diff --git a/library/bignum.c b/library/bignum.c
index 3643326..d15bc1a 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -280,7 +280,7 @@
  *
  * \return The selected sign value.
  */
-static int mpi_safe_cond_select_sign( int a, int b, unsigned char second )
+static int mbedtls_cf_cond_select_sign( int a, int b, unsigned char second )
 {
     /* In order to avoid questions about what we can reasonnably assume about
      * the representations of signed integers, move everything to unsigned
@@ -304,10 +304,10 @@
  * dest and src must be arrays of limbs of size n.
  * assign must be 0 or 1.
  */
-static void mpi_safe_cond_assign( size_t n,
-                                  mbedtls_mpi_uint *dest,
-                                  const mbedtls_mpi_uint *src,
-                                  unsigned char assign )
+void mbedtls_cf_mpi_uint_cond_assign( size_t n,
+                                      mbedtls_mpi_uint *dest,
+                                      const mbedtls_mpi_uint *src,
+                                      unsigned char assign )
 {
     size_t i;
 
@@ -360,9 +360,9 @@
 
     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
 
-    X->s = mpi_safe_cond_select_sign( X->s, Y->s, assign );
+    X->s = mbedtls_cf_cond_select_sign( X->s, Y->s, assign );
 
-    mpi_safe_cond_assign( Y->n, X->p, Y->p, assign );
+    mbedtls_cf_mpi_uint_cond_assign( Y->n, X->p, Y->p, assign );
 
     for( i = Y->n; i < X->n; i++ )
         X->p[i] &= ~limb_mask;
@@ -409,8 +409,8 @@
     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( Y, X->n ) );
 
     s = X->s;
-    X->s = mpi_safe_cond_select_sign( X->s, Y->s, swap );
-    Y->s = mpi_safe_cond_select_sign( Y->s, s, swap );
+    X->s = mbedtls_cf_cond_select_sign( X->s, Y->s, swap );
+    Y->s = mbedtls_cf_cond_select_sign( Y->s, s, swap );
 
 
     for( i = 0; i < X->n; i++ )
@@ -1253,7 +1253,7 @@
  *
  * \return          1 if \p x is less than \p y, 0 otherwise
  */
-static unsigned ct_lt_mpi_uint( const mbedtls_mpi_uint x,
+static unsigned mbedtls_cf_mpi_uint_lt( const mbedtls_mpi_uint x,
         const mbedtls_mpi_uint y )
 {
     mbedtls_mpi_uint ret;
@@ -1328,7 +1328,7 @@
          * Again even if we can make a decision, we just mark the result and
          * the fact that we are done and continue looping.
          */
-        cond = ct_lt_mpi_uint( Y->p[i - 1], X->p[i - 1] );
+        cond = mbedtls_cf_mpi_uint_lt( Y->p[i - 1], X->p[i - 1] );
         *ret |= cond & ( 1 - done ) & X_is_negative;
         done |= cond;
 
@@ -1339,7 +1339,7 @@
          * Again even if we can make a decision, we just mark the result and
          * the fact that we are done and continue looping.
          */
-        cond = ct_lt_mpi_uint( X->p[i - 1], Y->p[i - 1] );
+        cond = mbedtls_cf_mpi_uint_lt( X->p[i - 1], Y->p[i - 1] );
         *ret |= cond & ( 1 - done ) & ( 1 - X_is_negative );
         done |= cond;
     }
@@ -2207,7 +2207,7 @@
      * so d[n] == 1 and we want to set A to the result of the subtraction
      * which is d - (2^biL)^n, i.e. the n least significant limbs of d.
      * This exactly corresponds to a conditional assignment. */
-    mpi_safe_cond_assign( n, A->p, d, (unsigned char) d[n] );
+    mbedtls_cf_mpi_uint_cond_assign( n, A->p, d, (unsigned char) d[n] );
 }
 
