Fix alignment complaints from Peter

paper/3-RFC.tex

@@ -13,14 +13,14 @@ Definition RFC (n: list Z) (p: list Z) : list Z :=
   let k := decodeScalar25519 n in
   let u := decodeUCoordinate p in
   let t := montgomery_rec
-    255  (* iterate 255 times *)
-    k    (* clamped n         *)
+    255  (* iterate 255 times  *)
+    k    (* clamped n          *)
     1    (* x_2                *)
     u    (* x_3                *)
     0    (* z_2                *)
     1    (* z_3                *)
-    0    (* dummy             *)
-    0    (* dummy             *)
+    0    (* dummy              *)
+    0    (* dummy              *)
     u    (* x_1                *) in
   let a := get_a t in
   let c := get_c t in
@@ -38,43 +38,43 @@ Fixpoint montgomery_rec (m : nat) (z : T')
 (* b: x3              *)
 (* c: z2              *)
 (* d: z3              *)
-(* e: temporary  var  *)
-(* f: temporary  var  *)
+(* e: temporary  var   *)
+(* f: temporary  var   *)
 (* x: x1              *)
 (T * T * T * T * T * T) :=
 match m with
 | 0%nat => (a,b,c,d,e,f)
 | S n =>
   let r := Getbit (Z.of_nat n) z in
-    (* k_t = (k >> t) & 1                       *)
-    (* swap <- k_t                              *)
+    (* k_t = (k >> t) & 1                         *)
+    (* swap <- k_t                                *)
   let (a, b) := (Sel25519 r a b, Sel25519 r b a) in
-    (* (x_2, x_3) = cswap(swap, x_2, x_3)            *)
+    (* (x_2, x_3) = cswap(swap, x_2, x_3)         *)
   let (c, d) := (Sel25519 r c d, Sel25519 r d c) in
-    (* (z_2, z_3) = cswap(swap, z_2, z_3)            *)
-  let e := a + c in  (* A = x_2 + z_2              *)
-  let a := a - c in  (* B = x_2 - z_2              *)
-  let c := b + d in  (* C = x_3 + z_3              *)
-  let b := b - d in  (* D = x_3 - z_3              *)
-  let d := e ^2 in    (* AA = A^2                  *)
-  let f := a ^2 in    (* BB = B^2                  *)
-  let a := c * a in  (* CB = C * B               *)
-  let c := b * e in  (* DA = D * A               *)
-  let e := a + c in  (* x_3 = (DA + CB)^2          *)
-  let a := a - c in  (* z_3 = x_1 * (DA - CB)^2     *)
-  let b := a ^2 in    (* z_3 = x_1 * (DA - CB)^2     *)
-  let c := d - f in  (* E = AA - BB             *)
+    (* (z_2, z_3) = cswap(swap, z_2, z_3)         *)
+  let e := a + c in (* A  = x_2+ z_2              *)
+  let a := a - c in (* B  = x_2- z_2              *)
+  let c := b + d in (* C  = x_3+ z_3              *)
+  let b := b - d in (* D  = x_3- z_3              *)
+  let d := e^2   in (* AA = A^2                   *)
+  let f := a^2   in (* BB = B^2                   *)
+  let a := c * a in (* CB = C * B                 *)
+  let c := b * e in (* DA = D * A                 *)
+  let e := a + c in (* x_3= (DA + CB)^2           *)
+  let a := a - c in (* z_3= x_1* (DA - CB)^2      *)
+  let b := a^2   in (* z_3= x_1* (DA - CB)^2      *)
+  let c := d - f in (* E  = AA - BB               *)
   let a := c * C_121665 in
-                     (* z_2 = E * (AA + a24 * E) *)
-  let a := a + d in  (* z_2 = E * (AA + a24 * E) *)
-  let c := c * a in  (* z_2 = E * (AA + a24 * E) *)
-  let a := d * f in  (* x_2 = AA * BB            *)
-  let d := b * x in  (* z_3 = x_1 * (DA - CB)^2    *)
-  let b := e ^2 in    (* x_3 = (DA + CB)^2         *)
+                    (* z_2 = E * (AA + a24 * E)   *)
+  let a := a + d in (* z_2 = E * (AA + a24 * E)   *)
+  let c := c * a in (* z_2 = E * (AA + a24 * E)   *)
+  let a := d * f in (* x_2 = AA * BB              *)
+  let d := b * x in (* z_3 = x_1* (DA - CB)^2     *)
+  let b := e ^2 in  (* x_3 = (DA + CB)^2          *)
   let (a, b) := (Sel25519 r a b, Sel25519 r b a) in
-    (* (x_2, x_3) = cswap(swap, x_2, x_3)           *)
+    (* (x_2, x_3) = cswap(swap, x_2, x_3)         *)
   let (c, d) := (Sel25519 r c d, Sel25519 r d c) in
-    (* (z_2, z_3) = cswap(swap, z_2, z_3)           *)
+    (* (z_2, z_3) = cswap(swap, z_2, z_3)         *)
   montgomery_rec n z a b c d e f x
 end.
 \end{lstlisting}

