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102 lines
3.1 KiB
Plaintext
102 lines
3.1 KiB
Plaintext
=pod
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=head1 NAME
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BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init,
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BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy,
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BN_from_montgomery, BN_to_montgomery - Montgomery multiplication
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=head1 SYNOPSIS
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#include <openssl/bn.h>
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BN_MONT_CTX *BN_MONT_CTX_new(void);
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void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
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void BN_MONT_CTX_free(BN_MONT_CTX *mont);
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int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
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BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
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int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
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BN_MONT_CTX *mont, BN_CTX *ctx);
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int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
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BN_CTX *ctx);
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int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
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BN_CTX *ctx);
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=head1 DESCRIPTION
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These functions implement Montgomery multiplication. They are used
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automatically when L<BN_mod_exp(3)|BN_mod_exp(3)> is called with suitable input,
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but they may be useful when several operations are to be performed
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using the same modulus.
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BN_MONT_CTX_new() allocates and initializes a B<BN_MONT_CTX> structure.
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BN_MONT_CTX_init() initializes an existing uninitialized B<BN_MONT_CTX>.
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BN_MONT_CTX_set() sets up the I<mont> structure from the modulus I<m>
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by precomputing its inverse and a value R.
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BN_MONT_CTX_copy() copies the B<BN_MONT_CTX> I<from> to I<to>.
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BN_MONT_CTX_free() frees the components of the B<BN_MONT_CTX>, and, if
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it was created by BN_MONT_CTX_new(), also the structure itself.
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BN_mod_mul_montgomery() computes Mont(I<a>,I<b>):=I<a>*I<b>*R^-1 and places
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the result in I<r>.
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BN_from_montgomery() performs the Montgomery reduction I<r> = I<a>*R^-1.
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BN_to_montgomery() computes Mont(I<a>,R^2), i.e. I<a>*R.
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Note that I<a> must be non-negative and smaller than the modulus.
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For all functions, I<ctx> is a previously allocated B<BN_CTX> used for
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temporary variables.
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The B<BN_MONT_CTX> structure is defined as follows:
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typedef struct bn_mont_ctx_st
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{
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int ri; /* number of bits in R */
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BIGNUM RR; /* R^2 (used to convert to Montgomery form) */
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BIGNUM N; /* The modulus */
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BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
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* (Ni is only stored for bignum algorithm) */
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BN_ULONG n0; /* least significant word of Ni */
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int flags;
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} BN_MONT_CTX;
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BN_to_montgomery() is a macro.
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=head1 RETURN VALUES
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BN_MONT_CTX_new() returns the newly allocated B<BN_MONT_CTX>, and NULL
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on error.
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BN_MONT_CTX_init() and BN_MONT_CTX_free() have no return values.
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For the other functions, 1 is returned for success, 0 on error.
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The error codes can be obtained by L<ERR_get_error(3)|ERR_get_error(3)>.
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=head1 WARNING
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The inputs must be reduced modulo B<m>, otherwise the result will be
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outside the expected range.
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=head1 SEE ALSO
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L<bn(3)|bn(3)>, L<err(3)|err(3)>, L<BN_add(3)|BN_add(3)>,
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L<BN_CTX_new(3)|BN_CTX_new(3)>
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=head1 HISTORY
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BN_MONT_CTX_new(), BN_MONT_CTX_free(), BN_MONT_CTX_set(),
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BN_mod_mul_montgomery(), BN_from_montgomery() and BN_to_montgomery()
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are available in all versions of SSLeay and OpenSSL.
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BN_MONT_CTX_init() and BN_MONT_CTX_copy() were added in SSLeay 0.9.1b.
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=cut
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