diff --git a/ChangeLog.d/driver-only-hashes.txt b/ChangeLog.d/driver-only-hashes.txt
new file mode 100644
index 0000000..4967bb1
--- /dev/null
+++ b/ChangeLog.d/driver-only-hashes.txt
@@ -0,0 +1,10 @@
+Features
+   * All modules that use hashes or HMAC can now take advantage of PSA Crypto
+     drivers when MBEDTLS_PSA_CRYPTO_C is enabled and psa_crypto_init() has
+     been called. Previously (in 3.3), this was restricted to a few modules,
+     and only in builds where MBEDTLS_MD_C was disabled; in particular the
+     entropy module was not covered which meant an external RNG had to be
+     provided - these limitations are lifted in this version. A new set of
+     feature macros, MBEDTLS_MD_CAN_xxx, has been introduced that can be used
+     to check for availability of hash algorithms, regardless of whether
+     they're provided by a built-in implementation, a driver or both.
diff --git a/docs/architecture/psa-migration/psa-limitations.md b/docs/architecture/psa-migration/psa-limitations.md
index c368023..b81aeb4 100644
--- a/docs/architecture/psa-migration/psa-limitations.md
+++ b/docs/architecture/psa-migration/psa-limitations.md
@@ -11,11 +11,15 @@
 Limitations relevant for G1 (performing crypto operations)
 ==========================================================
 
-Restartable ECC operations
---------------------------
+Restartable (aka interruptible) ECC operations
+----------------------------------------------
 
-There is currently no support for that in PSA at all, but it will be added at
-some point, see <https://github.com/orgs/Mbed-TLS/projects/1#column-18816849>.
+Support for interruptible ECDSA sign/verify was added to PSA in Mbed TLS 3.4.
+However support for interruptible ECDH is not present yet. Also, PK, X.509 and
+TLS have not yet been adapted to take advantage of the new PSA APIs. See:
+- <https://github.com/Mbed-TLS/mbedtls/issues/7292>;
+- <https://github.com/Mbed-TLS/mbedtls/issues/7293>;
+- <https://github.com/Mbed-TLS/mbedtls/issues/7294>.
 
 Currently, when `MBEDTLS_USE_PSA_CRYPTO` and `MBEDTLS_ECP_RESTARTABLE` are
 both enabled, some operations that should be restartable are not (ECDH in TLS
@@ -78,6 +82,10 @@
 migration by implementing RFC 7919. (Implementing RFC 7919 could be done any
 time; making it mandatory can only be done in 4.0 or another major version.)
 
+As of early 2023, the plan is to go with option 2 in Mbed TLS 4.0, which has
+been announced on the mailing-list and got no push-back, see
+<https://github.com/Mbed-TLS/mbedtls/issues/5278>.
+
 RSA-PSS parameters
 ------------------
 
@@ -321,6 +329,8 @@
    in the meantime. Such an extension seems inconvenient and not motivated by
 strong security arguments, so it's unclear whether it would be accepted.
 
+Since Mbed TLS 3.4, option 1 is implemented.
+
 Limitations relevant for G2 (isolation of long-term secrets)
 ============================================================
 
diff --git a/docs/architecture/psa-migration/strategy.md b/docs/architecture/psa-migration/strategy.md
index 1542324..b985a77 100644
--- a/docs/architecture/psa-migration/strategy.md
+++ b/docs/architecture/psa-migration/strategy.md
@@ -18,13 +18,17 @@
 implemented, see `docs/use-psa-crypto.md`, where new APIs are about (G2), and
 internal changes implement (G1).
 
+As of early 2023, work towards G5 is in progress: Mbed TLS 3.3 and 3.4 saw
+some improvements in this area, and more will be coming in future releases.
+
 Generally speaking, the numbering above doesn't mean that each goal requires
 the preceding ones to be completed.
 
