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<a href="#nested-classes">Data Structures</a> &#124;
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<p>FP12 Header File.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &quot;<a class="el" href="fp4__BN254_8h_source.html">fp4_BN254.h</a>&quot;</code><br />
</div>
<p><a href="fp12__BN254_8h_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="nested-classes"></a>
Data Structures</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structFP12__BN254.html">FP12_BN254</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">FP12 Structure - towered over three FP4. <a href="structFP12__BN254.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:aae15e1861ff301328ab065a0c6b2c736"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#aae15e1861ff301328ab065a0c6b2c736">FP12_BN254_iszilch</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x)</td></tr>
<tr class="memdesc:aae15e1861ff301328ab065a0c6b2c736"><td class="mdescLeft">&#160;</td><td class="mdescRight">Tests for FP12 equal to zero. <a href="#aae15e1861ff301328ab065a0c6b2c736">More...</a><br /></td></tr>
<tr class="separator:aae15e1861ff301328ab065a0c6b2c736"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa7d39065624cb99feb0da2b7ec2af565"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#aa7d39065624cb99feb0da2b7ec2af565">FP12_BN254_isunity</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x)</td></tr>
<tr class="memdesc:aa7d39065624cb99feb0da2b7ec2af565"><td class="mdescLeft">&#160;</td><td class="mdescRight">Tests for FP12 equal to unity. <a href="#aa7d39065624cb99feb0da2b7ec2af565">More...</a><br /></td></tr>
<tr class="separator:aa7d39065624cb99feb0da2b7ec2af565"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae477f2ee1dcfa1f4de954ec0eaf1ea68"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#ae477f2ee1dcfa1f4de954ec0eaf1ea68">FP12_BN254_copy</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x, <a class="el" href="structFP12__BN254.html">FP12_BN254</a> *y)</td></tr>
<tr class="memdesc:ae477f2ee1dcfa1f4de954ec0eaf1ea68"><td class="mdescLeft">&#160;</td><td class="mdescRight">Copy FP12 to another FP12. <a href="#ae477f2ee1dcfa1f4de954ec0eaf1ea68">More...</a><br /></td></tr>
<tr class="separator:ae477f2ee1dcfa1f4de954ec0eaf1ea68"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af8f9a442486fbdcfe1ad7f3ad5f9a018"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#af8f9a442486fbdcfe1ad7f3ad5f9a018">FP12_BN254_one</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x)</td></tr>
<tr class="memdesc:af8f9a442486fbdcfe1ad7f3ad5f9a018"><td class="mdescLeft">&#160;</td><td class="mdescRight">Set FP12 to unity. <a href="#af8f9a442486fbdcfe1ad7f3ad5f9a018">More...</a><br /></td></tr>
<tr class="separator:af8f9a442486fbdcfe1ad7f3ad5f9a018"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a72f651c3654012a00c7623d3d72a98d3"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#a72f651c3654012a00c7623d3d72a98d3">FP12_BN254_zero</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x)</td></tr>
<tr class="memdesc:a72f651c3654012a00c7623d3d72a98d3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Set FP12 to zero. <a href="#a72f651c3654012a00c7623d3d72a98d3">More...</a><br /></td></tr>
<tr class="separator:a72f651c3654012a00c7623d3d72a98d3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa063c0320cf01eb31e6bb02fee0a6959"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#aa063c0320cf01eb31e6bb02fee0a6959">FP12_BN254_equals</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x, <a class="el" href="structFP12__BN254.html">FP12_BN254</a> *y)</td></tr>
<tr class="memdesc:aa063c0320cf01eb31e6bb02fee0a6959"><td class="mdescLeft">&#160;</td><td class="mdescRight">Tests for equality of two FP12s. <a href="#aa063c0320cf01eb31e6bb02fee0a6959">More...</a><br /></td></tr>
<tr class="separator:aa063c0320cf01eb31e6bb02fee0a6959"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af56639e6a87580a04b32d770549c4914"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#af56639e6a87580a04b32d770549c4914">FP12_BN254_conj</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x, <a class="el" href="structFP12__BN254.html">FP12_BN254</a> *y)</td></tr>
<tr class="memdesc:af56639e6a87580a04b32d770549c4914"><td class="mdescLeft">&#160;</td><td class="mdescRight">Conjugation of FP12. <a href="#af56639e6a87580a04b32d770549c4914">More...</a><br /></td></tr>
<tr class="separator:af56639e6a87580a04b32d770549c4914"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a89a40e29e01905ab294888169ad6814d"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#a89a40e29e01905ab294888169ad6814d">FP12_BN254_from_FP4</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x, <a class="el" href="structFP4__BN254.html">FP4_BN254</a> *a)</td></tr>