paper/A2_coq.tex

@@ -17,8 +17,8 @@ Class Ops (T T': Type) (Mod: T -> T):=
   C_0 : T;                     (* Constant 0    *)
   C_1 : T;                     (* Constant 1    *)
   C_121665: T;                 (* const (a-2)/4 *)
-  Sel25519: Z -> T -> T -> T; (* CSWAP         *)
-  Getbit: Z -> T' -> Z;       (* ith bit       *)
+  Sel25519: Z -> T -> T -> T;  (* CSWAP         *)
+  Getbit: Z -> T' -> Z;        (* ith bit       *)
 }.
 
 Local Notation "X + Y" := (A X Y) (only parsing).
@@ -27,49 +27,49 @@ Local Notation "X * Y" := (M X Y) (only parsing).
 Local Notation "X ^2" := (Sq X) (at level 40,
   only parsing, left associativity).
 
-Fixpoint montgomery_rec (m: nat) (z: T')
+Fixpoint montgomery_rec (m : nat) (z : T')
 (a: T) (b: T) (c: T) (d: T) (e: T) (f: T) (x: T) :
 (* a: x2              *)
 (* b: x3              *)
 (* c: z2              *)
 (* d: z3              *)
-(* e: temporary  var  *)
-(* f: temporary  var  *)
+(* e: temporary  var   *)
+(* f: temporary  var   *)
 (* x: x1              *)
 (T * T * T * T * T * T) :=
 match m with
 | 0%nat => (a,b,c,d,e,f)
 | S n =>
   let r := Getbit (Z.of_nat n) z in
-    (* k_t = (k >> t) & 1                       *)
-    (* swap <- k_t                              *)
+    (* k_t = (k >> t) & 1                         *)
+    (* swap <- k_t                                *)
   let (a, b) := (Sel25519 r a b, Sel25519 r b a) in
-    (* (x_2, x_3) = cswap(swap, x_2, x_3)            *)
+    (* (x_2, x_3) = cswap(swap, x_2, x_3)         *)
   let (c, d) := (Sel25519 r c d, Sel25519 r d c) in
-    (* (z_2, z_3) = cswap(swap, z_2, z_3)            *)
-  let e := a + c in  (* A = x_2 + z_2              *)
-  let a := a - c in  (* B = x_2 - z_2              *)
-  let c := b + d in  (* C = x_3 + z_3              *)
-  let b := b - d in  (* D = x_3 - z_3              *)
-  let d := e ^2 in    (* AA = A^2                  *)
-  let f := a ^2 in    (* BB = B^2                  *)
-  let a := c * a in  (* CB = C * B               *)
-  let c := b * e in  (* DA = D * A               *)
-  let e := a + c in  (* x_3 = (DA + CB)^2          *)
-  let a := a - c in  (* z_3 = x_1 * (DA - CB)^2     *)
-  let b := a ^2 in    (* z_3 = x_1 * (DA - CB)^2     *)
-  let c := d - f in  (* E = AA - BB             *)
+    (* (z_2, z_3) = cswap(swap, z_2, z_3)         *)
+  let e := a + c in (* A  = x_2+ z_2              *)
+  let a := a - c in (* B  = x_2- z_2              *)
+  let c := b + d in (* C  = x_3+ z_3              *)
+  let b := b - d in (* D  = x_3- z_3              *)
+  let d := e^2   in (* AA = A^2                   *)
+  let f := a^2   in (* BB = B^2                   *)
+  let a := c * a in (* CB = C * B                 *)
+  let c := b * e in (* DA = D * A                 *)
+  let e := a + c in (* x_3= (DA + CB)^2           *)
+  let a := a - c in (* z_3= x_1* (DA - CB)^2      *)
+  let b := a^2   in (* z_3= x_1* (DA - CB)^2      *)
+  let c := d - f in (* E  = AA - BB               *)
   let a := c * C_121665 in
-                     (* z_2 = E * (AA + a24 * E) *)
-  let a := a + d in  (* z_2 = E * (AA + a24 * E) *)
-  let c := c * a in  (* z_2 = E * (AA + a24 * E) *)
-  let a := d * f in  (* x_2 = AA * BB            *)
-  let d := b * x in  (* z_3 = x_1 * (DA - CB)^2    *)
-  let b := e ^2 in    (* x_3 = (DA + CB)^2         *)
+                    (* z_2 = E * (AA + a24 * E)   *)
+  let a := a + d in (* z_2 = E * (AA + a24 * E)   *)
+  let c := c * a in (* z_2 = E * (AA + a24 * E)   *)
+  let a := d * f in (* x_2 = AA * BB              *)
+  let d := b * x in (* z_3 = x_1* (DA - CB)^2     *)
+  let b := e ^2 in  (* x_3 = (DA + CB)^2          *)
   let (a, b) := (Sel25519 r a b, Sel25519 r b a) in
-    (* (x_2, x_3) = cswap(swap, x_2, x_3)           *)
+    (* (x_2, x_3) = cswap(swap, x_2, x_3)         *)
   let (c, d) := (Sel25519 r c d, Sel25519 r d c) in
-    (* (z_2, z_3) = cswap(swap, z_2, z_3)           *)
+    (* (z_2, z_3) = cswap(swap, z_2, z_3)         *)
   montgomery_rec n z a b c d e f x
 end.
 