 /*
@@ -2238,7 +2238,7 @@
  * This function is implemented without using comparison operators, as those
  * might be translated to branches by some compilers on some platforms.
  */
-static size_t mbedtls_mpi_cf_bool_eq( size_t x, size_t y )
+static size_t mbedtls_cf_size_bool_eq( size_t x, size_t y )
 {
     /* diff = 0 if x == y, non-zero otherwise */
     const size_t diff = x ^ y;
@@ -2285,7 +2285,7 @@
     for( size_t i = 0; i < T_size; i++ )
     {
         MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( R, &T[i],
-                        (unsigned char) mbedtls_mpi_cf_bool_eq( i, idx ) ) );
+                        (unsigned char) mbedtls_cf_size_bool_eq( i, idx ) ) );
     }
 
 cleanup:
diff --git a/library/rsa.c b/library/rsa.c
index 268d025..02b40d0 100644
--- a/library/rsa.c
+++ b/library/rsa.c
@@ -1499,7 +1499,7 @@
  * \param value     The value to analyze.
  * \return          Zero if \p value is zero, otherwise all-bits-one.
  */
-static unsigned all_or_nothing_int( unsigned value )
+static unsigned mbedtls_cf_uint_mask( unsigned value )
 {
     /* MSVC has a warning about unary minus on unsigned, but this is
      * well-defined and precisely what we want to do here */
@@ -1523,7 +1523,7 @@
  * \return          \c 0 if `size <= max`.
  * \return          \c 1 if `size > max`.
  */
-static unsigned size_greater_than( size_t size, size_t max )
+static unsigned mbedtls_cf_size_gt( size_t size, size_t max )
 {
     /* Return the sign bit (1 for negative) of (max - size). */
     return( ( max - size ) >> ( sizeof( size_t ) * 8 - 1 ) );
@@ -1539,16 +1539,17 @@
  * \param if0       Value to use if \p cond is zero.
  * \return          \c if1 if \p cond is nonzero, otherwise \c if0.
  */
-static unsigned if_int( unsigned cond, unsigned if1, unsigned if0 )
+static unsigned mbedtls_cf_uint_if( unsigned cond, unsigned if1, unsigned if0 )
 {
-    unsigned mask = all_or_nothing_int( cond );
+    unsigned mask = mbedtls_cf_uint_mask( cond );
     return( ( mask & if1 ) | (~mask & if0 ) );
 }
 
