diff --git a/ChangeLog.d/fix-rsa-blinding.txt b/ChangeLog.d/fix-rsa-blinding.txt
new file mode 100644
index 000000000..a13572c9a
--- /dev/null
+++ b/ChangeLog.d/fix-rsa-blinding.txt
@@ -0,0 +1,6 @@
+Bugfix
+   * Fix rsa_prepare_blinding() to retry when the blinding value is not
+     invertible (mod N), instead of returning MBEDTLS_ERR_RSA_RNG_FAILED. This
+     addresses a regression but is rare in practice (approx. 1 in 2/sqrt(N)).
+     Found by Synopsys Coverity, fix contributed by Peter Kolbus (Garmin).
+     Fixes #3647.
diff --git a/library/rsa.c b/library/rsa.c
index 84d87de0d..d6abd65d4 100644
--- a/library/rsa.c
+++ b/library/rsa.c
@@ -811,15 +811,14 @@ static int rsa_prepare_blinding( mbedtls_rsa_context *ctx,
          * which one, we just loop and choose new values for both of them.
          * (Each iteration succeeds with overwhelming probability.) */
         ret = mbedtls_mpi_inv_mod( &ctx->Vi, &ctx->Vi, &ctx->N );
-        if( ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
-            continue;
-        if( ret != 0 )
+        if( ret != 0 && ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
             goto cleanup;
 
-        /* Finish the computation of Vf^-1 = R * (R Vf)^-1 */
-        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ctx->Vi, &ctx->Vi, &R ) );
-        MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &ctx->Vi, &ctx->Vi, &ctx->N ) );
-    } while( 0 );
+    } while( ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
+
+    /* Finish the computation of Vf^-1 = R * (R Vf)^-1 */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ctx->Vi, &ctx->Vi, &R ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &ctx->Vi, &ctx->Vi, &ctx->N ) );
 
     /* Blinding value: Vi = Vf^(-e) mod N
      * (Vi already contains Vf^-1 at this point) */