diff --git a/ChangeLog b/ChangeLog
index 6a32ba438..7824fc421 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -114,6 +114,9 @@ Bugfix
      curve picked by the server was actually allowed.
 
 Changes
+   * Remove bias in mpi_gen_prime (contributed by Pascal Junod).
+   * Remove potential sources of timing variations (some contributed by Pascal
+     Junod).
    * Options POLARSSL_HAVE_INT8 and POLARSSL_HAVE_INT16 are deprecated.
    * Enabling POLARSSL_NET_C without POLARSSL_HAVE_IPV6 is deprecated.
    * compat-1.2.h and openssl.h are deprecated.
diff --git a/library/bignum.c b/library/bignum.c
index 45f966760..07892c59e 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -223,8 +223,8 @@ int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned
     int ret = 0;
     size_t i;
 
-    /* make sure assign is 0 or 1 */
-    assign = ( assign != 0 );
+    /* make sure assign is 0 or 1 in a time-constant manner */
+    assign = (assign | (unsigned char)-assign) >> 7;
 
     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
 
@@ -255,8 +255,8 @@ int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char sw
     if( X == Y )
         return( 0 );
 
-    /* make sure swap is 0 or 1 */
-    swap = ( swap != 0 );
+    /* make sure swap is 0 or 1 in a time-constant manner */
+    swap = (swap | (unsigned char)-swap) >> 7;
 
     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( Y, X->n ) );
@@ -1958,8 +1958,8 @@ static int mpi_miller_rabin( const mbedtls_mpi *X,
                              int (*f_rng)(void *, unsigned char *, size_t),
                              void *p_rng )
 {
-    int ret;
-    size_t i, j, n, s;
+    int ret, count;
+    size_t i, j, k, n, s;
     mbedtls_mpi W, R, T, A, RR;
 
     mbedtls_mpi_init( &W ); mbedtls_mpi_init( &R ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &A );
@@ -1996,6 +1996,23 @@ static int mpi_miller_rabin( const mbedtls_mpi *X,
         }
         A.p[0] |= 3;
 
+        count = 0;
+        do {
+            MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &A, X->n * ciL, f_rng, p_rng ) );
+
+            j = mbedtls_mpi_msb( &A );
+            k = mbedtls_mpi_msb( &W );
+            if (j > k) {
+                MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &A, j - k ) );
+            }
+
+            if (count++ > 30) {
+                return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
+            }
+
+        } while ( mbedtls_mpi_cmp_mpi( &A, &W ) >= 0 ||
+                  mbedtls_mpi_cmp_int( &A, 1 )  <= 0    );
+
         /*
          * A = A^R mod |X|
          */
@@ -2092,10 +2109,11 @@ int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int dh_flag,
     MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( X, n * ciL, f_rng, p_rng ) );
 
     k = mbedtls_mpi_msb( X );
-    if( k < nbits ) MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( X, nbits - k ) );
-    if( k > nbits ) MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( X, k - nbits ) );
+    if( k > nbits ) MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( X, k - nbits + 1 ) );
 
-    X->p[0] |= 3;
+    mbedtls_mpi_set_bit( X, nbits-1, 1 );
+
+    X->p[0] |= 1;
 
     if( dh_flag == 0 )
     {
@@ -2114,6 +2132,9 @@ int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int dh_flag,
          * is X = 2 mod 3 (which is equivalent to Y = 2 mod 3).
          * Make sure it is satisfied, while keeping X = 3 mod 4
          */
+
+        X->p[0] |= 2;
+
         MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, 3 ) );
         if( r == 0 )
             MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 8 ) );
diff --git a/library/rsa.c b/library/rsa.c
index f6a88fd92..1d6fd4a7d 100644
--- a/library/rsa.c
+++ b/library/rsa.c
@@ -773,7 +773,7 @@ int mbedtls_rsa_rsaes_oaep_decrypt( mbedtls_rsa_context *ctx,
     for( i = 0; i < ilen - 2 * hlen - 2; i++ )
     {
         pad_done |= p[i];
-        pad_len += ( pad_done == 0 );
+        pad_len += ((pad_done | (unsigned char)-pad_done) >> 7) ^ 1;
     }
 
     p += pad_len;
@@ -847,8 +847,8 @@ int mbedtls_rsa_rsaes_pkcs1_v15_decrypt( mbedtls_rsa_context *ctx,
          * (minus one, for the 00 byte) */
         for( i = 0; i < ilen - 3; i++ )
         {
-            pad_done |= ( p[i] == 0 );
-            pad_count += ( pad_done == 0 );
+            pad_done  |= ((p[i] | (unsigned char)-p[i]) >> 7) ^ 1;
+            pad_count += ((pad_done | (unsigned char)-pad_done) >> 7) ^ 1;
         }
 
         p += pad_count;
diff --git a/library/ssl_srv.c b/library/ssl_srv.c
index 4d2032ea9..4eb546d2b 100644
--- a/library/ssl_srv.c
+++ b/library/ssl_srv.c
@@ -3235,7 +3235,7 @@ static int ssl_parse_encrypted_pms( mbedtls_ssl_context *ssl,
     unsigned char ver[2];
     unsigned char fake_pms[48], peer_pms[48];
     unsigned char mask;
-    size_t i;
+    size_t i, diff, peer_pmslen;
 
     if( ! mbedtls_pk_can_do( mbedtls_ssl_own_key( ssl ), MBEDTLS_PK_RSA ) )
     {
@@ -3280,16 +3280,17 @@ static int ssl_parse_encrypted_pms( mbedtls_ssl_context *ssl,
         return( ret );
 
     ret = mbedtls_pk_decrypt( mbedtls_ssl_own_key( ssl ), p, len,
-                      peer_pms, &ssl->handshake->pmslen,
+                      peer_pms, &peer_pmslen,
                       sizeof( peer_pms ),
                       ssl->f_rng, ssl->p_rng );
 
-    ret |= ssl->handshake->pmslen - 48;
-    ret |= peer_pms[0] - ver[0];
-    ret |= peer_pms[1] - ver[1];
+    diff  = (size_t) ret;
+    diff |= peer_pmslen ^ 48;
+    diff |= peer_pms[0] ^ ssl->handshake->max_major_ver;
+    diff |= peer_pms[1] ^ ssl->handshake->max_minor_ver;
 
-#if defined(MBEDTLS_SSL_DEBUG_ALL)
-    if( ret != 0 )
+#if defined(POLARSSL_SSL_DEBUG_ALL)
+    if( diff != 0 )
         MBEDTLS_SSL_DEBUG_MSG( 1, ( "bad client key exchange message" ) );
 #endif
 
@@ -3301,7 +3302,8 @@ static int ssl_parse_encrypted_pms( mbedtls_ssl_context *ssl,
     }
     ssl->handshake->pmslen = 48;
 
-    mask = (unsigned char)( - ( ret != 0 ) ); /* ret ? 0xff : 0x00 */
+    mask = ( diff | - diff ) >> ( sizeof( size_t ) * 8 - 1 );
+    mask = (unsigned char)( - ( ret != 0 ) ); /* mask = diff ? 0xff : 0x00 */
     for( i = 0; i < ssl->handshake->pmslen; i++ )
         pms[i] = ( mask & fake_pms[i] ) | ( (~mask) & peer_pms[i] );