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<span id="openzim-page-title" class="mw-page-title-main">Mod <span class="texhtml mvar" style="font-style:italic;">n</span> cryptanalysis</span>
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<p>In <a href="Cryptography" title="Cryptography">cryptography</a>, <b>mod <span class="texhtml mvar" style="font-style:italic;">n</span> cryptanalysis</b> is an <a href="Cryptanalysis" title="Cryptanalysis">attack</a> applicable to <a href="Block_cipher" title="Block cipher">block</a> and <a href="Stream_cipher" title="Stream cipher">stream ciphers</a>. It is a form of <a href="Partitioning_cryptanalysis" title="Partitioning cryptanalysis">partitioning cryptanalysis</a> that exploits unevenness in how the <a href="Cipher" title="Cipher">cipher</a> operates over <a href="Equivalence_class" title="Equivalence class">equivalence classes</a> (congruence classes) <a href="Modular_arithmetic" title="Modular arithmetic">modulo <span class="texhtml mvar" style="font-style:italic;">n</span></a>. The method was first suggested in 1999 by <a href="John_Kelsey_(cryptanalyst)" title="John Kelsey (cryptanalyst)">John Kelsey</a>, <a href="Bruce_Schneier" title="Bruce Schneier">Bruce Schneier</a>, and <a href="David_A._Wagner" title="David A. Wagner">David Wagner</a> and applied to RC5P (a variant of <a href="RC5" title="RC5">RC5</a>) and <a href="M6_(cipher)" title="M6 (cipher)">M6</a> (a family of block ciphers used in the <a href="FireWire" class="mw-redirect" title="FireWire">FireWire</a> standard). These attacks used the properties of binary addition and bit rotation modulo a <a href="Fermat_prime" class="mw-redirect" title="Fermat prime">Fermat prime</a>.
</p>
<div class="mw-heading mw-heading2"><h2 id="Mod_3_analysis_of_RC5P">Mod 3 analysis of RC5P</h2></div>
<p>For RC5P, analysis was conducted modulo 3. It was observed that the operations in the cipher (rotation and addition, both on 32-bit words) were somewhat biased over congruence classes mod 3. To illustrate the approach, consider left rotation by a single bit:
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X\lll 1=\left\{{\begin{matrix}2X,&{\mbox{if }}X<2^{31}\\2X+1-2^{32},&{\mbox{if }}X\geq 2^{31}\end{matrix}}\right.}">
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<annotation encoding="application/x-tex">{\displaystyle X\lll 1=\left\{{\begin{matrix}2X,&{\mbox{if }}X<2^{31}\\2X+1-2^{32},&{\mbox{if }}X\geq 2^{31}\end{matrix}}\right.}</annotation>
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</math></span><img src="./340b914010c7d5edf6df5e926ec4026a8b0dcfbd.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:39.173ex; height:6.509ex;" alt="{\displaystyle X\lll 1=\left\{{\begin{matrix}2X,&{\mbox{if }}X<2^{31}\\2X+1-2^{32},&{\mbox{if }}X\geq 2^{31}\end{matrix}}\right.}" loading="lazy"></span></dd></dl>
<p>Then, because
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2^{32}\equiv 1{\pmod {3}},\,}">
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<annotation encoding="application/x-tex">{\displaystyle 2^{32}\equiv 1{\pmod {3}},\,}</annotation>
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</math></span><img src="./83fada42b82d11c8fa08b569206d478b9a0abd25.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.18ex; height:3.176ex;" alt="{\displaystyle 2^{32}\equiv 1{\pmod {3}},\,}" loading="lazy"></span></dd></dl>
<p>it follows that
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X\lll 1\equiv 2X{\pmod {3}}.}">
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<annotation encoding="application/x-tex">{\displaystyle X\lll 1\equiv 2X{\pmod {3}}.}</annotation>
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</math></span><img src="./5b353348301bb01d93c4bdd3e760350ca4fe30af.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.264ex; height:2.843ex;" alt="{\displaystyle X\lll 1\equiv 2X{\pmod {3}}.}" loading="lazy"></span></dd></dl>
<p>Thus left rotation by a single bit has a simple description modulo 3. Analysis of other operations (data dependent rotation and modular addition) reveals similar, notable biases. Although there are some theoretical problems analysing the operations in combination, the bias can be detected experimentally for the entire cipher. In (Kelsey et al., 1999), experiments were conducted up to seven rounds, and based on this they conjecture that as many as 19 or 20 rounds of RC5P can be <a href="Distinguishing_attack" title="Distinguishing attack">distinguished from random</a> using this attack. There is also a corresponding method for recovering the secret <a href="Key_(cryptography)" title="Key (cryptography)">key</a>.
