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<h1>Modes of Operation</h1>
<div style="text-align:left; margin-top:19px; margin-bottom:19px; padding-top:0px; padding-bottom:0px">
<br style="text-align:left">
The mode of operation used by VeraCrypt for encrypted partitions, drives, and virtual volumes is XTS.
<br style="text-align:left">
<br style="text-align:left">
XTS mode is in fact XEX mode <a href="http://www.cs.ucdavis.edu/%7Erogaway/papers/offsets.pdf">
[12]</a>, which was designed by Phillip Rogaway in 2003, with a minor modification (XEX mode uses a single key for two different purposes, whereas XTS mode uses two independent keys).<br style="text-align:left">
<br style="text-align:left">
In 2010, XTS mode was approved by NIST for protecting the confidentiality of data on storage devices [24]. In 2007, it was also approved by the IEEE for cryptographic protection of data on block-oriented storage devices (IEEE 1619).</div>
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<h2 style="text-align:left; margin-top:19px; margin-bottom:19px; padding-top:0px; padding-bottom:0px">
<strong style="text-align:left">Description of XTS mode</strong>:</h2>
<div style="text-align:left; margin-top:19px; margin-bottom:19px; padding-top:0px; padding-bottom:0px">
<em style="text-align:left">C<sub style="text-align:left; font-size:85%">i</sub></em> =
<em style="text-align:left">E</em><sub style="text-align:left; font-size:85%"><em style="text-align:left">K</em>1</sub>(<em style="text-align:left">P<sub style="text-align:left; font-size:85%">i</sub></em> ^ (<em style="text-align:left">E</em><sub style="text-align:left; font-size:85%"><em style="text-align:left">K</em>2</sub>(<em style="text-align:left">n</em>)
<img src="gf2_mul.gif" alt="" width="10" height="10">
<em style="text-align:left">a<sup style="text-align:left; font-size:85%">i</sup></em>)) ^ (<em style="text-align:left">E</em><sub style="text-align:left; font-size:85%"><em style="text-align:left">K</em>2</sub>(<em style="text-align:left">n</em>)
<img src="gf2_mul.gif" alt="" width="10" height="10"><em style="text-align:left"> a<sup style="text-align:left; font-size:85%">i</sup></em>)</div>
<div style="text-align:left; margin-top:19px; margin-bottom:19px; padding-top:0px; padding-bottom:0px">
Where:</div>
<table style="border-collapse:separate; border-spacing:0px; width:608px; text-align:left; font-size:11px; line-height:13px; font-family:Verdana,Arial,Helvetica,sans-serif; border:0px outset #999">
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<td style="vertical-align:top; color:#000000; text-align:left; font-size:11px; line-height:13px; font-family:Verdana,Arial,Helvetica,sans-serif; padding:0px">
<sup style="text-align:left; font-size:85%"> <img src="gf2_mul.gif" alt="" width="10" height="10"></sup></td>
<td style="vertical-align:top; color:#000000; text-align:left; font-size:11px; line-height:13px; font-family:Verdana,Arial,Helvetica,sans-serif; padding:0px">
denotes multiplication of two polynomials over the binary field GF(2) modulo <em style="text-align:left">
x</em><sup style="text-align:left; font-size:85%">128</sup>+<em style="text-align:left">x</em><sup style="text-align:left; font-size:85%">7</sup>+<em style="text-align:left">x</em><sup style="text-align:left; font-size:85%">2</sup>+<em style="text-align:left">x</em>+1</td>
</tr>
<tr style="text-align:left">
<td style="width:30px; vertical-align:top; color:#000000; text-align:left; font-size:11px; line-height:13px; font-family:Verdana,Arial,Helvetica,sans-serif; padding:0px">
<br style="text-align:left">
<em style="text-align:left">K</em>1</td>
<td style="width:578px; vertical-align:top; color:#000000; text-align:left; font-size:11px; line-height:13px; font-family:Verdana,Arial,Helvetica,sans-serif; padding:0px">