<tr class="memdesc:a89a40e29e01905ab294888169ad6814d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Initialise FP12 from single FP4. <a href="#a89a40e29e01905ab294888169ad6814d">More...</a><br /></td></tr>
<tr class="separator:a89a40e29e01905ab294888169ad6814d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae1aca4a39c060e7312cb4c206e0d0a13"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#ae1aca4a39c060e7312cb4c206e0d0a13">FP12_BN254_from_FP4s</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x, <a class="el" href="structFP4__BN254.html">FP4_BN254</a> *a, <a class="el" href="structFP4__BN254.html">FP4_BN254</a> *b, <a class="el" href="structFP4__BN254.html">FP4_BN254</a> *c)</td></tr>
<tr class="memdesc:ae1aca4a39c060e7312cb4c206e0d0a13"><td class="mdescLeft">&#160;</td><td class="mdescRight">Initialise FP12 from three FP4s. <a href="#ae1aca4a39c060e7312cb4c206e0d0a13">More...</a><br /></td></tr>
<tr class="separator:ae1aca4a39c060e7312cb4c206e0d0a13"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af68099cb4ba0a55908fae8a791fc0355"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#af68099cb4ba0a55908fae8a791fc0355">FP12_BN254_usqr</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x, <a class="el" href="structFP12__BN254.html">FP12_BN254</a> *y)</td></tr>
<tr class="memdesc:af68099cb4ba0a55908fae8a791fc0355"><td class="mdescLeft">&#160;</td><td class="mdescRight">Fast Squaring of an FP12 in "unitary" form. <a href="#af68099cb4ba0a55908fae8a791fc0355">More...</a><br /></td></tr>
<tr class="separator:af68099cb4ba0a55908fae8a791fc0355"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a54d1e4b6e41bf8d85bd0493376d7fe01"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#a54d1e4b6e41bf8d85bd0493376d7fe01">FP12_BN254_sqr</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x, <a class="el" href="structFP12__BN254.html">FP12_BN254</a> *y)</td></tr>
<tr class="memdesc:a54d1e4b6e41bf8d85bd0493376d7fe01"><td class="mdescLeft">&#160;</td><td class="mdescRight">Squaring an FP12. <a href="#a54d1e4b6e41bf8d85bd0493376d7fe01">More...</a><br /></td></tr>
<tr class="separator:a54d1e4b6e41bf8d85bd0493376d7fe01"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4111c0d28f2026074c451d390b8b207f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#a4111c0d28f2026074c451d390b8b207f">FP12_BN254_smul</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x, <a class="el" href="structFP12__BN254.html">FP12_BN254</a> *y)</td></tr>
<tr class="memdesc:a4111c0d28f2026074c451d390b8b207f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Fast multiplication of two sparse FP12s that arises from ATE pairing line functions. <a href="#a4111c0d28f2026074c451d390b8b207f">More...</a><br /></td></tr>
<tr class="separator:a4111c0d28f2026074c451d390b8b207f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a444b73ef39f3196da601abf55c2af416"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#a444b73ef39f3196da601abf55c2af416">FP12_BN254_ssmul</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x, <a class="el" href="structFP12__BN254.html">FP12_BN254</a> *y)</td></tr>
<tr class="memdesc:a444b73ef39f3196da601abf55c2af416"><td class="mdescLeft">&#160;</td><td class="mdescRight">Fast multiplication of what may be sparse multiplicands. <a href="#a444b73ef39f3196da601abf55c2af416">More...</a><br /></td></tr>
<tr class="separator:a444b73ef39f3196da601abf55c2af416"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ace1e5dd5bec1f8b4c9f71d8a732f2bc9"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#ace1e5dd5bec1f8b4c9f71d8a732f2bc9">FP12_BN254_mul</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x, <a class="el" href="structFP12__BN254.html">FP12_BN254</a> *y)</td></tr>
<tr class="memdesc:ace1e5dd5bec1f8b4c9f71d8a732f2bc9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Full unconditional Multiplication of two FP12s. <a href="#ace1e5dd5bec1f8b4c9f71d8a732f2bc9">More...</a><br /></td></tr>
<tr class="separator:ace1e5dd5bec1f8b4c9f71d8a732f2bc9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4cd7e3bc53727523c212ffe3f2a84a58"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#a4cd7e3bc53727523c212ffe3f2a84a58">FP12_BN254_inv</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x, <a class="el" href="structFP12__BN254.html">FP12_BN254</a> *y)</td></tr>
<tr class="memdesc:a4cd7e3bc53727523c212ffe3f2a84a58"><td class="mdescLeft">&#160;</td><td class="mdescRight">Inverting an FP12. <a href="#a4cd7e3bc53727523c212ffe3f2a84a58">More...</a><br /></td></tr>
<tr class="separator:a4cd7e3bc53727523c212ffe3f2a84a58"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab69293db6513f5c57d1fffc5a97a85aa"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#ab69293db6513f5c57d1fffc5a97a85aa">FP12_BN254_pow</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *r, <a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x, <a class="el" href="big__256__56_8h.html#abea3e70a8a87f28329ed8e48af7bb244">BIG_256_56</a> b)</td></tr>