 /** Shift some data towards the left inside a buffer without leaking
  * the length of the data through side channels.
  *
- * `mem_move_to_left(start, total, offset)` is functionally equivalent to
+ * `mbedtls_cf_mem_move_to_left(start, total, offset)` is functionally
+ * equivalent to
  * ```
  * memmove(start, start + offset, total - offset);
  * memset(start + offset, 0, total - offset);
@@ -1561,9 +1562,9 @@
  * \param total     Total size of the buffer.
  * \param offset    Offset from which to copy \p total - \p offset bytes.
  */
-static void mem_move_to_left( void *start,
-                              size_t total,
-                              size_t offset )
+static void mbedtls_cf_mem_move_to_left( void *start,
+                                         size_t total,
+                                         size_t offset )
 {
     volatile unsigned char *buf = start;
     size_t i, n;
@@ -1571,7 +1572,7 @@
         return;
     for( i = 0; i < total; i++ )
     {
-        unsigned no_op = size_greater_than( total - offset, i );
+        unsigned no_op = mbedtls_cf_size_gt( total - offset, i );
         /* The first `total - offset` passes are a no-op. The last
          * `offset` passes shift the data one byte to the left and
          * zero out the last byte. */
@@ -1579,9 +1580,9 @@
         {
             unsigned char current = buf[n];
             unsigned char next = buf[n+1];
-            buf[n] = if_int( no_op, current, next );
+            buf[n] = mbedtls_cf_uint_if( no_op, current, next );
         }
-        buf[total-1] = if_int( no_op, buf[total-1], 0 );
+        buf[total-1] = mbedtls_cf_uint_if( no_op, buf[total-1], 0 );
     }
 }
 
@@ -1669,17 +1670,17 @@
          * If there's a non-0xff byte in the padding, the padding is bad. */
         for( i = 2; i < ilen; i++ )
         {
-            pad_done |= if_int( buf[i], 0, 1 );
-            pad_count += if_int( pad_done, 0, 1 );
-            bad |= if_int( pad_done, 0, buf[i] ^ 0xFF );
+            pad_done |= mbedtls_cf_uint_if( buf[i], 0, 1 );
+            pad_count += mbedtls_cf_uint_if( pad_done, 0, 1 );
+            bad |= mbedtls_cf_uint_if( pad_done, 0, buf[i] ^ 0xFF );
         }
     }
 
     /* If pad_done is still zero, there's no data, only unfinished padding. */
-    bad |= if_int( pad_done, 0, 1 );
+    bad |= mbedtls_cf_uint_if( pad_done, 0, 1 );
 
     /* There must be at least 8 bytes of padding. */
-    bad |= size_greater_than( 8, pad_count );
+    bad |= mbedtls_cf_size_gt( 8, pad_count );
 
     /* If the padding is valid, set plaintext_size to the number of
      * remaining bytes after stripping the padding. If the padding
@@ -1688,23 +1689,25 @@
      * buffer. Do it without branches to avoid leaking the padding
      * validity through timing. RSA keys are small enough that all the
      * size_t values involved fit in unsigned int. */
-    plaintext_size = if_int( bad,
-                             (unsigned) plaintext_max_size,
-                             (unsigned) ( ilen - pad_count - 3 ) );
+    plaintext_size = mbedtls_cf_uint_if(
+                        bad, (unsigned) plaintext_max_size,
+                        (unsigned) ( ilen - pad_count - 3 ) );
 
     /* Set output_too_large to 0 if the plaintext fits in the output
      * buffer and to 1 otherwise. */
-    output_too_large = size_greater_than( plaintext_size,
-                                          plaintext_max_size );
+    output_too_large = mbedtls_cf_size_gt( plaintext_size,
+                                           plaintext_max_size );
 
     /* Set ret without branches to avoid timing attacks. Return:
      * - INVALID_PADDING if the padding is bad (bad != 0).
      * - OUTPUT_TOO_LARGE if the padding is good but the decrypted
      *   plaintext does not fit in the output buffer.
      * - 0 if the padding is correct. */
-    ret = - (int) if_int( bad, - MBEDTLS_ERR_RSA_INVALID_PADDING,
-                  if_int( output_too_large, - MBEDTLS_ERR_RSA_OUTPUT_TOO_LARGE,
