link + backquote fixes

README.md

@@ -2,7 +2,7 @@
 Cocks--Pinch curves with embedding degree 5 to 8 and optimal ate pairing
 ========================================================================
 
-This repository holds companion code for the paper.
+This repository holds companion code for the paper [Cocks-Pinch curves of embedding degrees five to eight and optimal ate pairing computation](https://ia.cr/2019/431).
 
 We provide code for the following tasks.
  * Generate tables with estimated costs of pairing computations for
@@ -38,6 +38,7 @@ paper.
 
 To reproduce this, one does as follows. Notice that the number of
 inversions depends on the parameter `i`.
+
     sage: load("final_expo_k57.py")
     sage: print_final_expo_k57()
     cost for k=5 i=1: 3p + 1c + 7M + 3T
@@ -55,6 +56,7 @@ For the cases `k=6` and `k=8`, the exact formulas depend on the chosen
 CM discriminant, and employ further optimizations. Formulas as well as
 costs, matching those found in §5.2 in the paper, can be obtained as
 follows:
+
     sage: load("final_expo_k68.sage")
     sage: formulas(6)
     [lots of output]
@@ -324,7 +326,7 @@ multiplication software. You have two options.
         localhost ~ $ HOME=/tmp/cm-data/ /tmp/cm/bin/classpoly 10000000147 0 19136268507011813102345745679502968108741656052980768772125358458053107229388560784972377216338036093499504796562349965064380467318189753451458608209221520383584470050757421467305085292271391865417111 /tmp/H5.txt
 
     The next step is to edit the resulting file `/tmp/H5.txt` to transform
-    it into valid sage code (e.g. `/tmp/H5.sage, with all coefficients of
+    it into valid sage code (e.g. `/tmp/H5.sage`, with all coefficients of
     the polynomial in one single line), and then load it into sage. Note
     that root finding takes about 20 minutes to complete.
 
@@ -515,7 +517,7 @@ Search for curves of embedding degree 6
 
 For k=6, we fix D=`3` in order to get efficient formulas from sextic twist.
 We are free to choose ht and hy with low hamming weight. This is
-done by passing `--hty_choice '2-naf<=5'.
+done by passing `--hty_choice '2-naf<=5'`.
 
 We choose `T` of hamming weight less or equal to 5 so that we have enough 
 choices to have `phi_6(T)` prime.
@@ -524,6 +526,7 @@ We decide to force `4 | #E` so that Edwards form can be used.
 
 We decompose the search in 8 fractions of the search space, done in two
 computers:
+
     sage search.sage -k 6 -D 3 --required_cofactor 4 --allowed_size_cofactor 10 --T_choice "2-naf<=5" --hty_choice "2-naf<=5" --lambdap 672 --lambdar 256  --save --check_small_subgroup_secure 15 --spawn 4 0 8
     sage search.sage -k 6 -D 3 --required_cofactor 4 --allowed_size_cofactor 10 --T_choice "2-naf<=5" --hty_choice "2-naf<=5" --lambdap 672 --lambdar 256  --save --check_small_subgroup_secure 15 --spawn 4 4 8
 
@@ -541,6 +544,7 @@ Search for curves of embedding degree 6 (second take with small h_t)
 For k=6, allowing arbitrary cofactors in `h_t` and `h_y` leads to an
 expensive second part of the final exponentiation. Therefore we restrict
 to `|ht|<=4`.
+
     search.sage -k 6 --D 3 --hty_choice '2-naf<=7,ht:max=4' --save --T_choice '2-naf<=5' --lambdap 672 --lambdar 256 --check_small_subgroup_secure 7 --required_cofactor 4 --allowed_automatic_cofactor 720 --allowed_cofactor 420 --allowed_size_cofactor 10
 
 and we obtain four curves for which G2 is also twist-secure :