+
 Compile-time options
 ====================
 
-We currently have two compile-time options that are relevant to the migration:
+We currently have a few compile-time options that are relevant to the migration:
 
 - `MBEDTLS_PSA_CRYPTO_C` - enabled by default, controls the presence of the PSA
   Crypto APIs.
@@ -36,7 +40,9 @@
 
 The reasons why `MBEDTLS_USE_PSA_CRYPTO` is optional and disabled by default
 are:
-- it's incompatible with `MBEDTLS_ECP_RESTARTABLE`;
+- it's not fully compatible with `MBEDTLS_ECP_RESTARTABLE`: you can enable
+  both, but then you won't get the full effect of RESTARTBLE (see the
+documentation of this option in `mbedtls_config.h`);
 - to avoid a hard/default dependency of TLS, X.509 and PK on
   `MBEDTLS_PSA_CRYPTO_C`, for backward compatibility reasons:
   - When `MBEDTLS_PSA_CRYPTO_C` is enabled and used, applications need to call
@@ -71,10 +77,10 @@
 TLS and X.509 layers can't both use only PSA APIs and get restartable
 behaviour.
 
-Supporting this in PSA is on our roadmap and currently planned for end of
-2022, see <https://github.com/orgs/Mbed-TLS/projects/1#column-18883250>.
+Support for restartable (aka interruptible) ECDSA sign/verify operation was
+added to PSA in Mbed TLS 3.4, but support for ECDH is not present yet.
 
-It will then require follow-up work to make use of the new PSA API in
+It will then require follow-up work to make use of the new PSA APIs in
 PK/X.509/TLS in all places where we currently allow restartable operations.
 
 ### Backward compatibility issues with making `MBEDTLS_USE_PSA_CRYPTO` always on
@@ -137,8 +143,11 @@
 - Downside: tricky to implement if the PSA implementation is currently done on
   top of that layer (dependency loop).
 
-This strategy is currently (early 2022) used for all operations in the PK
-layer.
+This strategy is currently (early 2023) used for all operations in the PK
+layer; the MD layer uses a variant where it dispatches to PSA if a driver is
+available and the driver subsystem has been initialized, regardless of whether
+`USE_PSA_CRYPTO` is enabled; see `md-cipher-dispatch.md` in the same directory
+for details.
 
 This strategy is not very well suited to the Cipher layer, as the PSA
 implementation is currently done on top of that layer.
@@ -161,8 +170,9 @@
   code size.
 - Downside: TLS/X.509 code has to be done for each operation.
 
-This strategy is currently (early 2022) used for the MD layer and the Cipher
-layer.
+This strategy is currently (early 2023) used for the MD layer and the Cipher
+layer in X.509 and TLS. Crypto modules however always call to MD which may
+then dispatch to PSA, see `md-cipher-dispatch.md`.
 
 Opt-in use of PSA from the abstraction layer
 --------------------------------------------
@@ -210,7 +220,10 @@
 - PK (for G1): silently call PSA
 - PK (for G2): opt-in use of PSA (new key type)
 - Cipher (G1): replace calls at each call site
-- MD (G1): replace calls at each call site
+- MD (G1, X.509 and TLS): replace calls at each call site (depending on
+  `USE_PSA_CRYPTO`)
+- MD (G5): silently call PSA when a driver is available, see
+  `md-cipher-dispatch.md`.
 
 
 Supporting builds with drivers without the software implementation
@@ -219,10 +232,6 @@
 This section presents a plan towards G5: save code size by compiling out our
 software implementation when a driver is available.
 
