> *R, int n)</td></tr>
<tr class="memdesc:a9ede4163e174ca5564b724d5d50c3242"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test if an FF is prime. <a href="#a9ede4163e174ca5564b724d5d50c3242">More...</a><br /></td></tr>
<tr class="separator:a9ede4163e174ca5564b724d5d50c3242"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ace63d2e10c65cb9446e496d4355bf3be"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="ff__2048_8h.html#ace63d2e10c65cb9446e496d4355bf3be">FF_2048_pow2</a> (<a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *r, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *x, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> e, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *y, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> f, <a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *m, int n)</td></tr>
<tr class="memdesc:ace63d2e10c65cb9446e496d4355bf3be"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculate r=x^e.y^f mod m. <a href="#ace63d2e10c65cb9446e496d4355bf3be">More...</a><br /></td></tr>
<tr class="separator:ace63d2e10c65cb9446e496d4355bf3be"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><dl class="section author"><dt>Author</dt><dd>Mike Scott </dd></dl>
</div><h2 class="groupheader">Macro Definition Documentation</h2>
<a id="a227e21d0b00faf73e541ec680ea433cc"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a227e21d0b00faf73e541ec680ea433cc">&#9670;&nbsp;</a></span>HFLEN_2048</h2>
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<td class="memname">#define HFLEN_2048&#160;&#160;&#160;(<a class="el" href="config__ff__2048_8h.html#a9d97b1d9ded0164b99640480ddac4f1e">FFLEN_2048</a>/2)</td>
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</div><div class="memdoc">
<p>Useful for half-size RSA private key operations </p>
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</div>
<a id="a48cd404e88e86911f940a7f7f1048db6"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a48cd404e88e86911f940a7f7f1048db6">&#9670;&nbsp;</a></span>P_EXCESS_2048</h2>
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<td class="memname">#define P_EXCESS_2048</td>
<td>(</td>
<td class="paramtype">&#160;</td>
<td class="paramname">a</td><td>)</td>
<td>&#160;&#160;&#160;(((a[<a class="el" href="big__1024__58_8h.html#a0a8882f5fa3bf70c96145d7a5a162e37">NLEN_1024_58</a>-1])&gt;&gt;(<a class="el" href="ff__2048_8h.html#a40c3a14228a7e89dae27ebad9d92953b">P_TBITS_2048</a>))+1)</td>
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</div><div class="memdoc">
<p>TODO </p>
</div>
</div>
<a id="acccacd653e03a0ab4188413033799714"></a>
<h2 class="memtitle"><span class="permalink"><a href="#acccacd653e03a0ab4188413033799714">&#9670;&nbsp;</a></span>P_FEXCESS_2048</h2>
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<td class="memname">#define P_FEXCESS_2048&#160;&#160;&#160;((<a class="el" href="arch_8h.html#a0dd4b8ab353c587b22c6acb0809323aa">chunk</a>)1&lt;&lt;(<a class="el" href="config__big__1024__58_8h.html#a0fdac7cd24ebe3f1dd4d890f201cad7c">BASEBITS_1024_58</a>*<a class="el" href="big__1024__58_8h.html#a0a8882f5fa3bf70c96145d7a5a162e37">NLEN_1024_58</a>-<a class="el" href="ff__2048_8h.html#ad1dbd4d4757d964e79ba37b306d7e55c">P_MBITS_2048</a>-1))</td>
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</div><div class="memdoc">
<p>TODO </p>
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</div>
<a id="ad1dbd4d4757d964e79ba37b306d7e55c"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ad1dbd4d4757d964e79ba37b306d7e55c">&#9670;&nbsp;</a></span>P_MBITS_2048</h2>
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<td class="memname">#define P_MBITS_2048&#160;&#160;&#160;(<a class="el" href="config__big__1024__58_8h.html#a9cbbac7724e17efc1d82ed6981378112">MODBYTES_1024_58</a>*8)</td>
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<p>Number of bits in modulus </p>
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<a id="a40c3a14228a7e89dae27ebad9d92953b"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a40c3a14228a7e89dae27ebad9d92953b">&#9670;&nbsp;</a></span>P_TBITS_2048</h2>
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<td class="memname">#define P_TBITS_2048&#160;&#160;&#160;(<a class="el" href="ff__2048_8h.html#ad1dbd4d4757d964e79ba37b306d7e55c">P_MBITS_2048</a>%<a class="el" href="config__big__1024__58_8h.html#a0fdac7cd24ebe3f1dd4d890f201cad7c">BASEBITS_1024_58</a>)</td>
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<p>TODO </p>
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<h2 class="groupheader">Function Documentation</h2>
<a id="a99bc0c23aa9bf3a1d8356cd1dcd838e1"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a99bc0c23aa9bf3a1d8356cd1dcd838e1">&#9670;&nbsp;</a></span>FF_2048_add()</h2>
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<td class="memname">void FF_2048_add </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>y</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>z</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
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<td></td>
<td>)</td>
<td></td><td></td>
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<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance, on exit = y+z </td></tr>
<tr><td class="paramname">y</td><td>FF instance </td></tr>
