data/66.json
{
"definitions" : {
"P_{i}" : [ "Plain text", { } ],
"E_{K}" : [ "Encryption", { } ],
"S_{i-1}" : [ "state of the shift register", { } ],
"x" : [ "number of bits", { } ],
"C_{i}" : [ "Chip text", { } ]
},
"constraints" : [ ],
"math_inputtex" : "P_i = \\mbox{head}(E_K (S_{i-1}), x) \\oplus C_i",
"math_inputtex_semantic" : "\\w{Q234460}{P}_i = \\wf{Q131030}{\\operatorname{head}}(\\wf{Q135035}{E}_K (\\wf{Q3505845}{S}_{i-1}), \\w{Q21199}{x}) \\oplus \\w{Q234460}{C}_i",
"correct_tex" : "P_i = \\mbox{head}(E_K (S_{i-1}), x) \\oplus C_i",
"correct_mml" : "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"p1.1.m1.1\" class=\"ltx_Math\" alttext=\"P_{i}=\\operatorname{head}(E_{K}(S_{i-1}),x)\\oplus C_{i}\" display=\"inline\">\n <semantics id=\"p1.1.m1.1a\">\n <mrow id=\"p1.1.m1.1.21\" xref=\"p1.1.m1.1.21.cmml\">\n <msub id=\"p1.1.m1.1.21.1\" xref=\"p1.1.m1.1.21.1.cmml\">\n <mi id=\"p1.1.m1.1.1\" xref=\"p1.1.m1.1.1.cmml\">P</mi>\n <mi id=\"p1.1.m1.1.2.1\" xref=\"p1.1.m1.1.2.1.cmml\">i</mi>\n </msub>\n <mo id=\"p1.1.m1.1.3\" xref=\"p1.1.m1.1.3.cmml\">=</mo>\n <mrow id=\"p1.1.m1.1.21.2\" xref=\"p1.1.m1.1.21.2.cmml\">\n <mrow id=\"p1.1.m1.1.21.2.1.2\" xref=\"p1.1.m1.1.21.2.1.1.cmml\">\n <mi id=\"p1.1.m1.1.7\" xref=\"p1.1.m1.1.7.cmml\">head</mi>\n <mo id=\"p1.1.m1.1.21.2.1.2a\" xref=\"p1.1.m1.1.21.2.1.1.cmml\"></mo>\n <mrow id=\"p1.1.m1.1.21.2.1.2.2\" xref=\"p1.1.m1.1.21.2.1.1.cmml\">\n <mo stretchy=\"false\" id=\"p1.1.m1.1.8\" xref=\"p1.1.m1.1.21.2.1.1.cmml\">(</mo>\n <mrow id=\"p1.1.m1.1.21.2.1.2.1.2\" xref=\"p1.1.m1.1.21.2.1.2.1.1.cmml\">\n <msub id=\"p1.1.m1.1.21.2.1.2.1.2.1\" xref=\"p1.1.m1.1.21.2.1.2.1.2.1.cmml\">\n <mi id=\"p1.1.m1.1.9\" xref=\"p1.1.m1.1.9.cmml\">E</mi>\n <mi id=\"p1.1.m1.1.10.1\" xref=\"p1.1.m1.1.10.1.cmml\">K</mi>\n </msub>\n <mo id=\"p1.1.m1.1.21.2.1.2.1.2a\" xref=\"p1.1.m1.1.21.2.1.2.1.1.cmml\"></mo>\n <mrow id=\"p1.1.m1.1.21.2.1.2.1.2.3\" xref=\"p1.1.m1.1.21.2.1.2.1.1.cmml\">\n <mo stretchy=\"false\" id=\"p1.1.m1.1.11\" xref=\"p1.1.m1.1.21.2.1.2.1.1.cmml\">(</mo>\n <msub id=\"p1.1.m1.1.21.2.1.2.1.2.2\" xref=\"p1.1.m1.1.21.2.1.2.1.2.2.cmml\">\n <mi id=\"p1.1.m1.1.12\" xref=\"p1.1.m1.1.12.cmml\">S</mi>\n <mrow id=\"p1.1.m1.1.13.1\" xref=\"p1.1.m1.1.13.1.cmml\">\n <mi id=\"p1.1.m1.1.13.1.1\" xref=\"p1.1.m1.1.13.1.1.cmml\">i</mi>\n <mo id=\"p1.1.m1.1.13.1.2\" xref=\"p1.1.m1.1.13.1.2.cmml\">-</mo>\n <mn id=\"p1.1.m1.1.13.1.3\" xref=\"p1.1.m1.1.13.1.3.cmml\">1</mn>\n </mrow>\n </msub>\n <mo stretchy=\"false\" id=\"p1.1.m1.1.14\" xref=\"p1.1.m1.1.21.2.1.2.1.1.cmml\">)</mo>\n </mrow>\n </mrow>\n <mo id=\"p1.1.m1.1.15\" xref=\"p1.1.m1.1.21.2.1.1.cmml\">,</mo>\n <mi id=\"p1.1.m1.1.16\" xref=\"p1.1.m1.1.16.cmml\">x</mi>\n <mo stretchy=\"false\" id=\"p1.1.m1.1.17\" xref=\"p1.1.m1.1.21.2.1.1.cmml\">)</mo>\n </mrow>\n </mrow>\n <mo id=\"p1.1.m1.1.18\" xref=\"p1.1.m1.1.18.cmml\">⊕</mo>\n <msub id=\"p1.1.m1.1.21.2.2\" xref=\"p1.1.m1.1.21.2.2.cmml\">\n <mi