-Additionally, we want to save code size by compiling out the
-abstractions layers that we are not using when `MBEDTLS_USE_PSA_CRYPTO` is
-enabled (see previous section): MD and Cipher.
-
 Let's expand a bit on the definition of the goal: in such a configuration
 (driver used, software implementation and abstraction layer compiled out),
 we want:
@@ -238,9 +247,10 @@
 We can roughly divide the work needed to get there in the following steps:
 
 0. Have a working driver interface for the algorithms we want to replace.
-1. Have users of these algorithms call to PSA, not the legacy API, for all
-   operations. (This is G1, and for PK, X.509 and TLS this is controlled by
-   `MBEDTLS_USE_PSA_CRYPTO`.) This needs to be done in the library and tests.
+1. Have users of these algorithms call to PSA or an abstraction layer than can
+   dispatch to PSA, but not the low-level legacy API, for all operations.
+(This is G1, and for PK, X.509 and TLS this is controlled by
+`MBEDTLS_USE_PSA_CRYPTO`.) This needs to be done in the library and tests.
 2. Have users of these algorithms not depend on the legacy API for information
    management (getting a size for a given algorithm, etc.)
 3. Adapt compile-time guards used to query availability of a given algorithm;
@@ -262,50 +272,32 @@
 is preferable to group with the next step(s) in the same PR until good test
 coverage can be reached.
 
-**Status as of Mbed TLS 3.2:**
+**Status as of end of March 2023 (shortly after 3.4):**
 
 - Step 0 is achieved for most algorithms, with only a few gaps remaining.
 - Step 1 is achieved for most of PK, X.509, and TLS when
   `MBEDTLS_USE_PSA_CRYPTO` is enabled with only a few gaps remaining (see
   docs/use-psa-crypto.md).
-- Step 1 is not achieved for a lot of the crypto library including the PSA
-  core. For example, `entropy.c` calls the legacy API
-  `mbedtls_sha256` (or `mbedtls_sha512` optionally); `hmac_drbg.c` calls the
-  legacy API `mbedtls_md` and `ctr_drbg.c` calls the legacy API `mbedtls_aes`;
-  the PSA core depends on the entropy module and at least one of the DRBG
-  modules (unless `MBEDTLS_PSA_CRYPTO_EXTERNAL_RNG` is used). Further, several
-  crypto modules have similar issues, for example RSA PKCS#1 v2.1 calls
-  `mbedtls_md` directly.
+- Step 1 is achieved for the crypto library regarding hashes: everything uses
+  MD (not low-level hash APIs), which then dispatches to PSA if applicable.
+- Step 1 is not achieved for all of the crypto library when it come to
+  ciphers. For example,`ctr_drbg.c` calls the legacy API `mbedtls_aes`.
 - Step 2 is achieved for most of X.509 and TLS (same gaps as step 1) when
-  `MBEDTLS_USE_PSA_CRYPTO` is enabled - this was tasks like #5795, #5796,
-  #5797. It is being done in PK and RSA PKCS#1 v1.5 by PR #6065.
-- Step 3 was mostly not started at all before 3.2; it is being done for PK by
-  PR #6065.
+  `MBEDTLS_USE_PSA_CRYPTO` is enabled.
+- Step 3 is done for hashes and top-level ECC modules (ECDSA, ECDH, ECJPAKE).
 
 **Strategy for step 1:**
 
 Regarding PK, X.509, and TLS, this is mostly achieved with only a few gaps.
 (The strategy was outlined in the previous section.)
 
-Regarding libmbedcrypto, outside of the RNG subsystem, for modules that
-currently depend on other legacy crypto modules, this can be achieved without
-backwards compatibility issues, by using the software implementation if
-available, and "falling back" to PSA only if it's not. The compile-time
-dependency changes from the current one (say, `MD_C` or `AES_C`) to "the
-previous dependency OR PSA Crypto with needed algorithms". When building
-without software implementation, users need to call `psa_crypto_init()` before
-calling any function from these modules. This condition does not constitute a
-break of backwards compatibility, as it was previously impossible to build in
-those configurations, and in configurations were the build was possible,
-application code keeps working unchanged. An work-in-progress example of
-applying this strategy, for RSA PKCS#1 v2.1, is here:
-<https://github.com/Mbed-TLS/mbedtls/pull/6141>
-
-There is a problem with the modules used for the PSA RNG, as currently the RNG
-is initialized before drivers and the key store. This part will need further
-study, but in the meantime we can proceed with everything that's not the
-entropy module of one of the DRBG modules, and that does not depend on one of
-those modules.
+Regarding libmbedcrypto:
+- for hashes and ciphers, see `md-cipher-dispatch.md` in the same directory;
+- for ECC, we have no internal uses of the top-level algorithms (ECDSA, ECDH,
+  ECJPAKE), however they all depend on `ECP_C` which in turn depends on
+`BIGNUM_C`. So, direct calls from TLS, X.509 and PK to ECP and Bignum will
+need to be replaced; see <https://github.com/Mbed-TLS/mbedtls/issues/6839> and
+linked issues for a summary of intermediate steps and open points.
 