-                          0 ) );
+    ret = - (int) mbedtls_cf_uint_if(
+                    bad, - MBEDTLS_ERR_RSA_INVALID_PADDING,
+                    mbedtls_cf_uint_if( output_too_large,
+                                        - MBEDTLS_ERR_RSA_OUTPUT_TOO_LARGE,
+                                        0 ) );
 
     /* If the padding is bad or the plaintext is too large, zero the
      * data that we're about to copy to the output buffer.
@@ -1712,7 +1715,7 @@
      * from the same buffer whether the padding is good or not to
      * avoid leaking the padding validity through overall timing or
      * through memory or cache access patterns. */
-    bad = all_or_nothing_int( bad | output_too_large );
+    bad = mbedtls_cf_uint_mask( bad | output_too_large );
     for( i = 11; i < ilen; i++ )
         buf[i] &= ~bad;
 
@@ -1720,9 +1723,9 @@
      * Copy anyway to avoid revealing the length through timing, because
      * revealing the length is as bad as revealing the padding validity
      * for a Bleichenbacher attack. */
-    plaintext_size = if_int( output_too_large,
-                             (unsigned) plaintext_max_size,
-                             (unsigned) plaintext_size );
+    plaintext_size = mbedtls_cf_uint_if( output_too_large,
+                                         (unsigned) plaintext_max_size,
+                                         (unsigned) plaintext_size );
 
     /* Move the plaintext to the leftmost position where it can start in
      * the working buffer, i.e. make it start plaintext_max_size from
@@ -1730,9 +1733,9 @@
      * does not depend on the plaintext size. After this move, the
      * starting location of the plaintext is no longer sensitive
      * information. */
-    mem_move_to_left( buf + ilen - plaintext_max_size,
-                      plaintext_max_size,
-                      plaintext_max_size - plaintext_size );
+    mbedtls_cf_mem_move_to_left( buf + ilen - plaintext_max_size,
+                                 plaintext_max_size,
+                                 plaintext_max_size - plaintext_size );
 
     /* Finally copy the decrypted plaintext plus trailing zeros into the output
      * buffer. If output_max_len is 0, then output may be an invalid pointer
diff --git a/library/ssl_invasive.h b/library/ssl_invasive.h
index babbc27..5cb29cb 100644
--- a/library/ssl_invasive.h
+++ b/library/ssl_invasive.h
@@ -65,7 +65,7 @@
  * \retval MBEDTLS_ERR_PLATFORM_HW_ACCEL_FAILED
  *         The hardware accelerator failed.
  */
-int mbedtls_ssl_cf_hmac(
+int mbedtls_cf_hmac(
         mbedtls_md_context_t *ctx,
         const unsigned char *add_data, size_t add_data_len,
         const unsigned char *data, size_t data_len_secret,
@@ -90,11 +90,11 @@
  * \param offset_max    The maximal value of \p offset_secret.
  * \param len           The number of bytes to copy.
  */
-void mbedtls_ssl_cf_memcpy_offset( unsigned char *dst,
-                                   const unsigned char *src_base,
-                                   size_t offset_secret,
-                                   size_t offset_min, size_t offset_max,
-                                   size_t len );
+void mbedtls_cf_memcpy_offset( unsigned char *dst,
+                               const unsigned char *src_base,
+                               size_t offset_secret,
+                               size_t offset_min, size_t offset_max,
+                               size_t len );
 #endif /* MBEDTLS_TEST_HOOKS && MBEDTLS_SSL_SOME_SUITES_USE_TLS_CBC */
 
 #endif /* MBEDTLS_SSL_INVASIVE_H */
diff --git a/library/ssl_msg.c b/library/ssl_msg.c
index 7da5674..916456f 100644
--- a/library/ssl_msg.c
+++ b/library/ssl_msg.c
@@ -1055,7 +1055,7 @@
  * This function is implemented without using comparison operators, as those
  * might be translated to branches by some compilers on some platforms.
  */
-static size_t mbedtls_ssl_cf_mask_from_bit( size_t bit )
