1=pod 2 3=head1 NAME 4 5BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init, 6BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy, 7BN_from_montgomery, BN_to_montgomery - Montgomery multiplication 8 9=head1 SYNOPSIS 10 11 #include <openssl/bn.h> 12 13 BN_MONT_CTX *BN_MONT_CTX_new(void); 14 void BN_MONT_CTX_init(BN_MONT_CTX *ctx); 15 void BN_MONT_CTX_free(BN_MONT_CTX *mont); 16 17 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx); 18 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from); 19 20 int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b, 21 BN_MONT_CTX *mont, BN_CTX *ctx); 22 23 int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont, 24 BN_CTX *ctx); 25 26 int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont, 27 BN_CTX *ctx); 28 29=head1 DESCRIPTION 30 31These functions implement Montgomery multiplication. They are used 32automatically when L<BN_mod_exp(3)|BN_mod_exp(3)> is called with suitable input, 33but they may be useful when several operations are to be performed 34using the same modulus. 35 36BN_MONT_CTX_new() allocates and initializes a B<BN_MONT_CTX> structure. 37BN_MONT_CTX_init() initializes an existing uninitialized B<BN_MONT_CTX>. 38 39BN_MONT_CTX_set() sets up the I<mont> structure from the modulus I<m> 40by precomputing its inverse and a value R. 41 42BN_MONT_CTX_copy() copies the B<BN_MONT_CTX> I<from> to I<to>. 43 44BN_MONT_CTX_free() frees the components of the B<BN_MONT_CTX>, and, if 45it was created by BN_MONT_CTX_new(), also the structure itself. 46 47BN_mod_mul_montgomery() computes Mont(I<a>,I<b>):=I<a>*I<b>*R^-1 and places 48the result in I<r>. 49 50BN_from_montgomery() performs the Montgomery reduction I<r> = I<a>*R^-1. 51 52BN_to_montgomery() computes Mont(I<a>,R^2), i.e. I<a>*R. 53Note that I<a> must be non-negative and smaller than the modulus. 54 55For all functions, I<ctx> is a previously allocated B<BN_CTX> used for 56temporary variables. 57 58The B<BN_MONT_CTX> structure is defined as follows: 59 60 typedef struct bn_mont_ctx_st 61 { 62 int ri; /* number of bits in R */ 63 BIGNUM RR; /* R^2 (used to convert to Montgomery form) */ 64 BIGNUM N; /* The modulus */ 65 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1 66 * (Ni is only stored for bignum algorithm) */ 67 BN_ULONG n0; /* least significant word of Ni */ 68 int flags; 69 } BN_MONT_CTX; 70 71BN_to_montgomery() is a macro. 72 73=head1 RETURN VALUES 74 75BN_MONT_CTX_new() returns the newly allocated B<BN_MONT_CTX>, and NULL 76on error. 77 78BN_MONT_CTX_init() and BN_MONT_CTX_free() have no return values. 79 80For the other functions, 1 is returned for success, 0 on error. 81The error codes can be obtained by L<ERR_get_error(3)|ERR_get_error(3)>. 82 83=head1 WARNING 84 85The inputs must be reduced modulo B<m>, otherwise the result will be 86outside the expected range. 87 88=head1 SEE ALSO 89 90L<bn(3)|bn(3)>, L<ERR_get_error(3)|ERR_get_error(3)>, L<BN_add(3)|BN_add(3)>, 91L<BN_CTX_new(3)|BN_CTX_new(3)> 92 93=head1 HISTORY 94 95BN_MONT_CTX_new(), BN_MONT_CTX_free(), BN_MONT_CTX_set(), 96BN_mod_mul_montgomery(), BN_from_montgomery() and BN_to_montgomery() 97are available in all versions of SSLeay and OpenSSL. 98 99BN_MONT_CTX_init() and BN_MONT_CTX_copy() were added in SSLeay 0.9.1b. 100 101=cut 102