progs/perftest.c: Use from Glibc syscall numbers.

[catacomb] / pub / x448.h

diff --git a/pub/x448.h b/pub/x448.h
index f1b0f2c..42c9fb9 100644 (file)
--- a/pub/x448.h
+++ b/pub/x448.h
@@ -36,12 +36,25 @@
  *
  * This is X448, as described in RFC7748, based on the elliptic curve defined
  * in Mike Hamburg, `Ed448-Goldilocks, a new elliptic curve', EUROCRYPT 2016,
- * https://eprint.iacr.org/2015/625/.
+ * https://eprint.iacr.org/2015/625/.  (The curve here is 4-isogenous to
+ * Hamburg's curve.)
  *
  * The RFC-specified operation is simpler than the Diffie--Hellman function
  * described in Hamburg's paper, since it doesn't involve the `Decaf'
  * cofactor elimination procedure.  Indeed, it looks very much like X25519
  * with Hamburg's curve slotted in in place of Bernstein's.
+ *
+ * The @x448@ function essentially performs incompatible cofactor
+ * multiplication on the elliptic curve %$E(k)$% containing points %$(x, y)$%
+ * in %$\proj^2(k)$% satisfying the Montgomery-form equation
+ *
+ *     %$y^3 = x^3 + 156326 x^2 + x$% ,
+ *
+ * where $k = \gf{p}$, with $p = \phi^2 - \phi - 1$%, where
+ * %$\phi = 2^{224}$%.  The curve has %$n = (p + 1) + {}$%
+ * %$28312320572429821613362531907042076847709625476988141958474579766324$%
+ * points; this is four times a prime %$\ell$%.  The points with
+ * %$x$%-coordinate 5 have order %$\ell$%.
  */
 
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