</p><p>Against M6 there are attacks mod 5 and mod 257 that are even more effective.
</p>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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</style><cite id="CITEREFJohn_Kelsey,_Bruce_Schneier,_David_Wagner1999" class="citation conference cs1"><a href="John_Kelsey_(cryptanalyst)" title="John Kelsey (cryptanalyst)">John Kelsey</a>, <a href="Bruce_Schneier" title="Bruce Schneier">Bruce Schneier</a>, <a href="David_A._Wagner" title="David A. Wagner">David Wagner</a> (March 1999). <a rel="nofollow" class="external text" href="http://www.schneier.com/paper-mod3.html"><i>Mod n Cryptanalysis, with Applications Against RC5P and M6</i></a> <span class="cs1-format">(<a href="PDF" title="PDF">PDF</a>/<a href="PostScript" title="PostScript">PostScript</a>)</span>. <a href="Fast_Software_Encryption" class="mw-redirect" title="Fast Software Encryption">Fast Software Encryption</a>, Sixth International Workshop Proceedings. <a href="Rome" title="Rome">Rome</a>: <a href="Springer-Verlag" class="mw-redirect" title="Springer-Verlag">Springer-Verlag</a>. pp. <span class="nowrap">139–</span>155<span class="reference-accessdate">. Retrieved <span class="nowrap">2007-02-12</span></span>.</cite><span class="cs1-maint citation-comment"><code class="cs1-code">{{cite conference}}</code>: CS1 maint: multiple names: authors list (link)</span></li>
<li><cite id="CITEREFVincent_Rijmen2003" class="citation journal cs1"><a href="Vincent_Rijmen" title="Vincent Rijmen">Vincent Rijmen</a> (2003-12-01). <a rel="nofollow" class="external text" href="http://www.cryptico.com/Files/filer/wp_modn_analysis.pdf">""mod n" Cryptanalysis of Rabbit"</a> <span class="cs1-format">(PDF)</span>. <a href="White_paper" title="White paper">White paper</a>, Version 1.0. <a href="Cryptico" class="mw-redirect" title="Cryptico">Cryptico</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2007-02-12</span></span>.</cite> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{cite journal}}</code>: </span><span class="cs1-visible-error citation-comment">Cite journal requires <code class="cs1-code">|journal=</code> (help)</span></li>
<li><cite id="CITEREFToshio_TokitaTsutomu_Matsumoto" class="citation journal cs1">Toshio Tokita; Tsutomu Matsumoto. "On Applicability of Differential Cryptanalysis, Linear Cryptanalysis and Mod n Cryptanalysis to an Encryption Algorithm <a href="M8_(cipher)" title="M8 (cipher)">M8</a> (ISO9979-20)". <i>Ipsj Journal</i>. <b>42</b> (8).</cite></li></ul>
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</style></div><div role="navigation" class="navbox" aria-label="Navbox0" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Block_ciphers_(security_summary)197" style="font-size:114%;margin:0 4em"><a href="Block_cipher" title="Block cipher">Block ciphers</a> (<a href="Cipher_security_summary" title="Cipher security summary">security summary</a>)</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Common<br>algorithms</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Advanced_Encryption_Standard" title="Advanced Encryption Standard">AES</a></li>
<li><a href="Blowfish_(cipher)" title="Blowfish (cipher)">Blowfish</a></li>
<li><a href="Data_Encryption_Standard" title="Data Encryption Standard">DES</a> (<a href="DES_supplementary_material" title="DES supplementary material">internal mechanics</a>, <a href="Triple_DES" title="Triple DES">Triple DES</a>)</li>
<li><a href="Serpent_(cipher)" title="Serpent (cipher)">Serpent</a></li>
<li><a href="SM4_(cipher)" title="SM4 (cipher)">SM4</a></li>