<tr class="memdesc:ab69293db6513f5c57d1fffc5a97a85aa"><td class="mdescLeft">&#160;</td><td class="mdescRight">Raises an FP12 to the power of a BIG. <a href="#ab69293db6513f5c57d1fffc5a97a85aa">More...</a><br /></td></tr>
<tr class="separator:ab69293db6513f5c57d1fffc5a97a85aa"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a87b1c05b6642b3762b2fbeea75945748"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#a87b1c05b6642b3762b2fbeea75945748">FP12_BN254_pinpow</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x, int i, int b)</td></tr>
<tr class="memdesc:a87b1c05b6642b3762b2fbeea75945748"><td class="mdescLeft">&#160;</td><td class="mdescRight">Raises an FP12 instance x to a small integer power, side-channel resistant. <a href="#a87b1c05b6642b3762b2fbeea75945748">More...</a><br /></td></tr>
<tr class="separator:a87b1c05b6642b3762b2fbeea75945748"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a13d2a12b87f9fe6af3ea838afb09ffd5"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#a13d2a12b87f9fe6af3ea838afb09ffd5">FP12_BN254_compow</a> (<a class="el" href="structFP4__BN254.html">FP4_BN254</a> *c, <a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x, <a class="el" href="big__256__56_8h.html#abea3e70a8a87f28329ed8e48af7bb244">BIG_256_56</a> e, <a class="el" href="big__256__56_8h.html#abea3e70a8a87f28329ed8e48af7bb244">BIG_256_56</a> r)</td></tr>
<tr class="memdesc:a13d2a12b87f9fe6af3ea838afb09ffd5"><td class="mdescLeft">&#160;</td><td class="mdescRight">Raises an FP12 instance x to a BIG power, compressed to FP4. <a href="#a13d2a12b87f9fe6af3ea838afb09ffd5">More...</a><br /></td></tr>
<tr class="separator:a13d2a12b87f9fe6af3ea838afb09ffd5"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0dbf99bd0c6ab179ac27365cff448b92"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#a0dbf99bd0c6ab179ac27365cff448b92">FP12_BN254_pow4</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *r, <a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x, <a class="el" href="big__256__56_8h.html#abea3e70a8a87f28329ed8e48af7bb244">BIG_256_56</a> *b)</td></tr>
<tr class="memdesc:a0dbf99bd0c6ab179ac27365cff448b92"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculate x[0]^b[0].x[1]^b[1].x[2]^b[2].x[3]^b[3], side-channel resistant. <a href="#a0dbf99bd0c6ab179ac27365cff448b92">More...</a><br /></td></tr>
<tr class="separator:a0dbf99bd0c6ab179ac27365cff448b92"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a331b9e461609cfe7aff7a061498c64e6"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#a331b9e461609cfe7aff7a061498c64e6">FP12_BN254_frob</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x, <a class="el" href="structFP2__BN254.html">FP2_BN254</a> *f)</td></tr>
<tr class="memdesc:a331b9e461609cfe7aff7a061498c64e6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Raises an FP12 to the power of the internal modulus p, using the Frobenius. <a href="#a331b9e461609cfe7aff7a061498c64e6">More...</a><br /></td></tr>
<tr class="separator:a331b9e461609cfe7aff7a061498c64e6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a905052268e5993526378269ff49223c1"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#a905052268e5993526378269ff49223c1">FP12_BN254_reduce</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x)</td></tr>
<tr class="memdesc:a905052268e5993526378269ff49223c1"><td class="mdescLeft">&#160;</td><td class="mdescRight">Reduces all components of possibly unreduced FP12 mod Modulus. <a href="#a905052268e5993526378269ff49223c1">More...</a><br /></td></tr>
<tr class="separator:a905052268e5993526378269ff49223c1"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a806882b9a6a5c52524ea1ed68357012f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#a806882b9a6a5c52524ea1ed68357012f">FP12_BN254_norm</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x)</td></tr>
<tr class="memdesc:a806882b9a6a5c52524ea1ed68357012f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Normalises the components of an FP12. <a href="#a806882b9a6a5c52524ea1ed68357012f">More...</a><br /></td></tr>
<tr class="separator:a806882b9a6a5c52524ea1ed68357012f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9ee6a456c43bf39e28fbca670a94b446"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#a9ee6a456c43bf39e28fbca670a94b446">FP12_BN254_output</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x)</td></tr>
<tr class="memdesc:a9ee6a456c43bf39e28fbca670a94b446"><td class="mdescLeft">&#160;</td><td class="mdescRight">Formats and outputs an FP12 to the console. <a href="#a9ee6a456c43bf39e28fbca670a94b446">More...</a><br /></td></tr>
