@@ -26,9 +26,9 @@ This allows us to state the result precisely, and makes it clear how each round
2626values of the previous rounds.
2727<p />
2828It seems convenient to change the round counter <math ><mi >q</mi ></math > to be 1-based (and
29- <math ><msup ><mi >X</mi ><mrow >(< mn >0</mn >) </mrow ></msup ></math >
29+ <math ><msup ><mi >X</mi ><mrow >< mo >(</ mo >< mn >0</mn >< mo >)</ mo > </mrow ></msup ></math >
3030is an alias for the initial value, <math ><mi >X</mi ></math >), so that the final result is
31- <math ><msup ><mi >X</mi ><mrow >(< mi >r</mi >) </mrow ></msup ></math >.
31+ <math ><msup ><mi >X</mi ><mrow >< mo >(</ mo >< mi >r</mi >< mo >)</ mo > </mrow ></msup ></math >.
3232</p >
3333</discussion >
3434
@@ -60,14 +60,14 @@ the <math><mi>i</mi></math>th element of <math><mi>Y</mi></math> after applying
6060and the length-<math ><mi >n</mi ></math > sequence <math ><mi >X</mi ></math > into a length-<math ><mi >n</mi ></math > output
6161sequence <math ><mi >Y</mi ></math >. Philox applies an <math ><mi >r</mi ></math >-round substitution-permutation network to
6262the values in <math ><mi >X</mi ></math >. <del >A single round of the generation algorithm performs the following steps:</del >
63- <ins >That is, there are intermediate values <math ><msup ><mi >X</mi ><mrow >(< mn >0</mn >) </mrow ></msup ></math >,
64- <math ><msup ><mi >X</mi ><mrow >(< mn >1</mn >) </mrow ></msup ></math >, … ,
65- <math ><msup ><mi >X</mi ><mrow >(< mi >r</mi >) </mrow ></msup ></math >, where
66- <math ><msup ><mi >X</mi ><mrow >(< mn >0</mn >) </mrow ></msup ><mo >:=</mo ><mi >X</mi ></math >, and for each round
63+ <ins >That is, there are intermediate values <math ><msup ><mi >X</mi ><mrow >< mo >(</ mo >< mn >0</mn >< mo >)</ mo > </mrow ></msup ></math >,
64+ <math ><msup ><mi >X</mi ><mrow >< mo >(</ mo >< mn >1</mn >< mo >)</ mo > </mrow ></msup ></math >, … ,
65+ <math ><msup ><mi >X</mi ><mrow >< mo >(</ mo >< mi >r</mi >< mo >)</ mo > </mrow ></msup ></math >, where
66+ <math ><msup ><mi >X</mi ><mrow >< mo >(</ mo >< mn >0</mn >< mo >)</ mo > </mrow ></msup ><mo >:=</mo ><mi >X</mi ></math >, and for each round
6767<math ><mi >q</mi ></math > (with <math ><mi >q</mi ><mo >=</mo ><mn >1</mn >, … , <mi >r</mi ></math >),
68- <math ><msup ><mi >X</mi ><mrow >(< mi >q</mi >) </mrow ></msup ></math > is computed from
69- <math ><msup ><mi >X</mi ><mrow >(< mi >q</mi ><mo >-</mo ><mn >1</mn >) </mrow ></msup ></math > as follows. The output sequence
70- is <math ><msup ><mi >X</mi ><mrow >(< mi >r</mi >) </mrow ></msup ></math >.</ins >
68+ <math ><msup ><mi >X</mi ><mrow >< mo >(</ mo >< mi >q</mi >< mo >)</ mo > </mrow ></msup ></math > is computed from
69+ <math ><msup ><mi >X</mi ><mrow >< mo >(</ mo >< mi >q</mi ><mo >-</mo ><mn >1</mn >< mo >)</ mo > </mrow ></msup ></math > as follows. The output sequence
70+ is <math ><msup ><mi >X</mi ><mrow >< mo >(</ mo >< mi >r</mi >< mo >)</ mo > </mrow ></msup ></math >.</ins >
7171</p >
7272<ol style =" list-style-type: none" >
7373<li ><p >(4.1) — <del >The output sequence <math ><mi >X</mi ><mi >'</mi ></math > of the previous round (<math ><mi >X</mi ></math >
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