diff --git a/library/ssl_tls13_generic.c b/library/ssl_tls13_generic.c
index c8601ce..e484b79 100644
--- a/library/ssl_tls13_generic.c
+++ b/library/ssl_tls13_generic.c
@@ -23,14 +23,15 @@
 
 #if defined(MBEDTLS_SSL_PROTO_TLS1_3_EXPERIMENTAL)
 
+#include <string.h>
+
 #include "mbedtls/error.h"
 #include "mbedtls/debug.h"
+#include "mbedtls/oid.h"
+#include "mbedtls/platform.h"
 
 #include "ssl_misc.h"
-#include <mbedtls/debug.h>
-#include <mbedtls/oid.h>
-#include <mbedtls/platform.h>
-
+#include "ssl_tls13_keys.h"
 
 int mbedtls_ssl_tls1_3_fetch_handshake_msg( mbedtls_ssl_context *ssl,
                                             unsigned hs_type,
@@ -217,9 +218,375 @@
     return( 0 );
 }
 
+/*
+ * The ssl_tls13_create_verify_structure() creates the verify structure.
+ * As input, it requires the transcript hash.
+ *
+ * The caller has to ensure that the buffer has size at least
+ * SSL_VERIFY_STRUCT_MAX_SIZE bytes.
+ */
+static void ssl_tls13_create_verify_structure( unsigned char *transcript_hash,
+                                               size_t transcript_hash_len,
+                                               unsigned char *verify_buffer,
+                                               size_t *verify_buffer_len,
+                                               int from )
+{
+    size_t idx = 0;
+
+    /* RFC 8446, Section 4.4.3:
+     *
+     * The digital signature [in the CertificateVerify message] is then
+     * computed over the concatenation of:
+     * -  A string that consists of octet 32 (0x20) repeated 64 times
+     * -  The context string
+     * -  A single 0 byte which serves as the separator
+     * -  The content to be signed
+     */
+    uint8_t const verify_padding_val = 0x20;
+    size_t const verify_padding_len = 64;
+
+    memset( verify_buffer + idx, verify_padding_val, verify_padding_len );
+    idx += verify_padding_len;
+
+    if( from == MBEDTLS_SSL_IS_CLIENT )
+    {
+        memcpy( verify_buffer + idx, MBEDTLS_SSL_TLS1_3_LBL_WITH_LEN( client_cv ) );
+        idx += MBEDTLS_SSL_TLS1_3_LBL_LEN( client_cv );
+    }
+    else
+    { /* from == MBEDTLS_SSL_IS_SERVER */
+        memcpy( verify_buffer + idx, MBEDTLS_SSL_TLS1_3_LBL_WITH_LEN( server_cv ) );
+        idx += MBEDTLS_SSL_TLS1_3_LBL_LEN( server_cv );
+    }
+
+    verify_buffer[idx++] = 0x0;
+
+    memcpy( verify_buffer + idx, transcript_hash, transcript_hash_len );
+    idx += transcript_hash_len;
+
+    *verify_buffer_len = idx;
+}
+
 #endif /* MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED */
 
 /*
+ * STATE HANDLING: Read CertificateVerify
+ */
+/* Macro to express the length of the verify structure length.
+ *
+ * The structure is computed per TLS 1.3 specification as:
+ *   - 64 bytes of octet 32,
+ *   - 33 bytes for the context string
+ *        (which is either "TLS 1.3, client CertificateVerify"
+ *         or "TLS 1.3, server CertificateVerify"),
+ *   - 1 byte for the octet 0x0, which servers as a separator,
+ *   - 32 or 48 bytes for the Transcript-Hash(Handshake Context, Certificate)
+ *     (depending on the size of the transcript_hash)
+ *
+ * This results in a total size of
+ * - 130 bytes for a SHA256-based transcript hash, or
+ *   (64 + 33 + 1 + 32 bytes)
+ * - 146 bytes for a SHA384-based transcript hash.
+ *   (64 + 33 + 1 + 48 bytes)
+ *
+ */
+#define SSL_VERIFY_STRUCT_MAX_SIZE  ( 64 +                 \
+                                      33 +                 \
+                                       1 +                 \
+                                      MBEDTLS_MD_MAX_SIZE  \
+                                    )
+/* Coordinate: Check whether a certificate verify message is expected.