<tr class="separator:a9ee6a456c43bf39e28fbca670a94b446"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aebfdaa2d39d9b8769e3e356e196d9c64"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#aebfdaa2d39d9b8769e3e356e196d9c64">FP12_BN254_toOctet</a> (<a class="el" href="structoctet.html">octet</a> *S, <a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x)</td></tr>
<tr class="memdesc:aebfdaa2d39d9b8769e3e356e196d9c64"><td class="mdescLeft">&#160;</td><td class="mdescRight">Formats and outputs an FP12 instance to an octet string. <a href="#aebfdaa2d39d9b8769e3e356e196d9c64">More...</a><br /></td></tr>
<tr class="separator:aebfdaa2d39d9b8769e3e356e196d9c64"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab7b29484caf6395255d8cb0ab6fde025"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#ab7b29484caf6395255d8cb0ab6fde025">FP12_BN254_fromOctet</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x, <a class="el" href="structoctet.html">octet</a> *S)</td></tr>
<tr class="memdesc:ab7b29484caf6395255d8cb0ab6fde025"><td class="mdescLeft">&#160;</td><td class="mdescRight">Creates an FP12 instance from an octet string. <a href="#ab7b29484caf6395255d8cb0ab6fde025">More...</a><br /></td></tr>
<tr class="separator:ab7b29484caf6395255d8cb0ab6fde025"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae4fa64cfbf0514eab36525971c46ab37"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#ae4fa64cfbf0514eab36525971c46ab37">FP12_BN254_trace</a> (<a class="el" href="structFP4__BN254.html">FP4_BN254</a> *t, <a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x)</td></tr>
<tr class="memdesc:ae4fa64cfbf0514eab36525971c46ab37"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculate the trace of an FP12. <a href="#ae4fa64cfbf0514eab36525971c46ab37">More...</a><br /></td></tr>
<tr class="separator:ae4fa64cfbf0514eab36525971c46ab37"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a262a426e8152512ec7bd81344a07c72c"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#a262a426e8152512ec7bd81344a07c72c">FP12_BN254_cmove</a> (<a class="el" href="structFP12__BN254.html">FP12_BN254</a> *x, <a class="el" href="structFP12__BN254.html">FP12_BN254</a> *y, int s)</td></tr>
<tr class="memdesc:a262a426e8152512ec7bd81344a07c72c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Conditional copy of FP12 number. <a href="#a262a426e8152512ec7bd81344a07c72c">More...</a><br /></td></tr>
<tr class="separator:a262a426e8152512ec7bd81344a07c72c"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="var-members"></a>
Variables</h2></td></tr>
<tr class="memitem:abf41342afa7230d0288d37a140d4ee9d"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="big__256__56_8h.html#abea3e70a8a87f28329ed8e48af7bb244">BIG_256_56</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#abf41342afa7230d0288d37a140d4ee9d">Fra_BN254</a></td></tr>
<tr class="separator:abf41342afa7230d0288d37a140d4ee9d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a85fadba81a01e0c26213ed65cbbe7471"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="big__256__56_8h.html#abea3e70a8a87f28329ed8e48af7bb244">BIG_256_56</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="fp12__BN254_8h.html#a85fadba81a01e0c26213ed65cbbe7471">Frb_BN254</a></td></tr>
<tr class="separator:a85fadba81a01e0c26213ed65cbbe7471"><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">Function Documentation</h2>
<a id="a262a426e8152512ec7bd81344a07c72c"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a262a426e8152512ec7bd81344a07c72c">&#9670;&nbsp;</a></span>FP12_BN254_cmove()</h2>
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<td class="memname">void FP12_BN254_cmove </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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="structFP12__BN254.html">FP12_BN254</a> *&#160;</td>
<td class="paramname"><em>y</em>, </td>
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<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>s</em>&#160;</td>
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<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>Conditionally copies second parameter to the first (without branching) </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FP12 instance, set to y if s!=0 </td></tr>
<tr><td class="paramname">y</td><td>another FP12 instance </td></tr>
<tr><td class="paramname">s</td><td>copy only takes place if not equal to 0 </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a13d2a12b87f9fe6af3ea838afb09ffd5"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a13d2a12b87f9fe6af3ea838afb09ffd5">&#9670;&nbsp;</a></span>FP12_BN254_compow()</h2>
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<td class="memname">void FP12_BN254_compow </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP4__BN254.html">FP4_BN254</a> *&#160;</td>