<tr><td class="paramname">z</td><td>FF instance </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a261bad7b5b39fd6eb3d98e3c9ae292de"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a261bad7b5b39fd6eb3d98e3c9ae292de">&#9670;&nbsp;</a></span>FF_2048_cfactor()</h2>
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<td class="memname">int FF_2048_cfactor </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="arch_8h.html#af31fcb3b74c4bcf6507f62d801277492">sign32</a>&#160;</td>
<td class="paramname"><em>s</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance to be tested </td></tr>
<tr><td class="paramname">s</td><td>the supplied integer </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>1 if gcd(x,s)!=1, else return 0 </dd></dl>
</div>
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<a id="a7375ad720811c0f9678492ea4da08549"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a7375ad720811c0f9678492ea4da08549">&#9670;&nbsp;</a></span>FF_2048_comp()</h2>
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<td class="memname">int FF_2048_comp </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>y</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
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<td></td>
<td>)</td>
<td></td><td></td>
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<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>first FF number to be compared </td></tr>
<tr><td class="paramname">y</td><td>second FF number to be compared </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>-1 is x&lt;y, 0 if x=y, 1 if x&gt;y </dd></dl>
</div>
</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a100f16a442d30fae06c81b5071fbc9e6">&#9670;&nbsp;</a></span>FF_2048_copy()</h2>
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<td class="memname">void FF_2048_copy </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>y</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
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<td></td>
<td>)</td>
<td></td><td></td>
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<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance to be copied to, on exit = y </td></tr>
<tr><td class="paramname">y</td><td>FF instance to be copied from </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a08c90508ecc6c2229143ec0de481888f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a08c90508ecc6c2229143ec0de481888f">&#9670;&nbsp;</a></span>FF_2048_dec()</h2>
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<td class="memname">void FF_2048_dec </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>m</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
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<td></td>
<td>)</td>
<td></td><td></td>
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<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance, on exit = x-m </td></tr>
<tr><td class="paramname">m</td><td>an integer to be subtracted from x </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
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<a id="a8b287a310c335b1e3a8693381d112eaf"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a8b287a310c335b1e3a8693381d112eaf">&#9670;&nbsp;</a></span>FF_2048_dmod()</h2>
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<td class="memname">void FF_2048_dmod </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>y</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>z</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
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<td></td>
<td>)</td>
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<p>This is slow </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance, on exit = y mod z </td></tr>
<tr><td class="paramname">y</td><td>FF instance, of double length 2*n </td></tr>
<tr><td class="paramname">z</td><td>FF modulus </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="acf36351fa465903335db78c4d1539fc6"></a>
<h2 class="memtitle"><span class="permalink"><a href="#acf36351fa465903335db78c4d1539fc6">&#9670;&nbsp;</a></span>FF_2048_fromOctet()</h2>
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<td class="memname">void FF_2048_fromOctet </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structoctet.html">octet</a> *&#160;</td>
<td class="paramname"><em>S</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
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<td>)</td>
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<p>Creates FF from big-endian base 256 form. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance to be created from an octet string </td></tr>
<tr><td class="paramname">S</td><td>input octet string </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a45a6fb55cb8695885e92427b95d93b0f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a45a6fb55cb8695885e92427b95d93b0f">&#9670;&nbsp;</a></span>FF_2048_inc()</h2>
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<td class="memname">void FF_2048_inc </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>m</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance, on exit = x+m </td></tr>
<tr><td class="paramname">m</td><td>an integer to be added to x </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="acc12c9e475768bc1a9960aa51903ffd3"></a>
<h2 class="memtitle"><span class="permalink"><a href="#acc12c9e475768bc1a9960aa51903ffd3">&#9670;&nbsp;</a></span>FF_2048_init()</h2>
