diff --git a/tests/data_files/Makefile b/tests/data_files/Makefile
index d1af18c..0aa78eb 100644
--- a/tests/data_files/Makefile
+++ b/tests/data_files/Makefile
@@ -786,6 +786,14 @@
 	$(OPENSSL) pkey -in $< -inform DER -out $@
 all_final += ec_prv.pk8param.pem
 
+###
+### A generic SECP521R1 private key
+###
+
+secp521r1_prv.der:
+	$(OPENSSL) ecparam -genkey -name secp521r1 -noout -out secp521r1_prv.der
+all_final += secp521r1_prv.der
+
 ################################################################
 ### Generate CSRs for X.509 write test suite
 ################################################################
diff --git a/tests/data_files/secp521r1_prv.der b/tests/data_files/secp521r1_prv.der
new file mode 100644
index 0000000..4d342bd
--- /dev/null
+++ b/tests/data_files/secp521r1_prv.der
Binary files differ
diff --git a/tests/scripts/all.sh b/tests/scripts/all.sh
index 369df15..b222ff5 100755
--- a/tests/scripts/all.sh
+++ b/tests/scripts/all.sh
@@ -611,6 +611,24 @@
 #### Build and test many configurations and targets
 ################################################################
 
+component_test_large_ecdsa_key_signature () {
+
+    SMALL_MPI_MAX_SIZE=136 # Small enough to interfere with the EC signatures
+
+    msg "build: cmake + MBEDTLS_MPI_MAX_SIZE=${SMALL_MPI_MAX_SIZE}, gcc, ASan" # ~ 1 min 50s
+    scripts/config.pl set MBEDTLS_MPI_MAX_SIZE $SMALL_MPI_MAX_SIZE
+    crypto/scripts/config.pl set MBEDTLS_MPI_MAX_SIZE $SMALL_MPI_MAX_SIZE
+    CC=gcc cmake -D CMAKE_BUILD_TYPE:String=Asan .
+    make
+
+    INEVITABLY_PRESENT_FILE=Makefile
+    SIGNATURE_FILE="${INEVITABLY_PRESENT_FILE}.sig" # Warning, this is rm -f'ed below
+
+    msg "test: pk_sign secp521r1_prv.der for MBEDTLS_MPI_MAX_SIZE=${SMALL_MPI_MAX_SIZE} (ASan build)" # ~ 5s
+    if_build_succeeded programs/pkey/pk_sign tests/data_files/secp521r1_prv.der $INEVITABLY_PRESENT_FILE
+    rm -f $SIGNATURE_FILE
+}
+
 component_test_default_out_of_box () {
     msg "build: make, default config (out-of-box)" # ~1min
     make