<td class="paramname"><em>c</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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__256__56_8h.html#abea3e70a8a87f28329ed8e48af7bb244">BIG_256_56</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__256__56_8h.html#abea3e70a8a87f28329ed8e48af7bb244">BIG_256_56</a>&#160;</td>
<td class="paramname"><em>r</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">c</td><td>FP4 instance, on exit = x^(e mod r) as FP4 </td></tr>
<tr><td class="paramname">x</td><td>FP12 input </td></tr>
<tr><td class="paramname">e</td><td>BIG exponent </td></tr>
<tr><td class="paramname">r</td><td>BIG group order </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="af56639e6a87580a04b32d770549c4914"></a>
<h2 class="memtitle"><span class="permalink"><a href="#af56639e6a87580a04b32d770549c4914">&#9670;&nbsp;</a></span>FP12_BN254_conj()</h2>
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<td class="memname">void FP12_BN254_conj </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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="structFP12__BN254.html">FP12_BN254</a> *&#160;</td>
<td class="paramname"><em>y</em>&#160;</td>
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<td></td>
<td>)</td>
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<p>If y=(a,b,c) (where a,b,c are its three FP4 components) on exit x=(conj(a),-conj(b),conj(c)) </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FP12 instance, on exit = conj(y) </td></tr>
<tr><td class="paramname">y</td><td>FP12 instance </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="ae477f2ee1dcfa1f4de954ec0eaf1ea68"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae477f2ee1dcfa1f4de954ec0eaf1ea68">&#9670;&nbsp;</a></span>FP12_BN254_copy()</h2>
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<td class="memname">void FP12_BN254_copy </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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="structFP12__BN254.html">FP12_BN254</a> *&#160;</td>
<td class="paramname"><em>y</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>FP12 instance, on exit = y </td></tr>
<tr><td class="paramname">y</td><td>FP12 instance to be copied </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="aa063c0320cf01eb31e6bb02fee0a6959"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aa063c0320cf01eb31e6bb02fee0a6959">&#9670;&nbsp;</a></span>FP12_BN254_equals()</h2>
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<td class="memname">int FP12_BN254_equals </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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="structFP12__BN254.html">FP12_BN254</a> *&#160;</td>
<td class="paramname"><em>y</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>FP12 instance to be compared </td></tr>
<tr><td class="paramname">y</td><td>FP12 instance to be compared </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>1 if x=y, else returns 0 </dd></dl>
</div>
</div>
<a id="a331b9e461609cfe7aff7a061498c64e6"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a331b9e461609cfe7aff7a061498c64e6">&#9670;&nbsp;</a></span>FP12_BN254_frob()</h2>
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<td class="memname">void FP12_BN254_frob </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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="structFP2__BN254.html">FP2_BN254</a> *&#160;</td>
<td class="paramname"><em>f</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>FP12 instance, on exit = x^p </td></tr>
<tr><td class="paramname">f</td><td>FP2 precalculated Frobenius constant </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a89a40e29e01905ab294888169ad6814d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a89a40e29e01905ab294888169ad6814d">&#9670;&nbsp;</a></span>FP12_BN254_from_FP4()</h2>
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<td class="memname">void FP12_BN254_from_FP4 </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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="structFP4__BN254.html">FP4_BN254</a> *&#160;</td>
<td class="paramname"><em>a</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
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<p>Sets first FP4 component of an FP12, other components set to zero </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FP12 instance to be initialised </td></tr>
<tr><td class="paramname">a</td><td>FP4 to form first part of FP4 </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="ae1aca4a39c060e7312cb4c206e0d0a13"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae1aca4a39c060e7312cb4c206e0d0a13">&#9670;&nbsp;</a></span>FP12_BN254_from_FP4s()</h2>
