Initial Commit

openssl-1.0.2f/doc/crypto/BN_mod_mul_montgomery.pod

@@ -0,0 +1,101 @@
+=pod
+
+=head1 NAME
+
+BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init,
+BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy,
+BN_from_montgomery, BN_to_montgomery - Montgomery multiplication
+
+=head1 SYNOPSIS
+
+ #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);
+ BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
+
+ int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
+         BN_MONT_CTX *mont, BN_CTX *ctx);
+
+ int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
+         BN_CTX *ctx);
+
+ int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
+         BN_CTX *ctx);
+
+=head1 DESCRIPTION
+
+These functions implement Montgomery multiplication. They are used
+automatically when L<BN_mod_exp(3)|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 I<mont> structure from the modulus I<m>
+by precomputing its inverse and a value R.
+
+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.
+
+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 I<r> = I<a>*R^-1.
+
+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, 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 ri;         /* number of bits in R */
+        BIGNUM RR;      /* R^2 (used to convert to Montgomery form) */
+        BIGNUM N;       /* The modulus */
+        BIGNUM Ni;      /* R*(1/R mod N) - N*Ni = 1
+                         * (Ni is only stored for bignum algorithm) */
+        BN_ULONG n0;    /* least significant word of Ni */
+        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.
+
+For the other functions, 1 is returned for success, 0 on error.
+The error codes can be obtained by L<ERR_get_error(3)|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
+
+L<bn(3)|bn(3)>, L<ERR_get_error(3)|ERR_get_error(3)>, L<BN_add(3)|BN_add(3)>,
+L<BN_CTX_new(3)|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() and BN_MONT_CTX_copy() were added in SSLeay 0.9.1b.
+
+=cut