<li><a href="Twofish" title="Twofish">Twofish</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Less common<br>algorithms</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="ARIA_(cipher)" title="ARIA (cipher)">ARIA</a></li>
<li><a href="Camellia_(cipher)" title="Camellia (cipher)">Camellia</a></li>
<li><a href="CAST-128" title="CAST-128">CAST-128</a></li>
<li><a href="GOST_(block_cipher)" title="GOST (block cipher)">GOST</a></li>
<li><a href="International_Data_Encryption_Algorithm" title="International Data Encryption Algorithm">IDEA</a></li>
<li><a href="LEA_(cipher)" title="LEA (cipher)">LEA</a></li>
<li><a href="RC5" title="RC5">RC5</a></li>
<li><a href="RC6" title="RC6">RC6</a></li>
<li><a href="SEED" title="SEED">SEED</a></li>
<li><a href="Skipjack_(cipher)" title="Skipjack (cipher)">Skipjack</a></li>
<li><a href="Tiny_Encryption_Algorithm" title="Tiny Encryption Algorithm">TEA</a></li>
<li><a href="XTEA" title="XTEA">XTEA</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other<br>algorithms</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="3-Way" title="3-Way">3-Way</a></li>
<li><a href="Adiantum_(cipher)" title="Adiantum (cipher)">Adiantum</a></li>
<li><a href="Akelarre_(cipher)" title="Akelarre (cipher)">Akelarre</a></li>
<li><a href="Anubis_(cipher)" title="Anubis (cipher)">Anubis</a></li>
<li><a href="Ascon_(cipher)" title="Ascon (cipher)">Ascon</a></li>
<li><a href="BaseKing" title="BaseKing">BaseKing</a></li>
<li><a href="BassOmatic" title="BassOmatic">BassOmatic</a></li>
<li><a href="BATON" title="BATON">BATON</a></li>
<li><a href="BEAR_and_LION_ciphers" title="BEAR and LION ciphers">BEAR and LION</a></li>
<li><a href="CAST-256" title="CAST-256">CAST-256</a></li>
<li><a href="Chiasmus_(cipher)" title="Chiasmus (cipher)">Chiasmus</a></li>
<li><a href="CIKS-1" title="CIKS-1">CIKS-1</a></li>
<li><a href="CIPHERUNICORN-A" title="CIPHERUNICORN-A">CIPHERUNICORN-A</a></li>
<li><a href="CIPHERUNICORN-E" title="CIPHERUNICORN-E">CIPHERUNICORN-E</a></li>
<li><a href="CLEFIA" title="CLEFIA">CLEFIA</a></li>
<li><a href="Cellular_Message_Encryption_Algorithm" title="Cellular Message Encryption Algorithm">CMEA</a></li>
<li><a href="Cobra_ciphers" title="Cobra ciphers">Cobra</a></li>
<li><a href="COCONUT98" title="COCONUT98">COCONUT98</a></li>
<li><a href="Crab_(cipher)" title="Crab (cipher)">Crab</a></li>
<li><a href="Cryptomeria_cipher" title="Cryptomeria cipher">Cryptomeria/C2</a></li>
<li><a href="CRYPTON" title="CRYPTON">CRYPTON</a></li>
<li><a href="CS-Cipher" title="CS-Cipher">CS-Cipher</a></li>
<li><a href="DEAL" title="DEAL">DEAL</a></li>
<li><a href="DES-X" title="DES-X">DES-X</a></li>
<li><a href="DFC_(cipher)" title="DFC (cipher)">DFC</a></li>
<li><a href="E2_(cipher)" title="E2 (cipher)">E2</a></li>
<li><a href="FEAL" title="FEAL">FEAL</a></li>
<li><a href="FEA-M" title="FEA-M">FEA-M</a></li>
<li><a href="FROG" title="FROG">FROG</a></li>
<li><a href="GDES" title="GDES">G-DES</a></li>
<li><a href="Grand_Cru_(cipher)" title="Grand Cru (cipher)">Grand Cru</a></li>
<li><a href="Hasty_Pudding_cipher" title="Hasty Pudding cipher">Hasty Pudding cipher</a></li>
<li><a href="Hierocrypt" title="Hierocrypt">Hierocrypt</a></li>
<li><a href="ICE_(cipher)" title="ICE (cipher)">ICE</a></li>
<li><a href="IDEA_NXT" title="IDEA NXT">IDEA NXT</a></li>
<li><a href="Intel_Cascade_Cipher" title="Intel Cascade Cipher">Intel Cascade Cipher</a></li>
<li><a href="Iraqi_block_cipher" title="Iraqi block cipher">Iraqi</a></li>
<li><a href="Kalyna_(cipher)" title="Kalyna (cipher)">Kalyna</a></li>