<br style="text-align:left">
is the encryption key (256-bit for each supported cipher; i.e, AES, Serpent, and Twofish)</td>
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<td style="vertical-align:top; color:#000000; text-align:left; font-size:11px; line-height:13px; font-family:Verdana,Arial,Helvetica,sans-serif; padding:0px">
<br style="text-align:left">
<em style="text-align:left">K</em>2</td>
<td style="vertical-align:top; color:#000000; text-align:left; font-size:11px; line-height:13px; font-family:Verdana,Arial,Helvetica,sans-serif; padding:0px">
<br style="text-align:left">
is the secondary key (256-bit for each supported cipher; i.e, AES, Serpent, and Twofish)</td>
</tr>
<tr style="text-align:left">
<td style="vertical-align:top; color:#000000; text-align:left; font-size:11px; line-height:13px; font-family:Verdana,Arial,Helvetica,sans-serif; padding:0px">
<br style="text-align:left">
<em style="text-align:left">i</em></td>
<td style="vertical-align:top; color:#000000; text-align:left; font-size:11px; line-height:13px; font-family:Verdana,Arial,Helvetica,sans-serif; padding:0px">
<br style="text-align:left">
is the cipher block index within a data unit; for the first cipher block within a data unit,
<em style="text-align:left">i</em> = 0</td>
</tr>
<tr style="text-align:left">
<td style="vertical-align:top; color:#000000; text-align:left; font-size:11px; line-height:13px; font-family:Verdana,Arial,Helvetica,sans-serif; padding:0px">
<br style="text-align:left">
<em style="text-align:left">n</em></td>
<td style="vertical-align:top; color:#000000; text-align:left; font-size:11px; line-height:13px; font-family:Verdana,Arial,Helvetica,sans-serif; padding:0px">
<br style="text-align:left">
is the data unit index within the scope of <em style="text-align:left">K</em>1; for the first data unit,
<em style="text-align:left">n</em> = 0</td>
</tr>
<tr style="text-align:left">
<td style="vertical-align:top; color:#000000; text-align:left; font-size:11px; line-height:13px; font-family:Verdana,Arial,Helvetica,sans-serif; padding:0px">
<br style="text-align:left">
<em style="text-align:left">a</em></td>
<td style="vertical-align:top; color:#000000; text-align:left; font-size:11px; line-height:13px; font-family:Verdana,Arial,Helvetica,sans-serif; padding:0px">
<br style="text-align:left">
is a primitive element of Galois Field (2<sup style="text-align:left; font-size:85%">128</sup>) that corresponds to polynomial
<em style="text-align:left">x</em> (i.e., 2)</td>
</tr>
<tr style="text-align:left">
<td colspan="2" style="vertical-align:top; color:#000000; text-align:left; font-size:11px; line-height:13px; font-family:Verdana,Arial,Helvetica,sans-serif; padding:0px">
<br style="text-align:left">
<span style="text-align:left; font-size:10px; line-height:12px">Note: The remaining symbols are defined in the section
<a href="Notation.html" style="text-align:left; color:#0080c0; text-decoration:none.html">
Notation</a>. </span></td>
</tr>
</tbody>
</table>
<div style="text-align:left; margin-top:19px; margin-bottom:19px; padding-top:0px; padding-bottom:0px">
<br style="text-align:left">
The size of each data unit is always 512 bytes (regardless of the sector size).</div>
<div style="text-align:left; margin-top:19px; margin-bottom:19px; padding-top:0px; padding-bottom:0px">
For further information pertaining to XTS mode, see e.g. <a href="http://www.cs.ucdavis.edu/%7Erogaway/papers/offsets.pdf" style="text-align:left; color:#0080c0; text-decoration:none">
[12]</a> and <a href="http://csrc.nist.gov/publications/nistpubs/800-38E/nist-sp-800-38E.pdf" style="text-align:left; color:#0080c0; text-decoration:none">
[24]</a>.</div>
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