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<td class="memname">void FP12_BN254_from_FP4s </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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="structFP4__BN254.html">FP4_BN254</a> *&#160;</td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structFP4__BN254.html">FP4_BN254</a> *&#160;</td>
<td class="paramname"><em>b</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structFP4__BN254.html">FP4_BN254</a> *&#160;</td>
<td class="paramname"><em>c</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>FP12 instance to be initialised </td></tr>
<tr><td class="paramname">a</td><td>FP4 to form first part of FP12 </td></tr>
<tr><td class="paramname">b</td><td>FP4 to form second part of FP12 </td></tr>
<tr><td class="paramname">c</td><td>FP4 to form third part of FP12 </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="ab7b29484caf6395255d8cb0ab6fde025"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ab7b29484caf6395255d8cb0ab6fde025">&#9670;&nbsp;</a></span>FP12_BN254_fromOctet()</h2>
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<td class="memname">void FP12_BN254_fromOctet </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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="structoctet.html">octet</a> *&#160;</td>
<td class="paramname"><em>S</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>De-serializes the components of an FP12 to create an FP12 from big-endian base 256 components. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FP12 instance to be created from an octet string </td></tr>
<tr><td class="paramname">S</td><td>input octet string </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a4cd7e3bc53727523c212ffe3f2a84a58"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a4cd7e3bc53727523c212ffe3f2a84a58">&#9670;&nbsp;</a></span>FP12_BN254_inv()</h2>
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<td class="memname">void FP12_BN254_inv </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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="structFP12__BN254.html">FP12_BN254</a> *&#160;</td>
<td class="paramname"><em>y</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>FP12 instance, on exit = 1/y </td></tr>
<tr><td class="paramname">y</td><td>FP12 instance </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="aa7d39065624cb99feb0da2b7ec2af565"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aa7d39065624cb99feb0da2b7ec2af565">&#9670;&nbsp;</a></span>FP12_BN254_isunity()</h2>
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<td class="memname">int FP12_BN254_isunity </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</a> *&#160;</td>
<td class="paramname"><em>x</em></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>FP12 number to be tested </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>1 if unity, else returns 0 </dd></dl>
</div>
</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aae15e1861ff301328ab065a0c6b2c736">&#9670;&nbsp;</a></span>FP12_BN254_iszilch()</h2>
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<div class="memproto">
<table class="memname">
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<td class="memname">int FP12_BN254_iszilch </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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>FP12 number to be tested </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>1 if zero, else returns 0 </dd></dl>
</div>
</div>
<a id="ace1e5dd5bec1f8b4c9f71d8a732f2bc9"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ace1e5dd5bec1f8b4c9f71d8a732f2bc9">&#9670;&nbsp;</a></span>FP12_BN254_mul()</h2>
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<td class="memname">void FP12_BN254_mul </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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="structFP12__BN254.html">FP12_BN254</a> *&#160;</td>
<td class="paramname"><em>y</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>FP12 instance, on exit = x*y </td></tr>
<tr><td class="paramname">y</td><td>FP12 instance, the multiplier </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a806882b9a6a5c52524ea1ed68357012f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a806882b9a6a5c52524ea1ed68357012f">&#9670;&nbsp;</a></span>FP12_BN254_norm()</h2>
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<td class="memname">void FP12_BN254_norm </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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>FP12 instance to be normalised </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="af8f9a442486fbdcfe1ad7f3ad5f9a018"></a>
<h2 class="memtitle"><span class="permalink"><a href="#af8f9a442486fbdcfe1ad7f3ad5f9a018">&#9670;&nbsp;</a></span>FP12_BN254_one()</h2>
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<td class="memname">void FP12_BN254_one </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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>FP12 instance to be set to one </td></tr>