<li><a href="KASUMI" title="KASUMI">KASUMI</a></li>
<li><a href="KeeLoq" title="KeeLoq">KeeLoq</a></li>
<li><a href="KHAZAD" title="KHAZAD">KHAZAD</a></li>
<li><a href="Khufu_and_Khafre" title="Khufu and Khafre">Khufu and Khafre</a></li>
<li><a href="KN-Cipher" title="KN-Cipher">KN-Cipher</a></li>
<li><a href="Kuznyechik" title="Kuznyechik">Kuznyechik</a></li>
<li><a href="Ladder-DES" title="Ladder-DES">Ladder-DES</a></li>
<li>LOKI (<a href="LOKI97" title="LOKI97">97</a>, <a href="LOKI" title="LOKI">89/91</a>)</li>
<li><a href="Lucifer_(cipher)" title="Lucifer (cipher)">Lucifer</a></li>
<li><a href="M6_(cipher)" title="M6 (cipher)">M6</a></li>
<li><a href="M8_(cipher)" title="M8 (cipher)">M8</a></li>
<li><a href="MacGuffin_(cipher)" title="MacGuffin (cipher)">MacGuffin</a></li>
<li><a href="Madryga" title="Madryga">Madryga</a></li>
<li><a href="MAGENTA" title="MAGENTA">MAGENTA</a></li>
<li><a href="MARS_(cipher)" title="MARS (cipher)">MARS</a></li>
<li><a href="Mercy_(cipher)" title="Mercy (cipher)">Mercy</a></li>
<li><a href="MESH_(cipher)" title="MESH (cipher)">MESH</a></li>
<li><a href="MISTY1" title="MISTY1">MISTY1</a></li>
<li><a href="MMB_(cipher)" title="MMB (cipher)">MMB</a></li>
<li><a href="MULTI2" title="MULTI2">MULTI2</a></li>
<li><a href="MultiSwap" title="MultiSwap">MultiSwap</a></li>
<li><a href="New_Data_Seal" title="New Data Seal">New Data Seal</a></li>
<li><a href="NewDES" title="NewDES">NewDES</a></li>
<li><a href="Nimbus_(cipher)" title="Nimbus (cipher)">Nimbus</a></li>
<li><a href="NOEKEON" title="NOEKEON">NOEKEON</a></li>
<li><a href="NUSH" title="NUSH">NUSH</a></li>
<li><a href="PRESENT" title="PRESENT">PRESENT</a></li>
<li><a href="Prince_(cipher)" title="Prince (cipher)">Prince</a></li>
<li><a href="Q_(cipher)" title="Q (cipher)">Q</a></li>
<li><a href="QARMA" title="QARMA">QARMA</a></li>
<li><a href="RC2" title="RC2">RC2</a></li>
<li><a href="REDOC" title="REDOC">REDOC</a></li>
<li><a href="Red_Pike_(cipher)" title="Red Pike (cipher)">Red Pike</a></li>
<li><a href="S-1_block_cipher" title="S-1 block cipher">S-1</a></li>
<li><a href="Secure_and_Fast_Encryption_Routine" title="Secure and Fast Encryption Routine">SAFER</a></li>
<li><a href="SAVILLE" title="SAVILLE">SAVILLE</a></li>
<li><a href="SC2000" title="SC2000">SC2000</a></li>
<li><a href="SHACAL" title="SHACAL">SHACAL</a></li>
<li><a href="SHARK" title="SHARK">SHARK</a></li>
<li><a href="Simon_(cipher)" title="Simon (cipher)">Simon</a></li>
<li><a href="Speck_(cipher)" title="Speck (cipher)">Speck</a></li>
<li><a href="Spectr-H64" title="Spectr-H64">Spectr-H64</a></li>
<li><a href="Square_(cipher)" title="Square (cipher)">Square</a></li>
<li><a href="SXAL/MBAL" title="SXAL/MBAL">SXAL/MBAL</a></li>
<li><a href="Threefish" title="Threefish">Threefish</a></li>
<li><a href="Treyfer" title="Treyfer">Treyfer</a></li>
<li><a href="UES_(cipher)" title="UES (cipher)">UES</a></li>
<li><a href="Xmx" title="Xmx">xmx</a></li>
<li><a href="XXTEA" title="XXTEA">XXTEA</a></li>
<li><a href="Zodiac_(cipher)" title="Zodiac (cipher)">Zodiac</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Design</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Feistel_cipher" title="Feistel cipher">Feistel network</a></li>
<li><a href="Key_schedule" title="Key schedule">Key schedule</a></li>
<li><a href="Lai%E2%80%93Massey_scheme" title="Lai–Massey scheme">Lai–Massey scheme</a></li>
<li><a href="Product_cipher" title="Product cipher">Product cipher</a></li>
<li><a href="S-box" title="S-box">S-box</a></li>
<li><a href="Permutation_box" title="Permutation box">P-box</a></li>
