diff --git a/include/mbedtls/config.h b/include/mbedtls/config.h
index ffd4b5b..1e6e052 100644
--- a/include/mbedtls/config.h
+++ b/include/mbedtls/config.h
@@ -1911,9 +1911,10 @@
  *
  * Enable testing of the constant-flow nature of some sensitive functions with
  * clang's MemorySanitizer. This causes some existing tests to also test
- * non-functional properties of the code under test.
+ * this non-functional property of the code under test.
  *
- * This setting requires compiling with clang -fsanitize=memory.
+ * This setting requires compiling with clang -fsanitize=memory. The test
+ * suites can then be run normally.
  *
  * \warning This macro is only used for extended testing; it is not considered
  * part of the library's API, so it may change or disappear at any time.
@@ -1923,6 +1924,25 @@
 //#define MBEDTLS_TEST_CONSTANT_FLOW_MEMSAN
 
 /**
+ * \def MBEDTLS_TEST_CONSTANT_FLOW_VALGRIND
+ *
+ * Enable testing of the constant-flow nature of some sensitive functions with
+ * valgrind's memcheck tool. This causes some existing tests to also test
+ * this non-functional property of the code under test.
+ *
+ * This setting requires valgrind headers for building, and is only useful for
+ * testing if the tests suites are run with valgrind's memcheck. This can be
+ * done for an individual test suite with 'valgrind ./test_suite_xxx', or when
+ * using CMake, this can be done for all test suites with 'make memcheck'.
+ *
+ * \warning This macro is only used for extended testing; it is not considered
+ * part of the library's API, so it may change or disappear at any time.
+ *
+ * Uncomment to enable testing of the constant-flow nature of selected code.
+ */
+//#define MBEDTLS_TEST_CONSTANT_FLOW_VALGRIND
+
+/**
  * \def MBEDTLS_TEST_HOOKS
  *
  * Enable features for invasive testing such as introspection functions and
diff --git a/library/ssl_invasive.h b/library/ssl_invasive.h
index cfe9b8d..babbc27 100644
--- a/library/ssl_invasive.h
+++ b/library/ssl_invasive.h
@@ -71,6 +71,30 @@
         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 c1552e7..3578265 100644
--- a/library/ssl_msg.c
+++ b/library/ssl_msg.c
@@ -312,27 +312,6 @@
 int (*mbedtls_ssl_hw_record_finish)( mbedtls_ssl_context *ssl ) = NULL;
 #endif /* MBEDTLS_SSL_HW_RECORD_ACCEL */
 
-/* The function below is only used in the Lucky 13 counter-measure in
- * mbedtls_ssl_decrypt_buf(). These are the defines that guard the call site. */
-#if defined(MBEDTLS_SSL_SOME_MODES_USE_MAC) && \
-    ( defined(MBEDTLS_SSL_PROTO_TLS1) || \
-      defined(MBEDTLS_SSL_PROTO_TLS1_1) || \
-      defined(MBEDTLS_SSL_PROTO_TLS1_2) )
-/* This function makes sure every byte in the memory region is accessed
- * (in ascending addresses order) */
-static void ssl_read_memory( const unsigned char *p, size_t len )
-{
-    unsigned char acc = 0;
-    volatile unsigned char force;
-
-    for( ; len != 0; p++, len-- )
-        acc ^= *p;
-
-    force = acc;
-    (void) force;
-}
-#endif /* SSL_SOME_MODES_USE_MAC && ( TLS1 || TLS1_1 || TLS1_2 ) */
-
 /*
  * Encryption/decryption functions
  */
@@ -1191,6 +1170,27 @@
     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 independent 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 )
+{
+    size_t offset;
+
+    for( offset = offset_min; offset <= offset_max; offset++ )
+    {
+        mbedtls_ssl_cf_memcpy_if_eq( dst, src_base + offset, len,
+                                     offset, offset_secret );
+    }
+}
 #endif /* MBEDTLS_SSL_SOME_SUITES_USE_TLS_CBC */
 
 int mbedtls_ssl_decrypt_buf( mbedtls_ssl_context const *ssl,
@@ -1635,6 +1635,7 @@
     if( auth_done == 0 )
     {
         unsigned char mac_expect[MBEDTLS_SSL_MAC_ADD];
+        unsigned char mac_peer[MBEDTLS_SSL_MAC_ADD];
 