</table>
</dd>
</dl>
</div>
</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a9ee6a456c43bf39e28fbca670a94b446">&#9670;&nbsp;</a></span>FP12_BN254_output()</h2>
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<td class="memname">void FP12_BN254_output </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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>FP12 instance to be printed </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a87b1c05b6642b3762b2fbeea75945748"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a87b1c05b6642b3762b2fbeea75945748">&#9670;&nbsp;</a></span>FP12_BN254_pinpow()</h2>
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<td class="memname">void FP12_BN254_pinpow </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</a> *&#160;</td>
<td class="paramname"><em>x</em>, </td>
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<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>i</em>, </td>
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<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>b</em>&#160;</td>
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<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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</table>
</div><div class="memdoc">
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>FP12 instance, on exit = x^i </td></tr>
<tr><td class="paramname">i</td><td>small integer exponent </td></tr>
<tr><td class="paramname">b</td><td>maximum number of bits in exponent </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="ab69293db6513f5c57d1fffc5a97a85aa"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ab69293db6513f5c57d1fffc5a97a85aa">&#9670;&nbsp;</a></span>FP12_BN254_pow()</h2>
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<td class="memname">void FP12_BN254_pow </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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="structFP12__BN254.html">FP12_BN254</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__256__56_8h.html#abea3e70a8a87f28329ed8e48af7bb244">BIG_256_56</a>&#160;</td>
<td class="paramname"><em>b</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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</table>
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<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">r</td><td>FP12 instance, on exit = y^b </td></tr>
<tr><td class="paramname">x</td><td>FP12 instance </td></tr>
<tr><td class="paramname">b</td><td>BIG number </td></tr>
</table>
</dd>
</dl>
</div>
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<a id="a0dbf99bd0c6ab179ac27365cff448b92"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a0dbf99bd0c6ab179ac27365cff448b92">&#9670;&nbsp;</a></span>FP12_BN254_pow4()</h2>
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<td class="memname">void FP12_BN254_pow4 </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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="structFP12__BN254.html">FP12_BN254</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__256__56_8h.html#abea3e70a8a87f28329ed8e48af7bb244">BIG_256_56</a> *&#160;</td>
<td class="paramname"><em>b</em>&#160;</td>
</tr>
<tr>
<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">r</td><td>FP12 instance, on exit = x[0]^b[0].x[1]^b[1].x[2]^b[2].x[3]^b[3] </td></tr>
<tr><td class="paramname">x</td><td>FP12 array with 4 FP12s </td></tr>
<tr><td class="paramname">b</td><td>BIG array of 4 exponents </td></tr>
</table>
</dd>
</dl>
</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a905052268e5993526378269ff49223c1">&#9670;&nbsp;</a></span>FP12_BN254_reduce()</h2>
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<td class="memname">void FP12_BN254_reduce </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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>FP12 instance, on exit reduced mod Modulus </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a4111c0d28f2026074c451d390b8b207f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a4111c0d28f2026074c451d390b8b207f">&#9670;&nbsp;</a></span>FP12_BN254_smul()</h2>
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<td class="memname">void FP12_BN254_smul </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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="structFP12__BN254.html">FP12_BN254</a> *&#160;</td>
<td class="paramname"><em>y</em>&#160;</td>
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<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>FP12 instance, on exit = x*y </td></tr>
<tr><td class="paramname">y</td><td>FP12 instance, of special form </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a54d1e4b6e41bf8d85bd0493376d7fe01"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a54d1e4b6e41bf8d85bd0493376d7fe01">&#9670;&nbsp;</a></span>FP12_BN254_sqr()</h2>
