+extern int mp_jacobi(mp */*a*/, mp */*n*/);
+
+/* --- @mp_modsqrt@ --- *
+ *
+ * Arguments: @mp *d@ = destination integer
+ * @mp *a@ = source integer
+ * @mp *p@ = modulus (must be prime)
+ *
+ * Returns: If %$a$% is a quadratic residue, a square root of %$a$%; else
+ * a null pointer.
+ *
+ * Use: Returns an integer %$x$% such that %$x^2 \equiv a \pmod{p}$%,
+ * if one exists; else a null pointer. This function will not
+ * work if %$p$% is composite: you must factor the modulus, take
+ * a square root mod each factor, and recombine the results
+ * using the Chinese Remainder Theorem.
+ *
+ * We guarantee that the square root returned is the smallest
+ * one (i.e., the `positive' square root).
+ */
+
+extern mp *mp_modsqrt(mp */*d*/, mp */*a*/, mp */*p*/);
+
+/* --- @mp_modexp@ --- *
+ *
+ * Arguments: @mp *d@ = fake destination
+ * @mp *x@ = base of exponentiation
+ * @mp *e@ = exponent
+ * @mp *n@ = modulus (must be positive)
+ *
+ * Returns: The value %$x^e \bmod n$%.
+ */
+
+extern mp *mp_modexp(mp */*d*/, mp */*x*/, mp */*e*/, mp */*n*/);