         /* If the initial value of padlen was such that
          * data_len < maclen + padlen + 1, then padlen
@@ -1661,6 +1662,7 @@
                      data, rec->data_len,
                      rec->ctr, rec->type,
                      mac_expect );
+            memcpy( mac_peer, data + rec->data_len, transform->maclen );
         }
         else
 #endif /* MBEDTLS_SSL_PROTO_SSL3 */
@@ -1670,7 +1672,7 @@
         {
             /*
              * 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.
@@ -1691,12 +1693,10 @@
                 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 );
+            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 || \
@@ -1708,10 +1708,10 @@
 
 #if defined(MBEDTLS_SSL_DEBUG_ALL)
         MBEDTLS_SSL_DEBUG_BUF( 4, "expected mac", mac_expect, transform->maclen );
-        MBEDTLS_SSL_DEBUG_BUF( 4, "message  mac", data + rec->data_len, transform->maclen );
+        MBEDTLS_SSL_DEBUG_BUF( 4, "message  mac", mac_peer, transform->maclen );
 #endif
 
-        if( mbedtls_ssl_safer_memcmp( data + rec->data_len, mac_expect,
+        if( mbedtls_ssl_safer_memcmp( mac_peer, mac_expect,
                                       transform->maclen ) != 0 )
         {
 #if defined(MBEDTLS_SSL_DEBUG_ALL)
diff --git a/library/version_features.c b/library/version_features.c
index 36ae2f2..d2840fa 100644
--- a/library/version_features.c
+++ b/library/version_features.c
@@ -558,6 +558,9 @@
 #if defined(MBEDTLS_TEST_CONSTANT_FLOW_MEMSAN)
     "MBEDTLS_TEST_CONSTANT_FLOW_MEMSAN",
 #endif /* MBEDTLS_TEST_CONSTANT_FLOW_MEMSAN */
+#if defined(MBEDTLS_TEST_CONSTANT_FLOW_VALGRIND)
+    "MBEDTLS_TEST_CONSTANT_FLOW_VALGRIND",
+#endif /* MBEDTLS_TEST_CONSTANT_FLOW_VALGRIND */
 #if defined(MBEDTLS_TEST_HOOKS)
     "MBEDTLS_TEST_HOOKS",
 #endif /* MBEDTLS_TEST_HOOKS */
diff --git a/programs/test/query_config.c b/programs/test/query_config.c
index cabf68b..f4c14d6 100644
--- a/programs/test/query_config.c
+++ b/programs/test/query_config.c
@@ -1544,6 +1544,14 @@
     }
 #endif /* MBEDTLS_TEST_CONSTANT_FLOW_MEMSAN */
 
+#if defined(MBEDTLS_TEST_CONSTANT_FLOW_VALGRIND)
+    if( strcmp( "MBEDTLS_TEST_CONSTANT_FLOW_VALGRIND", config ) == 0 )
+    {
+        MACRO_EXPANSION_TO_STR( MBEDTLS_TEST_CONSTANT_FLOW_VALGRIND );
+        return( 0 );
+    }
+#endif /* MBEDTLS_TEST_CONSTANT_FLOW_VALGRIND */
+
 #if defined(MBEDTLS_TEST_HOOKS)
     if( strcmp( "MBEDTLS_TEST_HOOKS", config ) == 0 )
     {
diff --git a/scripts/config.py b/scripts/config.py
index 0a18647..703e6e9 100755
--- a/scripts/config.py
+++ b/scripts/config.py
@@ -193,6 +193,7 @@
     'MBEDTLS_SHA512_NO_SHA384', # removes a feature
     'MBEDTLS_SSL_HW_RECORD_ACCEL', # build dependency (hook functions)
     'MBEDTLS_TEST_CONSTANT_FLOW_MEMSAN', # build dependency (clang+memsan)
+    'MBEDTLS_TEST_CONSTANT_FLOW_VALGRIND', # build dependency (valgrind headers)
     'MBEDTLS_TEST_NULL_ENTROPY', # removes a feature
     'MBEDTLS_X509_ALLOW_UNSUPPORTED_CRITICAL_EXTENSION', # influences the use of X.509 in TLS
     'MBEDTLS_ZLIB_SUPPORT', # build dependency (libz)
diff --git a/tests/include/test/constant_flow.h b/tests/include/test/constant_flow.h
index 18daa4c..af64011 100644
--- a/tests/include/test/constant_flow.h
+++ b/tests/include/test/constant_flow.h
@@ -30,6 +30,28 @@
 #include MBEDTLS_CONFIG_FILE
 #endif
 