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<td class="memname">void FP12_BN254_sqr </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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="structFP12__BN254.html">FP12_BN254</a> *&#160;</td>
<td class="paramname"><em>y</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>FP12 instance, on exit = y^2 </td></tr>
<tr><td class="paramname">y</td><td>FP12 instance </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a444b73ef39f3196da601abf55c2af416"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a444b73ef39f3196da601abf55c2af416">&#9670;&nbsp;</a></span>FP12_BN254_ssmul()</h2>
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<td class="memname">void FP12_BN254_ssmul </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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="structFP12__BN254.html">FP12_BN254</a> *&#160;</td>
<td class="paramname"><em>y</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>FP12 instance, on exit = x*y </td></tr>
<tr><td class="paramname">y</td><td>FP12 instance, of special form </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="aebfdaa2d39d9b8769e3e356e196d9c64"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aebfdaa2d39d9b8769e3e356e196d9c64">&#9670;&nbsp;</a></span>FP12_BN254_toOctet()</h2>
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<td class="memname">void FP12_BN254_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="structFP12__BN254.html">FP12_BN254</a> *&#160;</td>
<td class="paramname"><em>x</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Serializes the components of an FP12 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>FP12 instance to be converted to an octet string </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="ae4fa64cfbf0514eab36525971c46ab37"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae4fa64cfbf0514eab36525971c46ab37">&#9670;&nbsp;</a></span>FP12_BN254_trace()</h2>
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<td class="memname">void FP12_BN254_trace </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP4__BN254.html">FP4_BN254</a> *&#160;</td>
<td class="paramname"><em>t</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</a> *&#160;</td>
<td class="paramname"><em>x</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">t</td><td>FP4 trace of x, on exit = tr(x) </td></tr>
<tr><td class="paramname">x</td><td>FP12 instance </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="af68099cb4ba0a55908fae8a791fc0355"></a>
<h2 class="memtitle"><span class="permalink"><a href="#af68099cb4ba0a55908fae8a791fc0355">&#9670;&nbsp;</a></span>FP12_BN254_usqr()</h2>
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<td class="memname">void FP12_BN254_usqr </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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="structFP12__BN254.html">FP12_BN254</a> *&#160;</td>
<td class="paramname"><em>y</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>FP12 instance, on exit = y^2 </td></tr>
<tr><td class="paramname">y</td><td>FP4 instance, must be unitary </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a72f651c3654012a00c7623d3d72a98d3"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a72f651c3654012a00c7623d3d72a98d3">&#9670;&nbsp;</a></span>FP12_BN254_zero()</h2>
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<td class="memname">void FP12_BN254_zero </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structFP12__BN254.html">FP12_BN254</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>FP12 instance to be set to zero </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<h2 class="groupheader">Variable Documentation</h2>
<a id="abf41342afa7230d0288d37a140d4ee9d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#abf41342afa7230d0288d37a140d4ee9d">&#9670;&nbsp;</a></span>Fra_BN254</h2>
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<td class="memname">const <a class="el" href="big__256__56_8h.html#abea3e70a8a87f28329ed8e48af7bb244">BIG_256_56</a> Fra_BN254</td>
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<p>real part of BN curve Frobenius Constant </p>
</div>
</div>
<a id="a85fadba81a01e0c26213ed65cbbe7471"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a85fadba81a01e0c26213ed65cbbe7471">&#9670;&nbsp;</a></span>Frb_BN254</h2>
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<td class="memname">const <a class="el" href="big__256__56_8h.html#abea3e70a8a87f28329ed8e48af7bb244">BIG_256_56</a> Frb_BN254</td>
</tr>
</table>
</div><div class="memdoc">
<p>imaginary part of BN curve Frobenius Constant </p>
</div>
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