<li><a href="Substitution%E2%80%93permutation_network" title="Substitution–permutation network">SPN</a></li>
<li><a href="Confusion_and_diffusion" title="Confusion and diffusion">Confusion and diffusion</a></li>
<li><a href="Round_(cryptography)" title="Round (cryptography)">Round</a></li>
<li><a href="Avalanche_effect" title="Avalanche effect">Avalanche effect</a></li>
<li><a href="Block_size_(cryptography)" title="Block size (cryptography)">Block size</a></li>
<li><a href="Key_size" title="Key size">Key size</a></li>
<li><a href="Key_whitening" title="Key whitening">Key whitening</a> (<a href="Whitening_transformation" title="Whitening transformation">Whitening transformation</a>)</li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Attack<br>(<a href="Cryptanalysis" title="Cryptanalysis">cryptanalysis</a>)</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Brute-force_attack" title="Brute-force attack">Brute-force</a> (<a href="EFF_DES_cracker" title="EFF DES cracker">EFF DES cracker</a>)</li>
<li><a href="Meet-in-the-middle_attack" title="Meet-in-the-middle attack">MITM</a>
<ul><li><a href="Biclique_attack" title="Biclique attack">Biclique attack</a></li>
<li><a href="3-subset_meet-in-the-middle_attack" title="3-subset meet-in-the-middle attack">3-subset MITM attack</a></li></ul></li>
<li><a href="Linear_cryptanalysis" title="Linear cryptanalysis">Linear</a> (<a href="Piling-up_lemma" title="Piling-up lemma">Piling-up lemma</a>)</li>
<li><a href="Differential_cryptanalysis" title="Differential cryptanalysis">Differential</a>
<ul><li><a href="Impossible_differential_cryptanalysis" title="Impossible differential cryptanalysis">Impossible</a></li>
<li><a href="Truncated_differential_cryptanalysis" title="Truncated differential cryptanalysis">Truncated</a></li>
<li><a href="Higher-order_differential_cryptanalysis" title="Higher-order differential cryptanalysis">Higher-order</a></li></ul></li>
<li><a href="Differential-linear_attack" title="Differential-linear attack">Differential-linear</a></li>
<li><a href="Distinguishing_attack" title="Distinguishing attack">Distinguishing</a> (<a href="Known-key_distinguishing_attack" title="Known-key distinguishing attack">Known-key</a>)</li>
<li><a href="Integral_cryptanalysis" title="Integral cryptanalysis">Integral/Square</a></li>
<li><a href="Boomerang_attack" title="Boomerang attack">Boomerang</a></li>
<li><a href="Related-key_attack" title="Related-key attack">Related-key</a></li>
<li><a href="Slide_attack" title="Slide attack">Slide</a></li>
<li><a href="Rotational_cryptanalysis" title="Rotational cryptanalysis">Rotational</a></li>
<li><a href="Side-channel_attack" title="Side-channel attack">Side-channel</a>
<ul><li><a href="Timing_attack" title="Timing attack">Timing</a></li>
<li><a href="Power_analysis" title="Power analysis">Power-monitoring</a></li>
<li><a href="Electromagnetic_attack" title="Electromagnetic attack">Electromagnetic</a></li>
<li><a href="Acoustic_cryptanalysis" title="Acoustic cryptanalysis">Acoustic</a></li>
<li><a href="Differential_fault_analysis" title="Differential fault analysis">Differential-fault</a></li></ul></li>
<li><a href="XSL_attack" title="XSL attack">XSL</a></li>
<li><a href="Interpolation_attack" title="Interpolation attack">Interpolation</a></li>
<li><a href="Partitioning_cryptanalysis" title="Partitioning cryptanalysis">Partitioning</a></li>
<li><a href="Rubber-hose_cryptanalysis" class="mw-redirect" title="Rubber-hose cryptanalysis">Rubber-hose</a></li>
<li><a href="Black-bag_cryptanalysis" title="Black-bag cryptanalysis">Black-bag</a></li>