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<td class="memname">void FF_2048_init </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="arch_8h.html#af31fcb3b74c4bcf6507f62d801277492">sign32</a>&#160;</td>
<td class="paramname"><em>m</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
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<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance to be copied to, on exit = m </td></tr>
<tr><td class="paramname">m</td><td>integer </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="aa4e3c92baa3179198a3cdefc5b61eac9"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aa4e3c92baa3179198a3cdefc5b61eac9">&#9670;&nbsp;</a></span>FF_2048_invmodp()</h2>
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<td class="memname">void FF_2048_invmodp </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>y</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>z</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
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<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
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<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance, on exit = 1/y mod z </td></tr>
<tr><td class="paramname">y</td><td>FF instance </td></tr>
<tr><td class="paramname">z</td><td>FF prime modulus </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="ab79fd4f6686b2fe714c3d33f20f4c48a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ab79fd4f6686b2fe714c3d33f20f4c48a">&#9670;&nbsp;</a></span>FF_2048_iszilch()</h2>
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<td class="memname">int FF_2048_iszilch </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF number to be tested </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>1 if zero, else returns 0 </dd></dl>
</div>
</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a5e75fed78290b43d0b440031b12ebf89">&#9670;&nbsp;</a></span>FF_2048_lastbits()</h2>
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<td class="memname">int FF_2048_lastbits </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>m</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF number </td></tr>
<tr><td class="paramname">m</td><td>number of bits to return. Assumed to be less than BASEBITS. </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>least significant n bits as an integer </dd></dl>
</div>
</div>
<a id="a7ed651a772be1e7c644d4153e67574f3"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a7ed651a772be1e7c644d4153e67574f3">&#9670;&nbsp;</a></span>FF_2048_mod()</h2>
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<td class="memname">void FF_2048_mod </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>This is slow </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance to be reduced mod m - on exit = x mod m </td></tr>
<tr><td class="paramname">m</td><td>FF modulus </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="ac5970b0360b38a0c3bde877abac7fe90"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ac5970b0360b38a0c3bde877abac7fe90">&#9670;&nbsp;</a></span>FF_2048_mul()</h2>
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<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void FF_2048_mul </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>y</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>z</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Uses Karatsuba method internally </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance, on exit = y*z </td></tr>
<tr><td class="paramname">y</td><td>FF instance </td></tr>
<tr><td class="paramname">z</td><td>FF instance </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a84c276a9cb2fb6b8c88677c8a5241174"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a84c276a9cb2fb6b8c88677c8a5241174">&#9670;&nbsp;</a></span>FF_2048_norm()</h2>
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<td class="memname">void FF_2048_norm </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance to be normalised </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="af59e05d4afd7575e07300199a60a1484"></a>
<h2 class="memtitle"><span class="permalink"><a href="#af59e05d4afd7575e07300199a60a1484">&#9670;&nbsp;</a></span>FF_2048_one()</h2>
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<td class="memname">void FF_2048_one </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance to be set to unity </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a8011729411cf198d0a19a0a1ffa17ae1"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a8011729411cf198d0a19a0a1ffa17ae1">&#9670;&nbsp;</a></span>FF_2048_output()</h2>
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<td class="memname">void FF_2048_output </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance to be printed </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a0445b77f49dbfb68babf95a6cd2ecbea"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a0445b77f49dbfb68babf95a6cd2ecbea">&#9670;&nbsp;</a></span>FF_2048_parity()</h2>
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<td class="memname">int FF_2048_parity </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF number </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>0 or 1 </dd></dl>
</div>
</div>