+static size_t mbedtls_cf_size_mask( size_t bit )
 {
     /* MSVC has a warning about unary minus on unsigned integer types,
      * but this is well-defined and precisely what we want to do here. */
@@ -1080,7 +1080,7 @@
  * This function is implemented without using comparison operators, as those
  * might be translated to branches by some compilers on some platforms.
  */
-static size_t mbedtls_ssl_cf_mask_lt( size_t x, size_t y )
+static size_t mbedtls_cf_size_mask_lt( size_t x, size_t y )
 {
     /* This has the most significant bit set if and only if x < y */
     const size_t sub = x - y;
@@ -1089,7 +1089,7 @@
     const size_t sub1 = sub >> ( sizeof( sub ) * 8 - 1 );
 
     /* mask = (x < y) ? 0xff... : 0x00... */
-    const size_t mask = mbedtls_ssl_cf_mask_from_bit( sub1 );
+    const size_t mask = mbedtls_cf_size_mask( sub1 );
 
     return( mask );
 }
@@ -1105,9 +1105,9 @@
  * This function is implemented without using comparison operators, as those
  * might be translated to branches by some compilers on some platforms.
  */
-static size_t mbedtls_ssl_cf_mask_ge( size_t x, size_t y )
+static size_t mbedtls_cf_size_mask_ge( size_t x, size_t y )
 {
-    return( ~mbedtls_ssl_cf_mask_lt( x, y ) );
+    return( ~mbedtls_cf_size_mask_lt( x, y ) );
 }
 
 /*
@@ -1116,12 +1116,12 @@
  *
  * This function can be used to write constant-time code by replacing branches
  * with bit operations - it can be used in conjunction with
- * mbedtls_ssl_cf_mask_from_bit().
+ * mbedtls_cf_size_mask().
  *
  * This function is implemented without using comparison operators, as those
  * might be translated to branches by some compilers on some platforms.
  */
-static size_t mbedtls_ssl_cf_bool_eq( size_t x, size_t y )
+static size_t mbedtls_cf_size_bool_eq( size_t x, size_t y )
 {
     /* diff = 0 if x == y, non-zero otherwise */
     const size_t diff = x ^ y;
@@ -1155,14 +1155,14 @@
  * This function is implemented without using comparison operators, as those
  * might be translated to branches by some compilers on some platforms.
  */
-static void mbedtls_ssl_cf_memcpy_if_eq( unsigned char *dst,
-                                         const unsigned char *src,
-                                         size_t len,
-                                         size_t c1, size_t c2 )
+static void mbedtls_cf_memcpy_if_eq( unsigned char *dst,
+                                     const unsigned char *src,
+                                     size_t len,
+                                     size_t c1, size_t c2 )
 {
     /* mask = c1 == c2 ? 0xff : 0x00 */
-    const size_t equal = mbedtls_ssl_cf_bool_eq( c1, c2 );
-    const unsigned char mask = (unsigned char) mbedtls_ssl_cf_mask_from_bit( equal );
+    const size_t equal = mbedtls_cf_size_bool_eq( c1, c2 );
+    const unsigned char mask = (unsigned char) mbedtls_cf_size_mask( equal );
 
     /* dst[i] = c1 == c2 ? src[i] : dst[i] */
     for( size_t i = 0; i < len; i++ )
@@ -1175,7 +1175,7 @@
  * Only works with MD-5, SHA-1, SHA-256 and SHA-384.
  * (Otherwise, computation of block_size needs to be adapted.)
  */
-MBEDTLS_STATIC_TESTABLE int mbedtls_ssl_cf_hmac(
+MBEDTLS_STATIC_TESTABLE int mbedtls_cf_hmac(
         mbedtls_md_context_t *ctx,
         const unsigned char *add_data, size_t add_data_len,
         const unsigned char *data, size_t data_len_secret,
@@ -1231,8 +1231,8 @@
         MD_CHK( mbedtls_md_clone( &aux, ctx ) );
         MD_CHK( mbedtls_md_finish( &aux, aux_out ) );
         /* Keep only the correct inner_hash in the output buffer */
-        mbedtls_ssl_cf_memcpy_if_eq( output, aux_out, hash_size,
-                                     offset, data_len_secret );
+        mbedtls_cf_memcpy_if_eq( output, aux_out, hash_size,
+                                 offset, data_len_secret );
 
         if( offset < max_data_len )
             MD_CHK( mbedtls_md_update( ctx, data + offset, 1 ) );
@@ -1262,7 +1262,7 @@
  * - functionally equivalent to memcpy(dst, src + offset_secret, len)