+/*
+ * This file defines the two macros
+ *
+ *  #define TEST_CF_SECRET(ptr, size)
+ *  #define TEST_CF_PUBLIC(ptr, size)
+ *
+ * that can be used in tests to mark a memory area as secret (no branch or
+ * memory access should depend on it) or public (default, only needs to be
+ * marked explicitly when it was derived from secret data).
+ *
+ * Arguments:
+ * - ptr: a pointer to the memory area to be marked
+ * - size: the size in bytes of the memory area
+ *
+ * Implementation:
+ * The basic idea is that of ctgrind <https://github.com/agl/ctgrind>: we can
+ * re-use tools that were designed for checking use of uninitialized memory.
+ * This file contains two implementations: one based on MemorySanitizer, the
+ * other on valgrind's memcheck. If none of them is enabled, dummy macros that
+ * do nothing are defined for convenience.
+ */
+
 #if defined(MBEDTLS_TEST_CONSTANT_FLOW_MEMSAN)
 #include <sanitizer/msan_interface.h>
 
@@ -39,11 +61,21 @@
 #define TEST_CF_PUBLIC  __msan_unpoison
 // void __msan_unpoison(const volatile void *a, size_t size);
 
-#else /* MBEDTLS_TEST_CONSTANT_FLOW_MEMSAN */
+#elif defined(MBEDTLS_TEST_CONSTANT_FLOW_VALGRIND)
+#include <valgrind/memcheck.h>
+
+#define TEST_CF_SECRET  VALGRIND_MAKE_MEM_UNDEFINED
+// VALGRIND_MAKE_MEM_UNDEFINED(_qzz_addr, _qzz_len)
+#define TEST_CF_PUBLIC  VALGRIND_MAKE_MEM_DEFINED
+// VALGRIND_MAKE_MEM_DEFINED(_qzz_addr, _qzz_len)
+
+#else /* MBEDTLS_TEST_CONSTANT_FLOW_MEMSAN ||
+         MBEDTLS_TEST_CONSTANT_FLOW_VALGRIND */
 
 #define TEST_CF_SECRET(ptr, size)
 #define TEST_CF_PUBLIC(ptr, size)
 
-#endif /* MBEDTLS_TEST_CONSTANT_FLOW_MEMSAN */
+#endif /* MBEDTLS_TEST_CONSTANT_FLOW_MEMSAN ||
+          MBEDTLS_TEST_CONSTANT_FLOW_VALGRIND */
 
 #endif /* TEST_CONSTANT_FLOW_H */
diff --git a/tests/scripts/all.sh b/tests/scripts/all.sh
index 082640a..0356923 100755
--- a/tests/scripts/all.sh
+++ b/tests/scripts/all.sh
@@ -1109,6 +1109,28 @@
     make test
 }
 
