diff --git a/bignum.h b/bignum.h
index 24158e0..64ed278 100644
--- a/bignum.h
+++ b/bignum.h
@@ -53,6 +53,8 @@
 # define mpz_combit mpz_combit
 # define mpz_import mpz_import
 # define mpz_export mpz_export
+/* Side-channel silent powm not available in mini-gmp. */
+# define mpz_powm_sec mpz_pwm
 #else
 # include <gmp.h>
 #endif
diff --git a/configure.ac b/configure.ac
index e1ee64c..1e88477 100644
--- a/configure.ac
+++ b/configure.ac
@@ -236,9 +236,9 @@ fi
 # Checks for libraries
 if test "x$enable_public_key" = "xyes" ; then
   if test "x$enable_mini_gmp" = "xno" ; then
-    AC_CHECK_LIB(gmp, __gmpz_getlimbn,,
+    AC_CHECK_LIB(gmp, __gmpz_powm_sec,,
         [AC_MSG_WARN(
-    [GNU MP not found, or not 3.1 or up, see http://gmplib.org/.
+    [GNU MP not found, or too old. GMP-5.0 or later is needed, see http://gmplib.org/.
     Support for public key algorithms will be unavailable.])]
         enable_public_key=no)
 
diff --git a/dsa-sign.c b/dsa-sign.c
index 62c7d4a..9d6bb18 100644
--- a/dsa-sign.c
+++ b/dsa-sign.c
@@ -65,7 +65,7 @@ dsa_sign(const struct dsa_params *params,
   mpz_add_ui(k, k, 1);
 
   /* Compute r = (g^k (mod p)) (mod q) */
-  mpz_powm(tmp, params->g, k, params->p);
+  mpz_powm_sec(tmp, params->g, k, params->p);
   mpz_fdiv_r(signature->r, tmp, params->q);
 
   /* Compute hash */
diff --git a/rsa-blind.c b/rsa-blind.c
index 7662f50..16b03d7 100644
--- a/rsa-blind.c
+++ b/rsa-blind.c
@@ -61,7 +61,7 @@ _rsa_blind (const struct rsa_public_key *pub,
   while (!mpz_invert (ri, r, pub->n));
 
   /* c = c*(r^e) mod n */
-  mpz_powm(r, r, pub->e, pub->n);
+  mpz_powm_sec(r, r, pub->e, pub->n);
   mpz_mul(c, c, r);
   mpz_fdiv_r(c, c, pub->n);
 
diff --git a/rsa-sign-tr.c b/rsa-sign-tr.c
index 3d80ed4..68233a3 100644
--- a/rsa-sign-tr.c
+++ b/rsa-sign-tr.c
@@ -60,7 +60,7 @@ rsa_blind (const struct rsa_public_key *pub,
   while (!mpz_invert (ri, r, pub->n));
 
   /* c = c*(r^e) mod n */
-  mpz_powm(r, r, pub->e, pub->n);
+  mpz_powm_sec(r, r, pub->e, pub->n);
   mpz_mul(c, m, r);
   mpz_fdiv_r(c, c, pub->n);
 
@@ -97,7 +97,7 @@ rsa_compute_root_tr(const struct rsa_public_key *pub,
 
   rsa_compute_root (key, xb, mb);
 
-  mpz_powm(t, xb, pub->e, pub->n);
+  mpz_powm_sec(t, xb, pub->e, pub->n);
   res = (mpz_cmp(mb, t) == 0);
 
   if (res)
diff --git a/rsa-sign.c b/rsa-sign.c
index eba7388..4832352 100644
--- a/rsa-sign.c
+++ b/rsa-sign.c
@@ -96,11 +96,11 @@ rsa_compute_root(const struct rsa_private_key *key,
 
   /* Compute xq = m^d % q = (m%q)^b % q */
   mpz_fdiv_r(xq, m, key->q);
-  mpz_powm(xq, xq, key->b, key->q);
+  mpz_powm_sec(xq, xq, key->b, key->q);
 
   /* Compute xp = m^d % p = (m%p)^a % p */
   mpz_fdiv_r(xp, m, key->p);
-  mpz_powm(xp, xp, key->a, key->p);
+  mpz_powm_sec(xp, xp, key->a, key->p);
 
   /* Set xp' = (xp - xq) c % p. */
   mpz_sub(xp, xp, xq);