  * - but with execution flow independent from the value of offset_secret.
  */
-MBEDTLS_STATIC_TESTABLE void mbedtls_ssl_cf_memcpy_offset(
+MBEDTLS_STATIC_TESTABLE void mbedtls_cf_memcpy_offset(
                                    unsigned char *dst,
                                    const unsigned char *src_base,
                                    size_t offset_secret,
@@ -1273,8 +1273,8 @@
 
     for( offset = offset_min; offset <= offset_max; offset++ )
     {
-        mbedtls_ssl_cf_memcpy_if_eq( dst, src_base + offset, len,
-                                     offset, offset_secret );
+        mbedtls_cf_memcpy_if_eq( dst, src_base + offset, len,
+                                 offset, offset_secret );
     }
 }
 #endif /* MBEDTLS_SSL_SOME_SUITES_USE_TLS_CBC */
@@ -1620,7 +1620,7 @@
 
         if( auth_done == 1 )
         {
-            const size_t mask = mbedtls_ssl_cf_mask_ge(
+            const size_t mask = mbedtls_cf_size_mask_ge(
                                 rec->data_len,
                                 padlen + 1 );
             correct &= mask;
@@ -1640,7 +1640,7 @@
             }
 #endif
 
-            const size_t mask = mbedtls_ssl_cf_mask_ge(
+            const size_t mask = mbedtls_cf_size_mask_ge(
                                 rec->data_len,
                                 transform->maclen + padlen + 1 );
             correct &= mask;
@@ -1696,18 +1696,18 @@
                 /* pad_count += (idx >= padding_idx) &&
                  *              (check[idx] == padlen - 1);
                  */
-                const size_t mask = mbedtls_ssl_cf_mask_ge( idx, padding_idx );
-                const size_t equal = mbedtls_ssl_cf_bool_eq( check[idx],
-                                                             padlen - 1 );
+                const size_t mask = mbedtls_cf_size_mask_ge( idx, padding_idx );
+                const size_t equal = mbedtls_cf_size_bool_eq( check[idx],
+                                                              padlen - 1 );
                 pad_count += mask & equal;
             }
-            correct &= mbedtls_ssl_cf_bool_eq( pad_count, padlen );
+            correct &= mbedtls_cf_size_bool_eq( pad_count, padlen );
 
 #if defined(MBEDTLS_SSL_DEBUG_ALL)
             if( padlen > 0 && correct == 0 )
                 MBEDTLS_SSL_DEBUG_MSG( 1, ( "bad padding byte detected" ) );
 #endif
-            padlen &= mbedtls_ssl_cf_mask_from_bit( correct );
+            padlen &= mbedtls_cf_size_mask( correct );
         }
         else
 #endif /* MBEDTLS_SSL_PROTO_TLS1 || MBEDTLS_SSL_PROTO_TLS1_1 || \
@@ -1791,20 +1791,20 @@
             const size_t max_len = rec->data_len + padlen;
             const size_t min_len = ( max_len > 256 ) ? max_len - 256 : 0;
 
-            ret = mbedtls_ssl_cf_hmac( &transform->md_ctx_dec,
-                                       add_data, add_data_len,
-                                       data, rec->data_len, min_len, max_len,
-                                       mac_expect );
+            ret = mbedtls_cf_hmac( &transform->md_ctx_dec,
+                                   add_data, add_data_len,
+                                   data, rec->data_len, min_len, max_len,
+                                   mac_expect );
             if( ret != 0 )
             {
                 MBEDTLS_SSL_DEBUG_RET( 1, "mbedtls_ssl_cf_hmac", ret );
                 return( ret );
             }
 
-            mbedtls_ssl_cf_memcpy_offset( mac_peer, data,
-                                          rec->data_len,
-                                          min_len, max_len,
-                                          transform->maclen );
+            mbedtls_cf_memcpy_offset( mac_peer, data,
+                                      rec->data_len,
+                                      min_len, max_len,
+                                      transform->maclen );
         }
         else
 #endif /* MBEDTLS_SSL_PROTO_TLS1 || MBEDTLS_SSL_PROTO_TLS1_1 || \