<a id="a7764e294274140465a4676717677f6b6"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a7764e294274140465a4676717677f6b6">&#9670;&nbsp;</a></span>FF_2048_pow()</h2>
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<td class="memname">void FF_2048_pow </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>r</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>e</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">r</td><td>FF instance, on exit = x^e mod p </td></tr>
<tr><td class="paramname">x</td><td>FF instance </td></tr>
<tr><td class="paramname">e</td><td>FF exponent </td></tr>
<tr><td class="paramname">m</td><td>FF modulus </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="ace63d2e10c65cb9446e496d4355bf3be"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ace63d2e10c65cb9446e496d4355bf3be">&#9670;&nbsp;</a></span>FF_2048_pow2()</h2>
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<div class="memproto">
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<td class="memname">void FF_2048_pow2 </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>r</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a>&#160;</td>
<td class="paramname"><em>e</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>y</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a>&#160;</td>
<td class="paramname"><em>f</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">r</td><td>FF instance, on exit = x^e.y^f mod p </td></tr>
<tr><td class="paramname">x</td><td>FF instance </td></tr>
<tr><td class="paramname">e</td><td>BIG exponent </td></tr>
<tr><td class="paramname">y</td><td>FF instance </td></tr>
<tr><td class="paramname">f</td><td>BIG exponent </td></tr>
<tr><td class="paramname">m</td><td>FF modulus </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a8b87d4ad585cbfaaeadca3d586ffb05a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a8b87d4ad585cbfaaeadca3d586ffb05a">&#9670;&nbsp;</a></span>FF_2048_power()</h2>
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<td class="memname">void FF_2048_power </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>r</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>e</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>For very short integer exponent </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">r</td><td>FF instance, on exit = x^e mod p </td></tr>
<tr><td class="paramname">x</td><td>FF instance </td></tr>
<tr><td class="paramname">e</td><td>integer exponent </td></tr>
<tr><td class="paramname">m</td><td>FF modulus </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a9ede4163e174ca5564b724d5d50c3242"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a9ede4163e174ca5564b724d5d50c3242">&#9670;&nbsp;</a></span>FF_2048_prime()</h2>
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<td class="memname">int FF_2048_prime </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structcsprng.html">csprng</a> *&#160;</td>
<td class="paramname"><em>R</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Uses Miller-Rabin Method </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance to be tested </td></tr>
<tr><td class="paramname">R</td><td>an instance of a Cryptographically Secure Random Number Generator </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>1 if x is (almost certainly) prime, else return 0 </dd></dl>
</div>
</div>
<a id="abda74d9b71138e17a7fbe7086426c3e7"></a>
<h2 class="memtitle"><span class="permalink"><a href="#abda74d9b71138e17a7fbe7086426c3e7">&#9670;&nbsp;</a></span>FF_2048_random()</h2>
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<div class="memproto">
<table class="memname">
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<td class="memname">void FF_2048_random </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structcsprng.html">csprng</a> *&#160;</td>
<td class="paramname"><em>R</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance, on exit x is a random number of length n BIGs with most significant bit a 1 </td></tr>
<tr><td class="paramname">R</td><td>an instance of a Cryptographically Secure Random Number Generator </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a7cfdc4c363575059d802b91713b03737"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a7cfdc4c363575059d802b91713b03737">&#9670;&nbsp;</a></span>FF_2048_randomnum()</h2>
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<div class="memproto">
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<td class="memname">void FF_2048_randomnum </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>y</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structcsprng.html">csprng</a> *&#160;</td>
<td class="paramname"><em>R</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance, on exit x is a random number &lt; y </td></tr>
<tr><td class="paramname">y</td><td>FF instance, the modulus </td></tr>
<tr><td class="paramname">R</td><td>an instance of a Cryptographically Secure Random Number Generator </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a0fa3a98953b3f941c4a1d77811c663da"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a0fa3a98953b3f941c4a1d77811c663da">&#9670;&nbsp;</a></span>FF_2048_rawoutput()</h2>
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<div class="memproto">
<table class="memname">