+ * Returns a negative value on failure, and otherwise
+ * - SSL_CERTIFICATE_VERIFY_SKIP
+ * - SSL_CERTIFICATE_VERIFY_READ
+ * to indicate if the CertificateVerify message should be present or not.
+ */
+#define SSL_CERTIFICATE_VERIFY_SKIP 0
+#define SSL_CERTIFICATE_VERIFY_READ 1
+static int ssl_tls13_process_certificate_verify_coordinate(
+                                    mbedtls_ssl_context *ssl )
+{
+    if( mbedtls_ssl_tls1_3_some_psk_enabled( ssl ) )
+        return( SSL_CERTIFICATE_VERIFY_SKIP );
+
+#if defined(MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED)
+    if( ssl->session_negotiate->peer_cert == NULL )
+        return( SSL_CERTIFICATE_VERIFY_SKIP );
+    return( SSL_CERTIFICATE_VERIFY_READ );
+#else
+    MBEDTLS_SSL_DEBUG_MSG( 1, ( "should never happen" ) );
+    return( MBEDTLS_ERR_SSL_INTERNAL_ERROR );
+#endif /* MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED */
+}
+
+#if defined(MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED)
+static int ssl_tls13_process_certificate_verify_parse( mbedtls_ssl_context *ssl,
+                                                       const unsigned char *buf,
+                                                       const unsigned char *end,
+                                                       const unsigned char *verify_buffer,
+                                                       size_t verify_buffer_len )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    const unsigned char *p = buf;
+    uint16_t algorithm;
+    const uint16_t *tls13_sig_alg = ssl->conf->tls13_sig_algs;
+    size_t signature_len;
+    mbedtls_pk_type_t sig_alg;
+    mbedtls_md_type_t md_alg;
+    unsigned char verify_hash[MBEDTLS_TLS1_3_MD_MAX_SIZE];
+    size_t verify_hash_len;
+
+    /*
+     * struct {
+     *     SignatureScheme algorithm;
+     *     opaque signature<0..2^16-1>;
+     * } CertificateVerify;
+     */
+    MBEDTLS_SSL_CHK_BUF_READ_PTR( p, end, 2 );
+    algorithm = MBEDTLS_GET_UINT16_BE( p, 0 );
+    p += 2;
+
+    /* RFC 8446 section 4.4.3
+     *
+     * If the CertificateVerify message is sent by a server, the signature algorithm
+     * MUST be one offered in the client's "signature_algorithms" extension unless
+     * no valid certificate chain can be produced without unsupported algorithms
+     *
+     * RFC 8446 section 4.4.2.2
+     *
+     * If the client cannot construct an acceptable chain using the provided
+     * certificates and decides to abort the handshake, then it MUST abort the handshake
+     * with an appropriate certificate-related alert (by default, "unsupported_certificate").
+     *
+     * Check if algorithm in offered signature algorithms. Send `unsupported_certificate`
+     * alert message on failure.
+     */
+    while( 1 )
+    {
+        /* Found algorithm in offered signature algorithms */
+        if( *tls13_sig_alg == algorithm )
+            break;
+
+        if( *tls13_sig_alg == MBEDTLS_TLS13_SIG_NONE )
+        {
+            /* End of offered signature algorithms list */
+            MBEDTLS_SSL_DEBUG_MSG( 1,
+                                   ( "signature algorithm(%04x) not in offered"
+                                     "signature algorithms ",
+                                     ( unsigned int ) algorithm ) );
+            MBEDTLS_SSL_PEND_FATAL_ALERT(
+                MBEDTLS_SSL_ALERT_MSG_UNSUPPORTED_CERT,
+                MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
+            return MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE;
+        }
+
+        tls13_sig_alg++;
+    }
+
+    /* We currently only support ECDSA-based signatures */
+    switch( algorithm )
+    {
+        case MBEDTLS_TLS13_SIG_ECDSA_SECP256R1_SHA256:
+            md_alg = MBEDTLS_MD_SHA256;
+            sig_alg = MBEDTLS_PK_ECDSA;
+            break;
+        case MBEDTLS_TLS13_SIG_ECDSA_SECP384R1_SHA384:
+            md_alg = MBEDTLS_MD_SHA384;
+            sig_alg = MBEDTLS_PK_ECDSA;
+            break;
+        case MBEDTLS_TLS13_SIG_ECDSA_SECP521R1_SHA512:
+            md_alg = MBEDTLS_MD_SHA512;
+            sig_alg = MBEDTLS_PK_ECDSA;
+            break;
+        default:
+            MBEDTLS_SSL_DEBUG_MSG( 1, ( "Certificate Verify: Unknown signature algorithm." ) );
+            MBEDTLS_SSL_PEND_FATAL_ALERT(
