diff --git a/library/ssl_invasive.h b/library/ssl_invasive.h
index f04b81668..60b62094e 100644
--- a/library/ssl_invasive.h
+++ b/library/ssl_invasive.h
@@ -73,6 +73,30 @@ int mbedtls_ssl_cf_hmac(
         const unsigned char *data, size_t data_len_secret,
         size_t min_data_len, size_t max_data_len,
         unsigned char *output );
+
+/** \brief Copy data from a secret position with constant flow.
+ *
+ * This function copies \p len bytes from \p src_base + \p offset_secret to \p
+ * dst, with a code flow and memory access pattern that does not depend on \p
+ * offset_secret, but only on \p offset_min, \p offset_max and \p len.
+ *
+ * \param dst           The destination buffer. This must point to a writable
+ *                      buffer of at least \p len bytes.
+ * \param src_base      The base of the source buffer. This must point to a
+ *                      readable buffer of at least \p offset_max + \p len
+ *                      bytes.
+ * \param offset_secret The offset in the source buffer from which to copy.
+ *                      This must be no less than \p offset_min and no greater
+ *                      than \p offset_max.
+ * \param offset_min    The minimal value of \p offset_secret.
+ * \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 );
 #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 e90e59993..5dc8012ba 100644
--- a/library/ssl_msg.c
+++ b/library/ssl_msg.c
@@ -1193,6 +1193,24 @@ cleanup:
     mbedtls_md_free( &aux );
     return( ret );
 }
+
+/*
+ * Constant-flow memcpy from variable position in buffer.
+ * - functionally equivalent to memcpy(dst, src + offset_secret, len)
+ * - but with execution flow independant from the value of offset_secret.
+ */
+MBEDTLS_STATIC_TESTABLE 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 )
+{
+    /* WIP - THIS IS NOT ACTUALLY CONSTANT-FLOW!
+     * This is just to be able to write tests and check they work. */
+    ssl_read_memory( src_base + offset_min, offset_max - offset_min + len );
+    memcpy( dst, src_base + offset_secret, len );
+}
 #endif /* MBEDTLS_SSL_SOME_SUITES_USE_TLS_CBC */
 
 int mbedtls_ssl_decrypt_buf( mbedtls_ssl_context const *ssl,
@@ -1674,7 +1692,7 @@ int mbedtls_ssl_decrypt_buf( mbedtls_ssl_context const *ssl,
         {
             /*
              * The next two sizes are the minimum and maximum values of
-             * in_msglen over all padlen values.
+             * data_len over all padlen values.
              *
              * They're independent of padlen, since we previously did
              * data_len -= padlen.
@@ -1695,13 +1713,10 @@ int mbedtls_ssl_decrypt_buf( mbedtls_ssl_context const *ssl,
                 return( ret );
             }
 
-            /* Make sure we access all the memory that could contain the MAC,
-             * before we check it in the next code block. This makes the
-             * synchronisation requirements for just-in-time Prime+Probe
-             * attacks much tighter and hopefully impractical. */
-            ssl_read_memory( data + min_len,
-                             max_len - min_len + transform->maclen );
-            memcpy( mac_peer, data + rec->data_len, transform->maclen );
+            mbedtls_ssl_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 || \
diff --git a/tests/suites/test_suite_ssl.data b/tests/suites/test_suite_ssl.data
index 3afa39a2b..1b7919104 100644
--- a/tests/suites/test_suite_ssl.data
+++ b/tests/suites/test_suite_ssl.data
@@ -10545,3 +10545,15 @@ ssl_cf_hmac:MBEDTLS_MD_SHA256
 Constant-flow HMAC: SHA384
 depends_on:MBEDTLS_SHA512_C:!MBEDTLS_SHA512_NO_SHA384
 ssl_cf_hmac:MBEDTLS_MD_SHA384
+
+# these are the numbers we'd get with an empty plaintext and truncated HMAC
+Constant-flow memcpy from offset: small
+ssl_cf_memcpy_offset:0:5:10
+
+# we could get this with 255-bytes plaintext and untruncated SHA-256
+Constant-flow memcpy from offset: medium
+ssl_cf_memcpy_offset:0:255:32
+
+# we could get this with 255-bytes plaintext and untruncated SHA-384
+Constant-flow memcpy from offset: large
+ssl_cf_memcpy_offset:100:339:48
diff --git a/tests/suites/test_suite_ssl.function b/tests/suites/test_suite_ssl.function
index f7c9be051..7c4f865e9 100644
--- a/tests/suites/test_suite_ssl.function
+++ b/tests/suites/test_suite_ssl.function
@@ -4361,3 +4361,36 @@ exit:
     mbedtls_free( out );
 }
 /* END_CASE */
+
+/* BEGIN_CASE depends_on:MBEDTLS_SSL_SOME_SUITES_USE_TLS_CBC:MBEDTLS_TEST_HOOKS */
+void ssl_cf_memcpy_offset( int offset_min, int offset_max, int len )
+{
+    unsigned char *dst = NULL;
+    unsigned char *src = NULL;
+    size_t src_len = offset_max + len;
+    size_t secret;
+
+    ASSERT_ALLOC( dst, len );
+    ASSERT_ALLOC( src, src_len );
+
+    /* Fill src in a way that we can detect if we copied the right bytes */
+    mbedtls_test_rnd_std_rand( NULL, src, src_len );
+
+    for( secret = offset_min; secret <= (size_t) offset_max; secret++ )
+    {
+        test_set_step( (int) secret );
+
+        TEST_CF_SECRET( &secret, sizeof( secret ) );
+        mbedtls_ssl_cf_memcpy_offset( dst, src, secret,
+                                      offset_min, offset_max, len );
+        TEST_CF_PUBLIC( &secret, sizeof( secret ) );
+        TEST_CF_PUBLIC( dst, len );
+
+        ASSERT_COMPARE( dst, len, src + secret, len );
+    }
+
+exit:
+    mbedtls_free( dst );
+    mbedtls_free( src );
+}
+/* END_CASE */