+component_test_valgrind_constant_flow () {
+    # This tests both (1) everything that valgrind's memcheck usually checks
+    # (heap buffer overflows, use of uninitialized memory, use-after-free,
+    # etc.) and (2) branches or memory access depending on secret values,
+    # which will be reported as uninitialized memory. To distinguish between
+    # secret and actually uninitialized:
+    # - unset MBEDTLS_TEST_CONSTANT_FLOW_VALGRIND - does the failure persist?
+    # - or alternatively, build with debug info and manually run the offending
+    # test suite with valgrind --track-origins=yes, then check if the origin
+    # was TEST_CF_SECRET() or something else.
+    msg "build: cmake release GCC, full config with constant flow testing"
+    scripts/config.py full
+    scripts/config.py set MBEDTLS_TEST_CONSTANT_FLOW_VALGRIND
+    cmake -D CMAKE_BUILD_TYPE:String=Release .
+    make
+
+    # this only shows a summary of the results (how many of each type)
+    # details are left in Testing/<date>/DynamicAnalysis.xml
+    msg "test: main suites (valgrind + constant flow)"
+    make memcheck
+}
+
 component_test_default_no_deprecated () {
     # Test that removing the deprecated features from the default
     # configuration leaves something consistent.
diff --git a/tests/suites/test_suite_ssl.data b/tests/suites/test_suite_ssl.data
index 3afa39a..1b79191 100644
--- a/tests/suites/test_suite_ssl.data
+++ b/tests/suites/test_suite_ssl.data
@@ -10545,3 +10545,15 @@
 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 f7c9be0..7c4f865 100644
--- a/tests/suites/test_suite_ssl.function
+++ b/tests/suites/test_suite_ssl.function
@@ -4361,3 +4361,36 @@
     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 */
diff --git a/tests/suites/test_suite_x509write.function b/tests/suites/test_suite_x509write.function
index be9e0ae..31d6000 100644
--- a/tests/suites/test_suite_x509write.function
+++ b/tests/suites/test_suite_x509write.function
@@ -5,11 +5,25 @@
 #include "mbedtls/pem.h"
 #include "mbedtls/oid.h"
 #include "mbedtls/rsa.h"
-#if defined(MBEDTLS_USE_PSA_CRYPTO)
+
+/* These are the same depends as the test function x509_crs_check_opaque(),
+ * the only function using PSA here. Using a weaker condition would result in
+ * warnings about the static functions defined in psa_crypto_helpers.h being
+ * unused. */
+#if defined(MBEDTLS_USE_PSA_CRYPTO) && \
+    defined(MBEDTLS_PEM_WRITE_C) && \
+    defined(MBEDTLS_X509_CSR_WRITE_C)
 #include "psa/crypto.h"
 #include "mbedtls/psa_util.h"
-#endif
-
+#include "test/psa_crypto_helpers.h"
+#define PSA_INIT( ) PSA_ASSERT( psa_crypto_init( ) )
+#else
+/* Define empty macros so that we can use them in the preamble and teardown
+ * of every test function that uses PSA conditionally based on
+ * MBEDTLS_USE_PSA_CRYPTO. */
+#define PSA_INIT( ) ( (void) 0 )
+#define PSA_DONE( ) ( (void) 0 )
+#endif /* MBEDTLS_USE_PSA_CRYPTO && MBEDTLS_PEM_WRITE_C && MBEDTLS_X509_CSR_WRITE_C */
 
 #if defined(MBEDTLS_RSA_C)
 int mbedtls_rsa_decrypt_func( void *ctx, int mode, size_t *olen,
@@ -147,7 +161,7 @@
                                  int cert_type )
 {
     mbedtls_pk_context key;
-    psa_key_handle_t slot;
+    psa_key_handle_t slot = 0;
     psa_algorithm_t md_alg_psa;
     mbedtls_x509write_csr req;
     unsigned char buf[4096];
@@ -156,7 +170,7 @@
     const char *subject_name = "C=NL,O=PolarSSL,CN=PolarSSL Server 1";
     mbedtls_test_rnd_pseudo_info rnd_info;
 
-    psa_crypto_init();
+    PSA_INIT( );
     memset( &rnd_info, 0x2a, sizeof( mbedtls_test_rnd_pseudo_info ) );
 
     md_alg_psa = mbedtls_psa_translate_md( (mbedtls_md_type_t) md_type );
@@ -184,9 +198,12 @@
     buf[pem_len] = '\0';
     TEST_ASSERT( x509_crt_verifycsr( buf, pem_len + 1 ) == 0 );
 
+
 exit:
     mbedtls_x509write_csr_free( &req );
     mbedtls_pk_free( &key );
+    psa_destroy_key( slot );
+    PSA_DONE( );
 }
 /* END_CASE */