@@ -155,7 +155,7 @@ Proof.
   apply Mid.A.        (* instantiate +       *)
   apply Mid.M.        (* instantiate *       *)
   apply Mid.Zub.      (* instantiate -       *)
-  apply Mid.Sq.       (* instantiate x^2      *)
+  apply Mid.Sq.       (* instantiate x^2     *)
   apply Mid.C_0.      (* instantiate Const 0 *)
   apply Mid.C_1.      (* instantiate Const 1 *)
   apply Mid.C_121665. (* instantiate (a-2)/4 *)
@@ -177,14 +177,14 @@ Definition RFC (n: list Z) (p: list Z) : list Z :=
   let k := decodeScalar25519 n in
   let u := decodeUCoordinate p in
   let t := montgomery_rec
-    255  (* iterate 255 times *)
-    k    (* clamped n         *)
+    255  (* iterate 255 times  *)
+    k    (* clamped n          *)
     1    (* x_2                *)
     u    (* x_3                *)
     0    (* z_2                *)
     1    (* z_3                *)
-    0    (* dummy             *)
-    0    (* dummy             *)
+    0    (* dummy              *)
+    0    (* dummy              *)
     u    (* x_1                *) in
   let a := get_a t in
   let c := get_c t in

paper/setup.sty

@@ -35,7 +35,7 @@
 \renewcommand{\algorithmicrequire}{\textbf{Input:\ }}
 \renewcommand{\algorithmicensure}{\textbf{Output:\ }}
 
