=head1 NAME
-BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init,
+BN_mod_mul_montgomery, BN_MONT_CTX_new,
BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy,
BN_from_montgomery, BN_to_montgomery - Montgomery multiplication
#include <openssl/bn.h>
BN_MONT_CTX *BN_MONT_CTX_new(void);
- void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
void BN_MONT_CTX_free(BN_MONT_CTX *mont);
int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
=head1 DESCRIPTION
These functions implement Montgomery multiplication. They are used
-automatically when BN_mod_exp(3) is called with suitable input,
+automatically when L<BN_mod_exp(3)> is called with suitable input,
but they may be useful when several operations are to be performed
using the same modulus.
BN_MONT_CTX_new() allocates and initializes a B<BN_MONT_CTX> structure.
-BN_MONT_CTX_init() initializes an existing uninitialized B<BN_MONT_CTX>.
-BN_MONT_CTX_set() sets up the B<mont> structure from the modulus B<m>
+BN_MONT_CTX_set() sets up the I<mont> structure from the modulus I<m>
by precomputing its inverse and a value R.
-BN_MONT_CTX_copy() copies the B<N_MONT_CTX> B<from> to B<to>.
+BN_MONT_CTX_copy() copies the B<BN_MONT_CTX> I<from> to I<to>.
BN_MONT_CTX_free() frees the components of the B<BN_MONT_CTX>, and, if
it was created by BN_MONT_CTX_new(), also the structure itself.
+If B<mont> is NULL, nothing is done.
-BN_mod_mul_montgomery() computes Mont(B<a>,B<b>):=B<a>*B<b>*R^-1 and places
-the result in B<r>.
+BN_mod_mul_montgomery() computes Mont(I<a>,I<b>):=I<a>*I<b>*R^-1 and places
+the result in I<r>.
-BN_from_montgomery() performs the Montgomery reduction B<r> = B<a>*R^-1.
+BN_from_montgomery() performs the Montgomery reduction I<r> = I<a>*R^-1.
-BN_to_montgomery() computes Mont(B<a>,R^2).
+BN_to_montgomery() computes Mont(I<a>,R^2), i.e. I<a>*R.
+Note that I<a> must be non-negative and smaller than the modulus.
-For all functions, B<ctx> is a previously allocated B<BN_CTX> used for
+For all functions, I<ctx> is a previously allocated B<BN_CTX> used for
temporary variables.
-The B<BN_MONT_CTX> structure is defined as follows:
-
- typedef struct bn_mont_ctx_st
- {
- int use_word; /* 0 for word form, 1 for bignum form */
- int ri; /* number of bits in R */
- BIGNUM RR; /* R^2 (used to convert to Montgomery form) */
- BIGNUM N; /* The modulus */
- BIGNUM Ni; /* The inverse of N (bignum form) */
- BN_ULONG n0; /* The inverse of N in word form */
- int flags;
- } BN_MONT_CTX;
-
-BN_to_montgomery() is a macro.
-
=head1 RETURN VALUES
BN_MONT_CTX_new() returns the newly allocated B<BN_MONT_CTX>, and NULL
on error.
-BN_MONT_CTX_init() and BN_MONT_CTX_free() have no return values.
+BN_MONT_CTX_free() has no return value.
For the other functions, 1 is returned for success, 0 on error.
-The error codes can be obtained by ERR_get_error(3).
+The error codes can be obtained by L<ERR_get_error(3)>.
+
+=head1 WARNING
+
+The inputs must be reduced modulo B<m>, otherwise the result will be
+outside the expected range.
=head1 SEE ALSO
-bn(3), err(3), BN_add(3), BN_CTX_new(3)
+L<bn(3)>, L<ERR_get_error(3)>, L<BN_add(3)>,
+L<BN_CTX_new(3)>
=head1 HISTORY
-BN_MONT_CTX_new(), BN_MONT_CTX_free(), BN_MONT_CTX_set(),
-BN_mod_mul_montgomery(), BN_from_montgomery() and BN_to_montgomery()
-are available in all versions of SSLeay and OpenSSL.
+BN_MONT_CTX_init() was removed in OpenSSL 1.1.0
+
+=head1 COPYRIGHT
+
+Copyright 2000-2016 The OpenSSL Project Authors. All Rights Reserved.
-BN_MONT_CTX_init() and BN_MONT_CTX_copy() were added in SSLeay 0.9.1b.
+Licensed under the OpenSSL license (the "License"). You may not use
+this file except in compliance with the License. You can obtain a copy
+in the file LICENSE in the source distribution or at
+L<https://www.openssl.org/source/license.html>.
=cut