 **Strategy for step 2:**
 
@@ -315,14 +307,11 @@
 (such as `mbedtls_md_type_t`) in their API and can't assume PSA to be
 compiled in (such as `rsa.c`).
 
-It is suggested that, as a temporary solution until we clean this up
-later when removing the legacy API including its identifiers (G4), we may
-occasionally use ad-hoc internal functions, such as the ones introduced by PR
-6065 in `library/hash_info.[ch]`.
-
-An alternative would be to have two different code paths depending on whether
-`MBEDTLS_PSA_CRYPTO_C` is defined or not. However this is not great for
-readability or testability.
+When using an existing abstraction layer such as MD, it can provide
+information management functions. In other cases, information that was in a
+low-level module but logically belongs in a higher-level module can be moved
+to that module (for example, TLS identifiers of curves and there conversion
+to/from PSA or legacy identifiers belongs in TLS, not `ecp.c`).
 
 **Strategy for step 3:**
 
@@ -338,35 +327,15 @@
 if it is, the code want the algorithm available in PSA, otherwise, it wants it
 available via the legacy API(s) is it using (MD and/or low-level).
 
-The strategy for steps 1 and 2 above will introduce new situations: code that
-currently compute hashes using MD (resp. a low-level hash module) will gain
-the ability to "fall back" to using PSA if the legacy dependency isn't
-available. Data related to a certain hash (OID, sizes, translations) should
-only be included in the build if it is possible to use that hash in some way.
+As much as possible, we're trying to create for each algorithm a single new
+macro that can be used to express dependencies everywhere (except pure PSA
+code that should always use `PSA_WANT`). For example, for hashes this is the
+`MBEDTLS_MD_CAN_xxx` family. For ECC algorithms, we have similar
+`MBEDTLS_PK_CAN_xxx` macros.
 
-In order to cater to these new needs, new families of macros are introduced in
-`legacy_or_psa.h`, see its documentation for details.
-
-It should be noted that there are currently:
-- too many different ways of computing a hash (low-level, MD, PSA);
-- too many different ways to configure the library that influence which of
-  these ways is available and will be used (`MBEDTLS_USE_PSA_CRYPTO`,
-  `MBEDTLS_PSA_CRYPTO_CONFIG`, `mbedtls_config.h` + `psa/crypto_config.h`).
-
-As a result, we need more families of dependency macros than we'd like to.
-This is a temporary situation until we move to a place where everything is
-based on PSA Crypto. In the meantime, long and explicit names where chosen for
-the new macros in the hope of avoiding confusion.
-
-Note: the new macros supplement but do not replace the existing macros:
-- code that always uses PSA Crypto (for example, code specific to TLS 1.3)
-  should use `PSA_WANT_xxx`;
-- code that always uses the legacy API (for example, crypto modules that have
-  not undergone step 1 yet) should use `MBEDTLS_xxx_C`;
-- code that may use one of the two APIs, either based on
-  `MBEDTLS_USE_PSA_CRYPTO` (X.509, TLS 1.2, shared between TLS 1.2 and 1.3),
-  or based on availability (crypto modules after step 1), should use one of
-  the new macros from `legacy_or_psa.h`.
+Note that in order to achieve that goal, even for code that obeys
+`USE_PSA_CRYPTO`, it is useful to impose that all algorithms that are
+available via the legacy APIs are also available via PSA.
 