<li><a href="Davies_attack" title="Davies attack">Davies</a></li>
<li><a href="Rebound_attack" title="Rebound attack">Rebound</a></li>
<li><a href="Weak_key" title="Weak key">Weak key</a></li>
<li><a href="Kendall_rank_correlation_coefficient" title="Kendall rank correlation coefficient">Tau</a></li>
<li><a href="Chi-squared_test" title="Chi-squared test">Chi-square</a></li>
<li><a href="Time/memory/data_tradeoff_attack" title="Time/memory/data tradeoff attack">Time/memory/data tradeoff</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Standardization</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Advanced_Encryption_Standard_process" title="Advanced Encryption Standard process">AES process</a></li>
<li><a href="CRYPTREC" title="CRYPTREC">CRYPTREC</a></li>
<li><a href="NESSIE" title="NESSIE">NESSIE</a></li>
<li><a href="NSA_Suite_B_Cryptography" title="NSA Suite B Cryptography">NSA Suite B</a></li>
<li><a href="Commercial_National_Security_Algorithm_Suite" title="Commercial National Security Algorithm Suite">CNSA</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Utilization</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Initialization_vector" title="Initialization vector">Initialization vector</a></li>
<li><a href="Block_cipher_mode_of_operation" title="Block cipher mode of operation">Mode of operation</a></li>
<li><a href="Padding_(cryptography)" title="Padding (cryptography)">Padding</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Cryptography149" style="font-size:114%;margin:0 4em"><a href="Cryptography" title="Cryptography">Cryptography</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="History_of_cryptography" title="History of cryptography">History of cryptography</a></li>
<li><a href="Outline_of_cryptography" title="Outline of cryptography">Outline of cryptography</a></li>
<li><a href="Classical_cipher" title="Classical cipher">Classical cipher</a></li>
<li><a href="Cryptographic_protocol" title="Cryptographic protocol">Cryptographic protocol</a>
<ul><li><a href="Authentication_protocol" title="Authentication protocol">Authentication protocol</a></li></ul></li>
<li><a href="Cryptographic_primitive" title="Cryptographic primitive">Cryptographic primitive</a></li>
<li><a href="Cryptanalysis" title="Cryptanalysis">Cryptanalysis</a></li>
<li><a href="Cryptocurrency" title="Cryptocurrency">Cryptocurrency</a></li>
<li><a href="Cryptosystem" title="Cryptosystem">Cryptosystem</a></li>
<li><a href="Cryptographic_nonce" title="Cryptographic nonce">Cryptographic nonce</a></li>
<li><a href="Cryptovirology" title="Cryptovirology">Cryptovirology</a></li>
<li><a href="Hash_function" title="Hash function">Hash function</a>
<ul><li><a href="Cryptographic_hash_function" title="Cryptographic hash function">Cryptographic hash function</a></li>
<li><a href="Key_derivation_function" title="Key derivation function">Key derivation function</a></li>
<li><a href="Secure_Hash_Algorithms" title="Secure Hash Algorithms">Secure Hash Algorithms</a></li></ul></li>
<li><a href="Digital_signature" title="Digital signature">Digital signature</a></li>
<li><a href="Kleptography" title="Kleptography">Kleptography</a></li>
<li><a href="Key_(cryptography)" title="Key (cryptography)">Key (cryptography)</a></li>
<li><a href="Key_exchange" title="Key exchange">Key exchange</a></li>
<li><a href="Key_generator" title="Key generator">Key generator</a></li>
<li><a href="Key_schedule" title="Key schedule">Key schedule</a></li>
<li><a href="Key_stretching" title="Key stretching">Key stretching</a></li>
