diff --git a/ChangeLog.d/mpi_sub_abs.txt b/ChangeLog.d/mpi_sub_abs.txt
new file mode 100644
index 000000000..9f34ee74b
--- /dev/null
+++ b/ChangeLog.d/mpi_sub_abs.txt
@@ -0,0 +1,7 @@
+Security
+   * Fix a buffer overflow in mbedtls_mpi_sub_abs() when calculating
+     |A| - |B| where |B| is larger than |A| and has more limbs (so the
+     function should return MBEDTLS_ERR_MPI_NEGATIVE_VALUE). Only
+     applications calling mbedtls_mpi_sub_abs() directly are affected:
+     all calls inside the library were safe since this function is
+     only called with |A| >= |B|. Reported by Guido Vranken in #4042.
diff --git a/library/bignum.c b/library/bignum.c
index 9cc5d66e3..e74a1ade0 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -1401,6 +1401,12 @@ int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi
     for( n = B->n; n > 0; n-- )
         if( B->p[n - 1] != 0 )
             break;
+    if( n > A->n )
+    {
+        /* B >= (2^ciL)^n > A */
+        ret = MBEDTLS_ERR_MPI_NEGATIVE_VALUE;
+        goto cleanup;
+    }
 
     carry = mpi_sub_hlp( n, X->p, B->p );
     if( carry != 0 )
diff --git a/tests/suites/test_suite_mpi.data b/tests/suites/test_suite_mpi.data
index 0966393df..b5f68447f 100644
--- a/tests/suites/test_suite_mpi.data
+++ b/tests/suites/test_suite_mpi.data
@@ -484,18 +484,30 @@ mbedtls_mpi_add_int:10:"20395687835640197740576586692903457728019399331434826309
 Test mbedtls_mpi_add_int #2
 mbedtls_mpi_add_int:10:"2039568783564019774057658669290345772801939933143482630947726464532830627227012776329":-9871232:10:"2039568783564019774057658669290345772801939933143482630947726464532830627227002905097"
 
-Base test mbedtls_mpi_sub_abs #1 (Test with larger second input)
+Base test mbedtls_mpi_sub_abs #1 (|B| > |A|)
 mbedtls_mpi_sub_abs:10:"5":10:"7":10:"0":MBEDTLS_ERR_MPI_NEGATIVE_VALUE
 
-Base test mbedtls_mpi_sub_abs #2 (Test with larger second input)
+Base test mbedtls_mpi_sub_abs #2 (|B| > |A|)
 mbedtls_mpi_sub_abs:10:"-5":10:"-7":10:"0":MBEDTLS_ERR_MPI_NEGATIVE_VALUE
 
-Base test mbedtls_mpi_sub_abs #3 (Test with larger second input)
+Base test mbedtls_mpi_sub_abs #3 (|B| > |A|)
 mbedtls_mpi_sub_abs:10:"-5":10:"7":10:"0":MBEDTLS_ERR_MPI_NEGATIVE_VALUE
 
-Base test mbedtls_mpi_sub_abs #4 (Test with larger second input)
+Base test mbedtls_mpi_sub_abs #4 (|B| > |A|)
 mbedtls_mpi_sub_abs:10:"5":10:"-7":10:"0":MBEDTLS_ERR_MPI_NEGATIVE_VALUE
 
+Base test mbedtls_mpi_sub_abs #1 (|B| >> |A| with more limbs)
+mbedtls_mpi_sub_abs:10:"5":16:"123456789abcdef01":10:"0":MBEDTLS_ERR_MPI_NEGATIVE_VALUE
+
+Base test mbedtls_mpi_sub_abs #2 (|B| >> |A| with more limbs)
+mbedtls_mpi_sub_abs:10:"-5":16:"-123456789abcdef01":10:"0":MBEDTLS_ERR_MPI_NEGATIVE_VALUE
+
+Base test mbedtls_mpi_sub_abs #3 (|B| >> |A| with more limbs)
+mbedtls_mpi_sub_abs:10:"-5":16:"123456789abcdef01":10:"0":MBEDTLS_ERR_MPI_NEGATIVE_VALUE
+
+Base test mbedtls_mpi_sub_abs #4 (|B| >> |A| with more limbs)
+mbedtls_mpi_sub_abs:10:"5":16:"-123456789abcdef01":10:"0":MBEDTLS_ERR_MPI_NEGATIVE_VALUE
+
 Base test mbedtls_mpi_sub_abs #1
 mbedtls_mpi_sub_abs:10:"7":10:"5":10:"2":0