 Executing step 3 will mostly consist of using the right dependency macros in
 the right places (once the previous steps are done).
diff --git a/docs/use-psa-crypto.md b/docs/use-psa-crypto.md
index c63e65a..4d72f99 100644
--- a/docs/use-psa-crypto.md
+++ b/docs/use-psa-crypto.md
@@ -1,8 +1,12 @@
 This document describes the compile-time configuration option
 `MBEDTLS_USE_PSA_CRYPTO` from a user's perspective.
 
-This option makes the X.509 and TLS library use PSA for cryptographic
-operations, and enables new APIs for using keys handled by PSA Crypto.
+This option:
+- makes the X.509 and TLS libraries use PSA for cryptographic operations as
+  much as possible, see "Internal changes" below;
+- enables new APIs for using keys handled by PSA Crypto, such as
+  `mbedtls_pk_setup_opaque()` and `mbedtls_ssl_conf_psk_opaque()`, see
+"New APIs / API extensions" below.
 
 General considerations
 ----------------------
@@ -11,9 +15,25 @@
 `psa_crypto_init()` before calling any function from the SSL/TLS, X.509 or PK
 module.
 
-**Scope:** `MBEDTLS_USE_PSA_CRYPTO` has no effect on the most of the TLS 1.3
-code, which always uses PSA crypto. The parts of the TLS 1.3 code that will
-use PSA Crypto or not depending on the value of this option are:
+**Relationship with other options:** This option depends on
+`MBEDTLS_PSA_CRYPTO_C`. These two options differ in the following way:
+- `MBEDTLS_PSA_CRYPTO_C` enables the implementation of the PSA Crypto API.
+  When it is enabled, `psa_xxx()` APIs are available and you must call
+`psa_crypto_init()` before you call any other `psa_xxx()` function. Other
+modules in the library (non-PSA crypto APIs, X.509, TLS) may or may not use
+PSA Crypto but you're not required to call `psa_crypto_init()` before calling
+non-PSA functions, unless when explicitly documented (TLS 1.3).
+- `MBEDTLS_USE_PSA_CRYPTO` means that X.509 and TLS will use PSA Crypto as
+  much as possible (that is, everywhere except for features that are not
+supported by PSA Crypto, see "Internal Changes" below for a complete list of
+exceptions). When it is enabled, you need to call `psa_crypto_init()` before
+calling any function from PK, X.509 or TLS; however it doesn't change anything
+for the rest of the library.
+
+**Scope:** `MBEDTLS_USE_PSA_CRYPTO` has no effect on modules other than PK,
+X.509 and TLS. It also has no effect on most of the TLS 1.3 code, which always
+uses PSA crypto. The parts of the TLS 1.3 code that will use PSA Crypto or not
+depending on this option being set or not are:
 - record protection;
 - running handshake hash;
 - asymmetric signature verification & generation;
@@ -21,6 +41,21 @@
 You need to enable `MBEDTLS_USE_PSA_CRYPTO` if you want TLS 1.3 to use PSA
 everywhere.
 
+**Historical note:** This option was introduced at a time when PSA Crypto was
+still beta and not ready for production, so we made its use in X.509 and TLS
+opt-in: by default, these modules would keep using the stable,
+production-ready legacy (pre-PSA) crypto APIs. So, the scope of was X.509 and
+TLS, as well as some of PK for technical reasons. Nowadays PSA Crypto is no
+longer beta, and production quality, so there's no longer any reason to make
+its use in other modules opt-in. However, PSA Crypto functions require that
+`psa_crypto_init()` has been called before their use, and for backwards
+compatibility reasons we can't impose this requirement on non-PSA functions
+that didn't have such a requirement before. So, nowadays the main meaning of
+`MBEDTLS_USE_PSA_CRYPTO` is that the user promises to call `psa_crypto_init()`
+before calling any PK, X.509 or TLS functions. For the same compatibility
+reasons, we can't extend its scope. However, new modules in the library, such
+as TLS 1.3, can be introduced with a requirement to call `psa_crypto_init()`.
+
 New APIs / API extensions
 -------------------------
 
@@ -63,6 +98,19 @@
 **Use in TLS:** opt-in. The application needs to register the key using one of
 the new APIs to get the benefits.
 