<li><a href="Keygen" title="Keygen">Keygen</a></li>
<li>Machines</li>
<li><a href="Cryptojacking_malware" class="mw-redirect" title="Cryptojacking malware">Cryptojacking malware</a></li>
<li><a href="Ransomware" title="Ransomware">Ransomware</a></li>
<li><a href="Random_number_generation" title="Random number generation">Random number generation</a>
<ul><li><a href="Cryptographically_secure_pseudorandom_number_generator" title="Cryptographically secure pseudorandom number generator">Cryptographically secure pseudorandom number generator</a> (CSPRNG)</li></ul></li>
<li><a href="Pseudorandom_noise" title="Pseudorandom noise">Pseudorandom noise</a> (PRN)</li>
<li><a href="Secure_channel" title="Secure channel">Secure channel</a></li>
<li><a href="Insecure_channel" class="mw-redirect" title="Insecure channel">Insecure channel</a></li>
<li><a href="Subliminal_channel" title="Subliminal channel">Subliminal channel</a></li>
<li><a href="Encryption" title="Encryption">Encryption</a></li>
<li><a href="Decryption" class="mw-redirect" title="Decryption">Decryption</a></li>
<li><a href="End-to-end_encryption" title="End-to-end encryption">End-to-end encryption</a></li>
<li><a href="Harvest_now%2C_decrypt_later" title="Harvest now, decrypt later">Harvest now, decrypt later</a></li>
<li><a href="Information-theoretic_security" title="Information-theoretic security">Information-theoretic security</a></li>
<li><a href="Plaintext" title="Plaintext">Plaintext</a></li>
<li><a href="Codetext" class="mw-redirect" title="Codetext">Codetext</a></li>
<li><a href="Ciphertext" title="Ciphertext">Ciphertext</a></li>
<li><a href="Shared_secret" title="Shared secret">Shared secret</a></li>
<li><a href="Trapdoor_function" title="Trapdoor function">Trapdoor function</a></li>
<li><a href="Trusted_timestamping" title="Trusted timestamping">Trusted timestamping</a></li>
<li><a href="Key-based_routing" title="Key-based routing">Key-based routing</a></li>
<li><a href="Onion_routing" title="Onion routing">Onion routing</a></li>
<li><a href="Garlic_routing" title="Garlic routing">Garlic routing</a></li>
<li><a href="Kademlia" title="Kademlia">Kademlia</a></li>
<li><a href="Mix_network" title="Mix network">Mix network</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Mathematics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Cryptographic_hash_function" title="Cryptographic hash function">Cryptographic hash function</a></li>
<li><a href="Block_cipher" title="Block cipher">Block cipher</a></li>
<li><a href="Stream_cipher" title="Stream cipher">Stream cipher</a></li>
<li><a href="Symmetric-key_algorithm" title="Symmetric-key algorithm">Symmetric-key algorithm</a></li>
<li><a href="Authenticated_encryption" title="Authenticated encryption">Authenticated encryption</a></li>
<li><a href="Public-key_cryptography" title="Public-key cryptography">Public-key cryptography</a></li>
<li><a href="Quantum_key_distribution" title="Quantum key distribution">Quantum key distribution</a></li>
<li><a href="Quantum_cryptography" title="Quantum cryptography">Quantum cryptography</a></li>
<li><a href="Post-quantum_cryptography" title="Post-quantum cryptography">Post-quantum cryptography</a></li>
<li><a href="Message_authentication_code" title="Message authentication code">Message authentication code</a></li>
<li><a href="Cryptographically_secure_pseudorandom_number_generator" title="Cryptographically secure pseudorandom number generator">Random numbers</a></li>
<li><a href="Steganography" title="Steganography">Steganography</a></li></ul>
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