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<td class="memname">void FF_2048_rawoutput </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance to be printed </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a175d8db0f1789c940961189bb00dc009"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a175d8db0f1789c940961189bb00dc009">&#9670;&nbsp;</a></span>FF_2048_shl()</h2>
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<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void FF_2048_shl </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance to be shifted left </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a85f56b1a48a3867295e4af39275ca836"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a85f56b1a48a3867295e4af39275ca836">&#9670;&nbsp;</a></span>FF_2048_shr()</h2>
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<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void FF_2048_shr </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance to be shifted right </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a2789a44182bc8d1fb91fd048a23361b9"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a2789a44182bc8d1fb91fd048a23361b9">&#9670;&nbsp;</a></span>FF_2048_skpow()</h2>
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<div class="memproto">
<table class="memname">
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<td class="memname">void FF_2048_skpow </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>r</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>e</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">r</td><td>FF instance, on exit = x^e mod p </td></tr>
<tr><td class="paramname">x</td><td>FF instance </td></tr>
<tr><td class="paramname">e</td><td>FF exponent </td></tr>
<tr><td class="paramname">m</td><td>FF modulus </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="acadc23a6f6c053b971d7afaf121d7196"></a>
<h2 class="memtitle"><span class="permalink"><a href="#acadc23a6f6c053b971d7afaf121d7196">&#9670;&nbsp;</a></span>FF_2048_skspow()</h2>
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<div class="memproto">
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<td class="memname">void FF_2048_skspow </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>r</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a>&#160;</td>
<td class="paramname"><em>e</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>For short BIG exponent </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">r</td><td>FF instance, on exit = x^e mod p </td></tr>
<tr><td class="paramname">x</td><td>FF instance </td></tr>
<tr><td class="paramname">e</td><td>BIG exponent </td></tr>
<tr><td class="paramname">m</td><td>FF modulus </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a2ba04edfe1eb1b4e925598bebf135b8f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a2ba04edfe1eb1b4e925598bebf135b8f">&#9670;&nbsp;</a></span>FF_2048_sqr()</h2>
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<div class="memproto">
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<td class="memname">void FF_2048_sqr </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>y</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Uses Karatsuba method internally </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance, on exit = y^2 </td></tr>
<tr><td class="paramname">y</td><td>FF instance to be squared </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="aebafa634bb7c45532f0cc30b005fece7"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aebafa634bb7c45532f0cc30b005fece7">&#9670;&nbsp;</a></span>FF_2048_sub()</h2>
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<td class="memname">void FF_2048_sub </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>y</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>z</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance, on exit = y-z </td></tr>
<tr><td class="paramname">y</td><td>FF instance </td></tr>
<tr><td class="paramname">z</td><td>FF instance </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a7cea17d94848af54dc71659f4aa78121"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a7cea17d94848af54dc71659f4aa78121">&#9670;&nbsp;</a></span>FF_2048_toOctet()</h2>
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<table class="memname">
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<td class="memname">void FF_2048_toOctet </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structoctet.html">octet</a> *&#160;</td>
<td class="paramname"><em>S</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Converts an FF to big-endian base 256 form. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">S</td><td>output octet string </td></tr>
<tr><td class="paramname">x</td><td>FF instance to be converted to an octet string </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a9a3486518d9dcf2ef743a6dd2aa56336"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a9a3486518d9dcf2ef743a6dd2aa56336">&#9670;&nbsp;</a></span>FF_2048_zero()</h2>
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<td class="memname">void FF_2048_zero </td>
<td>(</td>
<td class="paramtype"><a class="el" href="big__1024__58_8h.html#a9b2910ed8e28bc385736f45a3d668691">BIG_1024_58</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FF instance to be set to zero </td></tr>
<tr><td class="paramname">n</td><td>size of FF in BIGs </td></tr>
</table>
</dd>
</dl>
</div>
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