+### PSA-held (opaque) keys for TLS 1.2 EC J-PAKE key exchange
+
+**New API function:** `mbedtls_ssl_set_hs_ecjpake_password_opaque()`.
+Call this function from an application to register a PSA key for use with the
+TLS 1.2 EC J-PAKE key exchange.
+
+**Benefits:** isolation of long-term secrets.
+
+**Limitations:** none.
+
+**Use in TLS:** opt-in. The application needs to register the key using one of
+the new APIs to get the benefits.
+
 ### PSA-based operations in the Cipher layer
 
 There is a new API function `mbedtls_cipher_setup_psa()` to set up a context
diff --git a/include/mbedtls/mbedtls_config.h b/include/mbedtls/mbedtls_config.h
index c8e215b..da48cc4 100644
--- a/include/mbedtls/mbedtls_config.h
+++ b/include/mbedtls/mbedtls_config.h
@@ -1567,13 +1567,14 @@
  * Enable support for TLS 1.2 (and DTLS 1.2 if DTLS is enabled).
  *
  * Requires: Without MBEDTLS_USE_PSA_CRYPTO: MBEDTLS_MD_C and
- *              (MBEDTLS_SHA1_C or MBEDTLS_SHA256_C or MBEDTLS_SHA512_C)
+ *              (MBEDTLS_SHA256_C or MBEDTLS_SHA384_C or
+ *               SHA-256 or SHA-512 provided by a PSA driver)
  *           With MBEDTLS_USE_PSA_CRYPTO:
- *              PSA_WANT_ALG_SHA_1 or PSA_WANT_ALG_SHA_256 or
- *              PSA_WANT_ALG_SHA_512
+ *              PSA_WANT_ALG_SHA_256 or PSA_WANT_ALG_SHA_384
  *
- * \warning If building with MBEDTLS_USE_PSA_CRYPTO, you must call
- * psa_crypto_init() before doing any TLS operations.
+ * \warning If building with MBEDTLS_USE_PSA_CRYPTO, or if the hash(es) used
+ * are only provided by PSA drivers, you must call psa_crypto_init() before
+ * doing any TLS operations.
  *
  * Comment this macro to disable support for TLS 1.2 / DTLS 1.2
  */
@@ -1921,20 +1922,23 @@
 /**
  * \def MBEDTLS_USE_PSA_CRYPTO
  *
- * Make the X.509 and TLS library use PSA for cryptographic operations, and
- * enable new APIs for using keys handled by PSA Crypto.
+ * Make the X.509 and TLS libraries use PSA for cryptographic operations as
+ * much as possible, and enable new APIs for using keys handled by PSA Crypto.
  *
  * \note Development of this option is currently in progress, and parts of Mbed
  * TLS's X.509 and TLS modules are not ported to PSA yet. However, these parts
  * will still continue to work as usual, so enabling this option should not
  * break backwards compatibility.
  *
- * \note See docs/use-psa-crypto.md for a complete description of what this
- * option currently does, and of parts that are not affected by it so far.
- *
  * \warning If you enable this option, you need to call `psa_crypto_init()`
  * before calling any function from the SSL/TLS, X.509 or PK modules.
  *
+ * \note Even with this option disabled, some code in PK, X.509, TLS or the
+ * crypto library might still use PSA drivers, if it can determine it's safe
+ * to do so.
+ *
+ * \note See docs/use-psa-crypto.md for a complete description this option.
+ *
  * Requires: MBEDTLS_PSA_CRYPTO_C.
  *
  * Uncomment this to enable internal use of PSA Crypto and new associated APIs.