+                MBEDTLS_SSL_ALERT_MSG_UNSUPPORTED_CERT,
+                MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
+            return( MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
+    }
+
+    MBEDTLS_SSL_DEBUG_MSG( 3, ( "Certificate Verify: Signature algorithm ( %04x )",
+                                ( unsigned int ) algorithm ) );
+
+    /*
+     * Check the certificate's key type matches the signature alg
+     */
+    if( !mbedtls_pk_can_do( &ssl->session_negotiate->peer_cert->pk, sig_alg ) )
+    {
+        MBEDTLS_SSL_DEBUG_MSG( 1, ( "signature algorithm doesn't match cert key" ) );
+        MBEDTLS_SSL_PEND_FATAL_ALERT(
+            MBEDTLS_SSL_ALERT_MSG_UNSUPPORTED_CERT,
+            MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
+        return( MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
+    }
+
+    MBEDTLS_SSL_CHK_BUF_READ_PTR( p, end, 2 );
+    signature_len = MBEDTLS_GET_UINT16_BE( p, 0 );
+    p += 2;
+    MBEDTLS_SSL_CHK_BUF_READ_PTR( p, end, signature_len );
+
+    /* Hash verify buffer with indicated hash function */
+    switch( md_alg )
+    {
+#if defined(MBEDTLS_SHA256_C)
+        case MBEDTLS_MD_SHA256:
+            verify_hash_len = 32;
+            if( ( ret = mbedtls_sha256( verify_buffer,
+                                        verify_buffer_len,
+                                        verify_hash,
+                                        0 ) ) != 0 )
+            {
+                MBEDTLS_SSL_DEBUG_RET( 1, "mbedtls_sha256", ret );
+                MBEDTLS_SSL_PEND_FATAL_ALERT(
+                    MBEDTLS_SSL_ALERT_MSG_UNSUPPORTED_CERT,
+                    MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
+                return( MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
+            }
+            break;
+#endif /* MBEDTLS_SHA256_C */
+
+#if defined(MBEDTLS_SHA384_C)
+        case MBEDTLS_MD_SHA384:
+            verify_hash_len = 48;
+            if( ( ret = mbedtls_sha512( verify_buffer,
+                                        verify_buffer_len,
+                                        verify_hash,
+                                        1 ) ) != 0 )
+            {
+                MBEDTLS_SSL_DEBUG_RET( 1, "mbedtls_sha384", ret );
+                MBEDTLS_SSL_PEND_FATAL_ALERT(
+                    MBEDTLS_SSL_ALERT_MSG_UNSUPPORTED_CERT,
+                    MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
+                return( MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
+            }
+            break;
+#endif /* MBEDTLS_SHA384_C */
+
+#if defined(MBEDTLS_SHA512_C)
+        case MBEDTLS_MD_SHA512:
+            verify_hash_len = 64;
+            if( ( ret = mbedtls_sha512( verify_buffer,
+                                        verify_buffer_len,
+                                        verify_hash,
+                                        0 ) ) != 0 )
+            {
+                MBEDTLS_SSL_DEBUG_RET( 1, "mbedtls_sha512", ret );
+                MBEDTLS_SSL_PEND_FATAL_ALERT(
+                    MBEDTLS_SSL_ALERT_MSG_UNSUPPORTED_CERT,
+                    MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
+                return( MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
+            }
+            break;
+#endif /* MBEDTLS_SHA512_C */
+
+    default:
+        MBEDTLS_SSL_DEBUG_MSG( 1, ( "Certificate Verify: Unknown signature algorithm." ) );
+        MBEDTLS_SSL_PEND_FATAL_ALERT(
+                    MBEDTLS_SSL_ALERT_MSG_UNSUPPORTED_CERT,
+                    MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
+        return( MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
+    }
+
+    MBEDTLS_SSL_DEBUG_BUF( 3, "verify hash", verify_hash, verify_hash_len );
+
+    if( ( ret = mbedtls_pk_verify_ext( sig_alg, NULL,
+                                       &ssl->session_negotiate->peer_cert->pk,
+                                       md_alg, verify_hash, verify_hash_len,
+                                       buf, signature_len ) ) != 0 )
+    {
+        MBEDTLS_SSL_DEBUG_RET( 1, "mbedtls_pk_verify_ext", ret );
+
+        /* RFC 8446 section 4.4.3
+         *
+         * If the verification fails, the receiver MUST terminate the handshake
+         * with a "decrypt_error" alert.