id=\"p1.1.m1.1.19\" xref=\"p1.1.m1.1.19.cmml\">C</mi>\n <mi id=\"p1.1.m1.1.20.1\" xref=\"p1.1.m1.1.20.1.cmml\">i</mi>\n </msub>\n </mrow>\n </mrow>\n <annotation-xml encoding=\"MathML-Content\" id=\"p1.1.m1.1b\">\n <apply id=\"p1.1.m1.1.21.cmml\" xref=\"p1.1.m1.1.21\">\n <eq id=\"p1.1.m1.1.3.cmml\" xref=\"p1.1.m1.1.3\"/>\n <apply id=\"p1.1.m1.1.21.1.cmml\" xref=\"p1.1.m1.1.21.1\">\n <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.21.1.1.cmml\" xref=\"p1.1.m1.1.21.1\">subscript</csymbol>\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.1.cmml\" xref=\"p1.1.m1.1.1\">Q234460</csymbol>\n <ci id=\"p1.1.m1.1.2.1.cmml\" xref=\"p1.1.m1.1.2.1\">𝑖</ci>\n </apply>\n <apply id=\"p1.1.m1.1.21.2.cmml\" xref=\"p1.1.m1.1.21.2\">\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.18.cmml\" xref=\"p1.1.m1.1.18\">direct-sum</csymbol>\n <apply id=\"p1.1.m1.1.21.2.1.1.cmml\" xref=\"p1.1.m1.1.21.2.1.2\">\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.7.cmml\" xref=\"p1.1.m1.1.7\">Q131030</csymbol>\n <apply id=\"p1.1.m1.1.21.2.1.2.1.1.cmml\" xref=\"p1.1.m1.1.21.2.1.2.1.2\">\n <apply id=\"p1.1.m1.1.21.2.1.2.1.2.1.cmml\" xref=\"p1.1.m1.1.21.2.1.2.1.2.1\">\n <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.21.2.1.2.1.2.1.1.cmml\" xref=\"p1.1.m1.1.21.2.1.2.1.2.1\">subscript</csymbol>\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.9.cmml\" xref=\"p1.1.m1.1.9\">Q135035</csymbol>\n <ci id=\"p1.1.m1.1.10.1.cmml\" xref=\"p1.1.m1.1.10.1\">𝐾</ci>\n </apply>\n <apply id=\"p1.1.m1.1.21.2.1.2.1.2.2.cmml\" xref=\"p1.1.m1.1.21.2.1.2.1.2.2\">\n <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.21.2.1.2.1.2.2.1.cmml\" xref=\"p1.1.m1.1.21.2.1.2.1.2.2\">subscript</csymbol>\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.12.cmml\" xref=\"p1.1.m1.1.12\">Q3505845</csymbol>\n <apply id=\"p1.1.m1.1.13.1.cmml\" xref=\"p1.1.m1.1.13.1\">\n <minus id=\"p1.1.m1.1.13.1.2.cmml\" xref=\"p1.1.m1.1.13.1.2\"/>\n <ci id=\"p1.1.m1.1.13.1.1.cmml\" xref=\"p1.1.m1.1.13.1.1\">𝑖</ci>\n <cn type=\"integer\" id=\"p1.1.m1.1.13.1.3.cmml\" xref=\"p1.1.m1.1.13.1.3\">1</cn>\n </apply>\n </apply>\n </apply>\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.16.cmml\" xref=\"p1.1.m1.1.16\">Q21199</csymbol>\n </apply>\n <apply id=\"p1.1.m1.1.21.2.2.cmml\" xref=\"p1.1.m1.1.21.2.2\">\n <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.21.2.2.1.cmml\" xref=\"p1.1.m1.1.21.2.2\">subscript</csymbol>\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.19.cmml\" xref=\"p1.1.m1.1.19\">Q234460</csymbol>\n <ci id=\"p1.1.m1.1.20.1.cmml\" xref=\"p1.1.m1.1.20.1\">𝑖</ci>\n </apply>\n </apply>\n </apply>\n </annotation-xml>\n <annotation encoding=\"application/x-tex\" id=\"p1.1.m1.1c\">P_{i}=\\operatorname{head}(E_{K}(S_{i-1}),x)\\oplus C_{i}</annotation>\n </semantics>\n</math>",
"uri" : "https://en.formulasearchengine.com/w/index.php?oldid=2482#math2482.8",
"title" : "Block_cipher_mode_of_operation",
"type" : "equation"
}