diff --git a/ChangeLog b/ChangeLog
index 08edd77..0cf927e 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -24,6 +24,10 @@
      to not annihilate fatal errors in authentication mode
      MBEDTLS_SSL_VERIFY_OPTIONAL and to reflect bad EC curves
      within verification result.
+   * Fix modular inversion function on invalid modulus 1.
+     Found by blaufish. Fixes #641.
+   * Fix incorrect sign computation in modular exponentiation
+     when dealing with negative MPI. Found by Guido Vranken.
 
 Changes
    * Send fatal alerts in many more cases instead of dropping the connection.
diff --git a/include/mbedtls/bignum.h b/include/mbedtls/bignum.h
index aa51556..a713313 100644
--- a/include/mbedtls/bignum.h
+++ b/include/mbedtls/bignum.h
@@ -665,8 +665,8 @@
  *
  * \return         0 if successful,
  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
- *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is negative or nil
-                   MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N
+ *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is <= 1,
+                   MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N.
  */
 int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N );
 
diff --git a/library/bignum.c b/library/bignum.c
index 8b9082c..8df2510 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -1790,7 +1790,7 @@
      */
     MBEDTLS_MPI_CHK( mpi_montred( X, N, mm, &T ) );
 
-    if( neg )
+    if( neg && E->n != 0 && ( E->p[0] & 1 ) != 0 )
     {
         X->s = -1;
         MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, N, X ) );
@@ -1893,7 +1893,7 @@
     int ret;
     mbedtls_mpi G, TA, TU, U1, U2, TB, TV, V1, V2;
 
-    if( mbedtls_mpi_cmp_int( N, 0 ) <= 0 )
+    if( mbedtls_mpi_cmp_int( N, 1 ) <= 0 )
         return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
 
     mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TU ); mbedtls_mpi_init( &U1 ); mbedtls_mpi_init( &U2 );
diff --git a/tests/suites/test_suite_mpi.data b/tests/suites/test_suite_mpi.data
index da830fe..17cf350 100644
--- a/tests/suites/test_suite_mpi.data
+++ b/tests/suites/test_suite_mpi.data
@@ -521,7 +521,7 @@
 mbedtls_mpi_exp_mod:10:"433019240910377478217373572959560109819648647016096560523769010881172869083338285573756574557395862965095016483867813043663981946477698466501451832407592327356331263124555137732393938242285782144928753919588632679050799198937132922145084847":10:"5781538327977828897150909166778407659250458379645823062042492461576758526757490910073628008613977550546382774775570888130029763571528699574717583228939535960234464230882573615930384979100379102915657483866755371559811718767760594919456971354184113721":10:"583137007797276923956891216216022144052044091311388601652961409557516421612874571554415606746479105795833145583959622117418531166391184939066520869800857530421873250114773204354963864729386957427276448683092491947566992077136553066273207777134303397724679138833126700957":10:"":10:"114597449276684355144920670007147953232659436380163461553186940113929777196018164149703566472936578890991049344459204199888254907113495794730452699842273939581048142004834330369483813876618772578869083248061616444392091693787039636316845512292127097865026290173004860736":0
 
 Test mbedtls_mpi_exp_mod (Negative base)
-mbedtls_mpi_exp_mod:10:"-10000000000":10:"10000000000":10:"99999":10:"":10:"99998":0
+mbedtls_mpi_exp_mod:10:"-10000000000":10:"10000000000":10:"99999":10:"":10:"1":0
 
 Test mbedtls_mpi_exp_mod (Negative base)
 mbedtls_mpi_exp_mod:16:"-9f13012cd92aa72fb86ac8879d2fde4f7fd661aaae43a00971f081cc60ca277059d5c37e89652e2af2585d281d66ef6a9d38a117e9608e9e7574cd142dc55278838a2161dd56db9470d4c1da2d5df15a908ee2eb886aaa890f23be16de59386663a12f1afbb325431a3e835e3fd89b98b96a6f77382f458ef9a37e1f84a03045c8676ab55291a94c2228ea15448ee96b626b998":16:"40a54d1b9e86789f06d9607fb158672d64867665c73ee9abb545fc7a785634b354c7bae5b962ce8040cf45f2c1f3d3659b2ee5ede17534c8fc2ec85c815e8df1fe7048d12c90ee31b88a68a081f17f0d8ce5f4030521e9400083bcea73a429031d4ca7949c2000d597088e0c39a6014d8bf962b73bb2e8083bd0390a4e00b9b3":16:"eeaf0ab9adb38dd69c33f80afa8fc5e86072618775ff3c0b9ea2314c9c256576d674df7496ea81d3383b4813d692c6e0e0d5d8e250b98be48e495c1d6089dad15dc7d7b46154d6b6ce8ef4ad69b15d4982559b297bcf1885c529f566660e57ec68edbc3c05726cc02fd4cbf4976eaa9afd5138fe8376435b9fc61d2fc0eb06e3":16:"":16:"21acc7199e1b90f9b4844ffe12c19f00ec548c5d32b21c647d48b6015d8eb9ec9db05b4f3d44db4227a2b5659c1a7cceb9d5fa8fa60376047953ce7397d90aaeb7465e14e820734f84aa52ad0fc66701bcbb991d57715806a11531268e1e83dd48288c72b424a6287e9ce4e5cc4db0dd67614aecc23b0124a5776d36e5c89483":0
@@ -550,6 +550,9 @@
 Base test mbedtls_mpi_inv_mod #4
 mbedtls_mpi_inv_mod:10:"2":10:"4":10:"0":MBEDTLS_ERR_MPI_NOT_ACCEPTABLE
 
+Base test mbedtls_mpi_inv_mod #5
+mbedtls_mpi_inv_mod:10:"3":10:"1":10:"0":MBEDTLS_ERR_MPI_BAD_INPUT_DATA
+
 Test mbedtls_mpi_inv_mod #1
 mbedtls_mpi_inv_mod:16:"aa4df5cb14b4c31237f98bd1faf527c283c2d0f3eec89718664ba33f9762907c":16:"fffbbd660b94412ae61ead9c2906a344116e316a256fd387874c6c675b1d587d":16:"8d6a5c1d7adeae3e94b9bcd2c47e0d46e778bc8804a2cc25c02d775dc3d05b0c":0