+         */
+        MBEDTLS_SSL_PEND_FATAL_ALERT( MBEDTLS_SSL_ALERT_MSG_DECRYPT_ERROR, ret );
+
+        return( ret );
+    }
+
+    return( ret );
+}
+#endif /* MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED */
+
+int mbedtls_ssl_tls13_process_certificate_verify( mbedtls_ssl_context *ssl )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+
+    /* Coordination step */
+    MBEDTLS_SSL_DEBUG_MSG( 2, ( "=> parse certificate verify" ) );
+
+    MBEDTLS_SSL_PROC_CHK_NEG( ssl_tls13_process_certificate_verify_coordinate( ssl ) );
+
+#if defined(MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED) // TBD: double-check
+    if( ret == SSL_CERTIFICATE_VERIFY_READ )
+    {
+        unsigned char verify_buffer[SSL_VERIFY_STRUCT_MAX_SIZE];
+        size_t verify_buffer_len;
+        unsigned char transcript[MBEDTLS_TLS1_3_MD_MAX_SIZE];
+        size_t transcript_len;
+        unsigned char *buf;
+        size_t buf_len;
+
+        /* Need to calculate the hash of the transcript first
+         * before reading the message since otherwise it gets
+         * included in the transcript
+         */
+        ret = mbedtls_ssl_get_handshake_transcript( ssl,
+                               ssl->handshake->ciphersuite_info->mac,
+                               transcript, sizeof( transcript ),
+                               &transcript_len );
+        if( ret != 0 )
+        {
+            MBEDTLS_SSL_PEND_FATAL_ALERT(
+                MBEDTLS_SSL_ALERT_MSG_INTERNAL_ERROR,
+                MBEDTLS_ERR_SSL_INTERNAL_ERROR );
+            return( ret );
+        }
+
+        MBEDTLS_SSL_DEBUG_BUF( 3, "handshake hash", transcript, transcript_len );
+
+        /* Create verify structure */
+        ssl_tls13_create_verify_structure( transcript,
+                                           transcript_len,
+                                           verify_buffer,
+                                           &verify_buffer_len,
+                                           !ssl->conf->endpoint );
+
+        MBEDTLS_SSL_PROC_CHK(
+            mbedtls_ssl_tls1_3_fetch_handshake_msg( ssl,
+                    MBEDTLS_SSL_HS_CERTIFICATE_VERIFY, &buf, &buf_len ) );
+
+        /* Process the message contents */
+        MBEDTLS_SSL_PROC_CHK(
+            ssl_tls13_process_certificate_verify_parse( ssl,
+                buf, buf + buf_len, verify_buffer, verify_buffer_len ) );
+
+        mbedtls_ssl_tls1_3_add_hs_msg_to_checksum( ssl,
+                            MBEDTLS_SSL_HS_CERTIFICATE_VERIFY, buf, buf_len );
+    }
+    else
+#endif /* MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED */
+    if( ret == SSL_CERTIFICATE_VERIFY_SKIP )
+    {
+        MBEDTLS_SSL_DEBUG_MSG( 2, ( "<= skip parse certificate verify" ) );
+    }
+    else
+    {
+        MBEDTLS_SSL_DEBUG_MSG( 1, ( "should never happen" ) );
+        return( MBEDTLS_ERR_SSL_INTERNAL_ERROR );
+    }
+
+
+cleanup:
+
+    MBEDTLS_SSL_DEBUG_MSG( 2, ( "<= parse certificate verify" ) );
+    return( ret );
+}
+
+/*
  *
  * STATE HANDLING: Incoming Certificate, client-side only currently.
  *