Frobenius test is an addition now instead of an alternative. Documentation update

Author: czurnieden

doc/bn.tex

@@ -2204,9 +2204,8 @@ \subsection{Required Number of Tests}
 the diagonal from $(512,2^{-80})$ downwards and to the right to gain a lower probability of getting
 a composite declared a pseudoprime for the same amount of work or less.
 
-If this version of the library has the strong Lucas--Selfridge and/or the Frobenius--Underwood test
-implemented only one or two rounds of the Miller--Rabin test with a random base is necessary for
-numbers larger than or equal to $1024$ bits.
+If this version of the library has the extra strong Lucas test implemented only one or two rounds
+of the Miller--Rabin test with a random base is necessary for numbers larger than or equal to $1024$ bits.
 
 This function is meant for RSA. The number of rounds for DSA is $\lceil -log_2(p)/2\rceil$ with $p$
 the probability which is just the half of the absolute value of $p$ if given as a power of two.
@@ -2234,7 +2233,7 @@ \section{Frobenius (Underwood)	Test}
 \end{alltt}
 Performs the variant of the Frobenius test as described by Paul Underwood. It can be included at
 build--time if the preprocessor macro \texttt{LTM\_USE\_FROBENIUS\_TEST} is defined and will be
-used instead of the extra strong Lucas test.
+used after the extra strong Lucas test.
 
 It returns \texttt{MP\_ITER} if the number of iterations is exhausted, assumes a composite as the
 input and sets \texttt{result} accordingly. This will reduce the set of available pseudoprimes by a
@@ -2255,11 +2254,11 @@ \section{Primality Testing}
 mp_err mp_prime_is_prime(const mp_int *a, int t, bool *result)
 \end{alltt}
 This will perform a trial division followed by two rounds of Miller--Rabin with bases 2 and 3 and a
-Lucas--Selfridge test. The Frobenius--Underwood is available as a compile--time option with the
+extra strong Lucas test. The Frobenius--Underwood time is available as a compile--time option with the
 preprocessor macro \texttt{LTM\_USE\_FROBENIUS\_TEST}. See file \texttt{bn\_mp\_prime\_is\_prime.c}
 for the necessary details. It shall be noted that both functions are much slower than the
 Miller--Rabin test and if speed is an essential issue, the macro \texttt{LTM\_USE\_ONLY\_MR}
-switches the Frobenius--Underwood test and the Lucas--Selfridge test off and their code will not
+switches the Frobenius--Underwood test and the Lucas test off and their code will not
 even be compiled into the library.
 
 If $t$ is set to a positive value $t$ additional rounds of the Miller--Rabin test with random bases

mp_prime_is_prime.c

@@ -92,22 +92,26 @@ mp_err mp_prime_is_prime(const mp_int *a, int t, bool *result)
    }
 
    /*
-    * Both, the Frobenius-Underwood test and the the Lucas-Selfridge test are quite
+    * Both, the Frobenius-Underwood test and the the extra strong Lucas test are quite
     * slow so if speed is an issue, define LTM_USE_ONLY_MR to use M-R tests with
     * bases 2, 3 and t random bases.
     */
 #ifndef LTM_USE_ONLY_MR
    if (t >= 0) {
-#ifdef LTM_USE_FROBENIUS_TEST
-      err = mp_prime_frobenius_underwood(a, &res);
-      if ((err != MP_OKAY) && (err != MP_ITER)) {
+      if ((err = mp_prime_extra_strong_lucas(a, &res)) != MP_OKAY) {
          goto LBL_B;
       }
       if (!res) {
          goto LBL_B;
       }
-#else
-      if ((err = mp_prime_extra_strong_lucas(a, &res)) != MP_OKAY) {
+      /*
+         The Frobenius-Underwood pseudoprimes are sufficiently different from the
+         Extra Strong Lucas pseudoprimes with the parameters used in this library
+         to offer it as an additionally test (but it nearly doubles the runtime).
+       */
+#ifdef LTM_USE_FROBENIUS_TEST
+      err = mp_prime_frobenius_underwood(a, &res);
+      if ((err != MP_OKAY) && (err != MP_ITER)) {
          goto LBL_B;
       }
       if (!res) {