-\setlength{\abovecaptionskip}{-10pt}
+\setlength{\abovecaptionskip}{-9pt}
 
 \newcommand{\todo}[1]{
 {\color{red} \bf TODO: #1}
@@ -233,11 +233,11 @@ columns=[l]flexible,
 literate=
     % {\\forall}{{\color{dkgreen}{$\forall\;$}}}1
     % {\\exists}{{$\exists\;$}}1
-    {<-}{{$\leftarrow\;$}}1
+    {<-}{{\makebox[8pt][l]{$\leftarrow\;$}}}1
     {=>}{{$\Rightarrow\;$}}1
     {==>}{{\texttt{==>}\;}}1
 %    {:>}{{\texttt{:>}\;}}1
-    {->}{{$\rightarrow\;$}}1
+    {->}{{\makebox[8pt][l]{$\rightarrow\;$}}}1
     {<->}{{$\leftrightarrow\;$}}1
     {<=}{{$\leq\;$}}1
     {==}{{\texttt{==}\;}}1
@@ -274,38 +274,39 @@ literate=
     {^n}{{$^n$}}1
     {^+n}{{$^n$}}1
     {^m}{{$^m$}}1
-    {^2}{{$^2$}}1
-    {^+2}{{$^2$}}1
-    {^3}{{$^3$}}1
-    {^+3}{{$^3$}}1
+    {^2}{{\makebox[8pt][l]{$^2$}}}1
+    {^+2}{{\makebox[8pt][l]{$^2$}}}1
+    {^3}{{\makebox[8pt][l]{$^3$}}}1
+    {^+3}{{\makebox[8pt][l]{$^3$}}}1
     {^nd}{{$^{nd}$}}1
     {^rd}{{$^{rd}$}}1
     {^th}{{$^{th}$}}1
     {^255}{{$^{255}$}}1
     {^-1}{{$^{-1}$}}1
     {\%:R}{{}}1
-    {p1}{{p$_1$}}1
-    {p2}{{p$_2$}}1
-    {x1}{{x$_1$}}1
-    {x2}{{x$_2$}}1
-    {x3}{{x$_3$}}1
-    {x_1}{{x$_1$}}1
-    {x_2}{{x$_2$}}1
-    {x_3}{{x$_3$}}1
-    {x4}{{x$_4$}}1
-    {y1}{{y$_1$}}1
-    {y2}{{y$_2$}}1
-    {y3}{{y$_3$}}1
-    {y4}{{y$_4$}}1
-    {z1}{{z$_1$}}1
-    {z2}{{z$_2$}}1
-    {z3}{{z$_3$}}1
-    {z4}{{z$_4$}}1
-    {z_2}{{z$_2$}}1
-    {z_3}{{z$_3$}}1
-    {xs}{{x$_s$}}1
-    {\\-}{{$-$}}1
-    {\\+}{{$+$}}1
+    {p1}{{p\makebox[8pt][l]{$_1$}}}1
+    {p2}{{p\makebox[8pt][l]{$_2$}}}1
+    {x1}{{x\makebox[8pt][l]{$_1$}}}1
+    {x2}{{x\makebox[8pt][l]{$_2$}}}1
+    {x3}{{x\makebox[8pt][l]{$_3$}}}1
+    {x_1}{{x\makebox[8pt][l]{$_1$}}}1
+    {x_2}{{x\makebox[8pt][l]{$_2$}}}1
+    {x_3}{{x\makebox[8pt][l]{$_3$}}}1
+    {x4}{{x\makebox[8pt][l]{$_4$}}}1
+    {y1}{{y\makebox[8pt][l]{$_1$}}}1
+    {y2}{{y\makebox[8pt][l]{$_2$}}}1
+    {y3}{{y\makebox[8pt][l]{$_3$}}}1
+    {y4}{{y\makebox[8pt][l]{$_4$}}}1
+    {z1}{{z\makebox[8pt][l]{$_1$}}}1
+    {z2}{{z\makebox[8pt][l]{$_2$}}}1
+    {z3}{{z\makebox[8pt][l]{$_3$}}}1
+    {z4}{{z\makebox[8pt][l]{$_4$}}}1
+    {z_2}{{z\makebox[8pt][l]{$_2$}}}1
+    {z_3}{{z\makebox[8pt][l]{$_3$}}}1
+    {xs}{{x\makebox[8pt][l]{$_s$}}}1
+    {\\-}{{\makebox[9pt][c]{$-$}}}1
+    {\\+}{{\makebox[9pt][c]{$+$}}}1
+    {\\*}{{\makebox[9pt][c]{$*$}}}1
     {\\boxplus}{{$\boxplus$}}1
     {\\circ}{{$\circ$}}1
     {\\GF}{{$\mathbb{F}_{2^{255}-19}$}}1
@@ -385,7 +386,8 @@ literate=
   % basicstyle=\ttfamily\small, % font that is used for the code
   basicstyle=\ttfamily\footnotesize, % font that is used for the code
   identifierstyle=\color{doc@lstidentifier},
-  commentstyle=\color{doc@lstcomment}\itshape,
+  commentstyle=\color{doc@lstcomment}\footnotesize,
+  % \itshape,
   stringstyle=\color{doc@lststring},
   keywordstyle=\color{doc@lstkeyword},
   keywordstyle=[1]\color{doc@lstidentifiers2},