diff --git a/crypto/bn/exponentiation.c b/crypto/bn/exponentiation.c
index a24bb2e..c580248 100644
--- a/crypto/bn/exponentiation.c
+++ b/crypto/bn/exponentiation.c
@@ -613,17 +613,17 @@
 }
 
 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
-                    const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) {
+                    const BIGNUM *m, BN_CTX *ctx, const BN_MONT_CTX *mont) {
   int i, j, bits, ret = 0, wstart, window;
   int start = 1;
   BIGNUM *d, *r;
   const BIGNUM *aa;
   /* Table of variables obtained from 'ctx' */
   BIGNUM *val[TABLE_SIZE];
-  BN_MONT_CTX *mont = NULL;
+  BN_MONT_CTX *new_mont = NULL;
 
   if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
-    return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
+    return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, mont);
   }
 
   if (!BN_is_odd(m)) {
@@ -644,18 +644,13 @@
     goto err;
   }
 
-  /* If this is not done, things will break in the montgomery part */
-
-  if (in_mont != NULL) {
-    mont = in_mont;
-  } else {
-    mont = BN_MONT_CTX_new();
-    if (mont == NULL) {
+  /* Allocate a montgomery context if it was not supplied by the caller. */
+  if (mont == NULL) {
+    new_mont = BN_MONT_CTX_new();
+    if (new_mont == NULL || !BN_MONT_CTX_set(new_mont, m, ctx)) {
       goto err;
     }
-    if (!BN_MONT_CTX_set(mont, m, ctx)) {
-      goto err;
-    }
+    mont = new_mont;
   }
 
   if (a->neg || BN_ucmp(a, m) >= 0) {
@@ -774,9 +769,7 @@
   ret = 1;
 
 err:
-  if (in_mont == NULL) {
-    BN_MONT_CTX_free(mont);
-  }
+  BN_MONT_CTX_free(new_mont);
   BN_CTX_end(ctx);
   return ret;
 }
@@ -1198,8 +1191,9 @@
 }
 
 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
-                         const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) {
-  BN_MONT_CTX *mont = NULL;
+                         const BIGNUM *m, BN_CTX *ctx,
+                         const BN_MONT_CTX *mont) {
+  BN_MONT_CTX *new_mont = NULL;
   int b, bits, ret = 0;
   int r_is_one;
   BN_ULONG w, next_w;
@@ -1257,13 +1251,13 @@
     goto err;
   }
 
-  if (in_mont != NULL) {
-    mont = in_mont;
-  } else {
-    mont = BN_MONT_CTX_new();
-    if (mont == NULL || !BN_MONT_CTX_set(mont, m, ctx)) {
+  /* Allocate a montgomery context if it was not supplied by the caller. */
+  if (mont == NULL) {
+    new_mont = BN_MONT_CTX_new();
+    if (new_mont == NULL || !BN_MONT_CTX_set(new_mont, m, ctx)) {
       goto err;
     }
+    mont = new_mont;
   }
 
   r_is_one = 1; /* except for Montgomery factor */
@@ -1345,9 +1339,7 @@
   ret = 1;
 
 err:
-  if (in_mont == NULL) {
-    BN_MONT_CTX_free(mont);
-  }
+  BN_MONT_CTX_free(new_mont);
   BN_CTX_end(ctx);
   return ret;
 }
@@ -1356,7 +1348,7 @@
 
 int BN_mod_exp2_mont(BIGNUM *rr, const BIGNUM *a1, const BIGNUM *p1,
                      const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
-                     BN_CTX *ctx, BN_MONT_CTX *in_mont) {
+                     BN_CTX *ctx, const BN_MONT_CTX *mont) {
   int i, j, bits, b, bits1, bits2, ret = 0, wpos1, wpos2, window1, window2,
                                    wvalue1, wvalue2;
   int r_is_one = 1;
@@ -1364,7 +1356,7 @@
   const BIGNUM *a_mod_m;
   /* Tables of variables obtained from 'ctx' */
   BIGNUM *val1[TABLE_SIZE], *val2[TABLE_SIZE];
-  BN_MONT_CTX *mont = NULL;
+  BN_MONT_CTX *new_mont = NULL;
 
   if (!(m->d[0] & 1)) {
     OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);
@@ -1388,16 +1380,13 @@
     goto err;
   }
 
-  if (in_mont != NULL) {
-    mont = in_mont;
-  } else {
-    mont = BN_MONT_CTX_new();
-    if (mont == NULL) {
+  /* Allocate a montgomery context if it was not supplied by the caller. */
+  if (mont == NULL) {
+    new_mont = BN_MONT_CTX_new();
+    if (new_mont == NULL || !BN_MONT_CTX_set(new_mont, m, ctx)) {
       goto err;
     }
-    if (!BN_MONT_CTX_set(mont, m, ctx)) {
-      goto err;
-    }
+    mont = new_mont;
   }
 
   window1 = BN_window_bits_for_exponent_size(bits1);
@@ -1549,9 +1538,7 @@
   ret = 1;
 
 err:
-  if (in_mont == NULL) {
-    BN_MONT_CTX_free(mont);
-  }
+  BN_MONT_CTX_free(new_mont);
   BN_CTX_end(ctx);
   return ret;
 }
diff --git a/crypto/bn/montgomery.c b/crypto/bn/montgomery.c
index 3fec7e3..db673a1 100644
--- a/crypto/bn/montgomery.c
+++ b/crypto/bn/montgomery.c
@@ -149,7 +149,7 @@
   OPENSSL_free(mont);
 }
 
-BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from) {
+BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, const BN_MONT_CTX *from) {
   if (to == from) {
     return to;
   }
diff --git a/crypto/rsa/blinding.c b/crypto/rsa/blinding.c
index b6a06c8..d21633f 100644
--- a/crypto/rsa/blinding.c
+++ b/crypto/rsa/blinding.c
@@ -127,9 +127,11 @@
   BIGNUM *mod; /* just a reference */
   int counter;
   unsigned long flags;
-  BN_MONT_CTX *m_ctx;
+  /* mont is the Montgomery context used for this |BN_BLINDING|. It is not
+   * owned and must outlive this structure. */
+  const BN_MONT_CTX *mont;
   int (*bn_mod_exp)(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
-                    const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
+                    const BIGNUM *m, BN_CTX *ctx, const BN_MONT_CTX *mont);
 };
 
 BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, BIGNUM *mod) {
@@ -284,8 +286,8 @@
 BN_BLINDING *BN_BLINDING_create_param(
     BN_BLINDING *b, const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
     int (*bn_mod_exp)(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
-                      const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx),
-    BN_MONT_CTX *m_ctx) {
+                      const BIGNUM *m, BN_CTX *ctx, const BN_MONT_CTX *mont),
+    const BN_MONT_CTX *mont) {
   int retry_counter = 32;
   BN_BLINDING *ret = NULL;
 
@@ -317,8 +319,8 @@
   if (bn_mod_exp != NULL) {
     ret->bn_mod_exp = bn_mod_exp;
   }
-  if (m_ctx != NULL) {
-    ret->m_ctx = m_ctx;
+  if (mont != NULL) {
+    ret->mont = mont;
   }
 
   do {
@@ -343,8 +345,8 @@
     }
   } while (1);
 
-  if (ret->bn_mod_exp != NULL && ret->m_ctx != NULL) {
-    if (!ret->bn_mod_exp(ret->A, ret->A, ret->e, ret->mod, ctx, ret->m_ctx)) {
+  if (ret->bn_mod_exp != NULL && ret->mont != NULL) {
+    if (!ret->bn_mod_exp(ret->A, ret->A, ret->e, ret->mod, ctx, ret->mont)) {
       goto err;
     }
   } else {
diff --git a/crypto/rsa/internal.h b/crypto/rsa/internal.h
index 24eab90..4e896e2 100644
--- a/crypto/rsa/internal.h
+++ b/crypto/rsa/internal.h
@@ -106,8 +106,8 @@
 BN_BLINDING *BN_BLINDING_create_param(
     BN_BLINDING *b, const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
     int (*bn_mod_exp)(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
-                      const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx),
-    BN_MONT_CTX *m_ctx);
+                      const BIGNUM *m, BN_CTX *ctx, const BN_MONT_CTX *mont),
+    const BN_MONT_CTX *mont);
 BN_BLINDING *rsa_setup_blinding(RSA *rsa, BN_CTX *in_ctx);
 
 
diff --git a/include/openssl/bn.h b/include/openssl/bn.h
index 1a3958f..01115c8 100644
--- a/include/openssl/bn.h
+++ b/include/openssl/bn.h
@@ -737,7 +737,7 @@
 /* BN_MONT_CTX_copy sets |to| equal to |from|. It returns |to| on success or
  * NULL on error. */
 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,
-                                             BN_MONT_CTX *from);
+                                             const BN_MONT_CTX *from);
 
 /* BN_MONT_CTX_set sets up a Montgomery context given the modulus, |mod|. It
  * returns one on success and zero on error. */
@@ -787,7 +787,7 @@
 
 OPENSSL_EXPORT int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
                                    const BIGNUM *m, BN_CTX *ctx,
-                                   BN_MONT_CTX *m_ctx);
+                                   const BN_MONT_CTX *mont);
 
 OPENSSL_EXPORT int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a,
                                              const BIGNUM *p, const BIGNUM *m,
@@ -796,11 +796,11 @@
 
 OPENSSL_EXPORT int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
                                         const BIGNUM *m, BN_CTX *ctx,
-                                        BN_MONT_CTX *m_ctx);
+                                        const BN_MONT_CTX *mont);
 OPENSSL_EXPORT int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1,
                                     const BIGNUM *p1, const BIGNUM *a2,
                                     const BIGNUM *p2, const BIGNUM *m,
-                                    BN_CTX *ctx, BN_MONT_CTX *m_ctx);
+                                    BN_CTX *ctx, const BN_MONT_CTX *mont);
 
 
 /* Deprecated functions */
diff --git a/include/openssl/rsa.h b/include/openssl/rsa.h
index c970751..e624f7c 100644
--- a/include/openssl/rsa.h
+++ b/include/openssl/rsa.h
@@ -525,7 +525,7 @@
                  BN_CTX *ctx); /* Can be null */
   int (*bn_mod_exp)(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
                     const BIGNUM *m, BN_CTX *ctx,
-                    BN_MONT_CTX *m_ctx);
+                    const BN_MONT_CTX *mont);
 
   int flags;