.\" $OpenBSD: bn_dump.3,v 1.6 2016/12/10 21:32:14 schwarze Exp $ .\" OpenSSL crypto/bn/README.pod aebb9aac Jul 19 09:27:53 2016 -0400 .\" .\" This file was written by Ulf Moeller . .\" Copyright (c) 2000, 2003, 2006, 2009 The OpenSSL Project. .\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions .\" are met: .\" .\" 1. Redistributions of source code must retain the above copyright .\" notice, this list of conditions and the following disclaimer. .\" .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in .\" the documentation and/or other materials provided with the .\" distribution. .\" .\" 3. All advertising materials mentioning features or use of this .\" software must display the following acknowledgment: .\" "This product includes software developed by the OpenSSL Project .\" for use in the OpenSSL Toolkit. (http://www.openssl.org/)" .\" .\" 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to .\" endorse or promote products derived from this software without .\" prior written permission. For written permission, please contact .\" openssl-core@openssl.org. .\" .\" 5. Products derived from this software may not be called "OpenSSL" .\" nor may "OpenSSL" appear in their names without prior written .\" permission of the OpenSSL Project. .\" .\" 6. Redistributions of any form whatsoever must retain the following .\" acknowledgment: .\" "This product includes software developed by the OpenSSL Project .\" for use in the OpenSSL Toolkit (http://www.openssl.org/)" .\" .\" THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY .\" EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE .\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR .\" PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR .\" ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, .\" SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT .\" NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; .\" LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) .\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, .\" STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) .\" ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED .\" OF THE POSSIBILITY OF SUCH DAMAGE. .\" .Dd $Mdocdate: December 10 2016 $ .Dt BN_DUMP 3 .Os .Sh NAME .Nm bn_mul_words , .Nm bn_mul_add_words , .Nm bn_sqr_words , .Nm bn_div_words , .Nm bn_add_words , .Nm bn_sub_words , .Nm bn_mul_comba4 , .Nm bn_mul_comba8 , .Nm bn_sqr_comba4 , .Nm bn_sqr_comba8 , .Nm bn_cmp_words , .Nm bn_mul_normal , .Nm bn_mul_low_normal , .Nm bn_mul_recursive , .Nm bn_mul_part_recursive , .Nm bn_mul_low_recursive , .Nm bn_mul_high , .Nm bn_sqr_normal , .Nm bn_sqr_recursive , .Nm bn_expand , .Nm bn_wexpand , .Nm bn_expand2 , .Nm bn_fix_top , .Nm bn_check_top , .Nm bn_print , .Nm bn_dump , .Nm bn_set_max , .Nm bn_set_high , .Nm bn_set_low , .Nm mul , .Nm mul_add , .Nm sqr .Nd BIGNUM library internal functions .Sh SYNOPSIS .In openssl/bn.h .Ft BN_ULONG .Fo bn_mul_words .Fa "BN_ULONG *rp" .Fa "BN_ULONG *ap" .Fa "int num" .Fa "BN_ULONG w" .Fc .Ft BN_ULONG .Fo bn_mul_add_words .Fa "BN_ULONG *rp" .Fa "BN_ULONG *ap" .Fa "int num" .Fa "BN_ULONG w" .Fc .Ft void .Fo bn_sqr_words .Fa "BN_ULONG *rp" .Fa "BN_ULONG *ap" .Fa "int num" .Fc .Ft BN_ULONG .Fo bn_div_words .Fa "BN_ULONG h" .Fa "BN_ULONG l" .Fa "BN_ULONG d" .Fc .Ft BN_ULONG .Fo bn_add_words .Fa "BN_ULONG *rp" .Fa "BN_ULONG *ap" .Fa "BN_ULONG *bp" .Fa "int num" .Fc .Ft BN_ULONG .Fo bn_sub_words .Fa "BN_ULONG *rp" .Fa "BN_ULONG *ap" .Fa "BN_ULONG *bp" .Fa "int num" .Fc .Ft void .Fo bn_mul_comba4 .Fa "BN_ULONG *r" .Fa "BN_ULONG *a" .Fa "BN_ULONG *b" .Fc .Ft void .Fo bn_mul_comba8 .Fa "BN_ULONG *r" .Fa "BN_ULONG *a" .Fa "BN_ULONG *b" .Fc .Ft void .Fo bn_sqr_comba4 .Fa "BN_ULONG *r" .Fa "BN_ULONG *a" .Fc .Ft void .Fo bn_sqr_comba8 .Fa "BN_ULONG *r" .Fa "BN_ULONG *a" .Fc .Ft int .Fo bn_cmp_words .Fa "BN_ULONG *a" .Fa "BN_ULONG *b" .Fa "int n" .Fc .Ft void .Fo bn_mul_normal .Fa "BN_ULONG *r" .Fa "BN_ULONG *a" .Fa "int na" .Fa "BN_ULONG *b" .Fa "int nb" .Fc .Ft void .Fo bn_mul_low_normal .Fa "BN_ULONG *r" .Fa "BN_ULONG *a" .Fa "BN_ULONG *b" .Fa "int n" .Fc .Ft void .Fo bn_mul_recursive .Fa "BN_ULONG *r" .Fa "BN_ULONG *a" .Fa "BN_ULONG *b" .Fa "int n2" .Fa "int dna" .Fa "int dnb" .Fa "BN_ULONG *tmp" .Fc .Ft void .Fo bn_mul_part_recursive .Fa "BN_ULONG *r" .Fa "BN_ULONG *a" .Fa "BN_ULONG *b" .Fa "int n" .Fa "int tna" .Fa "int tnb" .Fa "BN_ULONG *tmp" .Fc .Ft void .Fo bn_mul_low_recursive .Fa "BN_ULONG *r" .Fa "BN_ULONG *a" .Fa "BN_ULONG *b" .Fa "int n2" .Fa "BN_ULONG *tmp" .Fc .Ft void .Fo bn_mul_high .Fa "BN_ULONG *r" .Fa "BN_ULONG *a" .Fa "BN_ULONG *b" .Fa "BN_ULONG *l" .Fa "int n2" .Fa "BN_ULONG *tmp" .Fc .Ft void .Fo bn_sqr_normal .Fa "BN_ULONG *r" .Fa "BN_ULONG *a" .Fa "int n" .Fa "BN_ULONG *tmp" .Fc .Ft void .Fo bn_sqr_recursive .Fa "BN_ULONG *r" .Fa "BN_ULONG *a" .Fa "int n2" .Fa "BN_ULONG *tmp" .Fc .Ft void .Fo mul .Fa "BN_ULONG r" .Fa "BN_ULONG a" .Fa "BN_ULONG w" .Fa "BN_ULONG c" .Fc .Ft void .Fo mul_add .Fa "BN_ULONG r" .Fa "BN_ULONG a" .Fa "BN_ULONG w" .Fa "BN_ULONG c" .Fc .Ft void .Fo sqr .Fa "BN_ULONG r0" .Fa "BN_ULONG r1" .Fa "BN_ULONG a" .Fc .Ft BIGNUM * .Fo bn_expand .Fa "BIGNUM *a" .Fa "int bits" .Fc .Ft BIGNUM * .Fo bn_wexpand .Fa "BIGNUM *a" .Fa "int n" .Fc .Ft BIGNUM * .Fo bn_expand2 .Fa "BIGNUM *a" .Fa "int n" .Fc .Ft void .Fo bn_fix_top .Fa "BIGNUM *a" .Fc .Ft void .Fo bn_check_top .Fa "BIGNUM *a" .Fc .Ft void .Fo bn_print .Fa "BIGNUM *a" .Fc .Ft void .Fo bn_dump .Fa "BN_ULONG *d" .Fa "int n" .Fc .Ft void .Fo bn_set_max .Fa "BIGNUM *a" .Fc .Ft void .Fo bn_set_high .Fa "BIGNUM *r" .Fa "BIGNUM *a" .Fa "int n" .Fc .Ft void .Fo bn_set_low .Fa "BIGNUM *r" .Fa "BIGNUM *a" .Fa "int n" .Fc .Sh DESCRIPTION This page documents the internal functions used by the OpenSSL .Vt BIGNUM implementation. They are described here to facilitate debugging and extending the library. They are .Em not to be used by applications. .Ss The BIGNUM structure .Bd -literal typedef struct bignum_st BIGNUM; struct bignum_st { BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */ int top; /* Index of last used d +1. */ /* The next are internal book keeping for bn_expand. */ int dmax; /* Size of the d array. */ int neg; /* one if the number is negative */ int flags; }; .Ed .Pp The integer value is stored in .Fa d , a .Xr malloc 3 Ap ed array of words .Pq Vt BN_ULONG , least significant word first. A .Vt BN_ULONG can be either 16, 32 or 64 bits in size, depending on the 'number of bits' .Pq Dv BITS2 specified in .In openssl/bn.h . .Pp .Fa dmax is the size of the .Fa d array that has been allocated. .Fa top is the number of words being used, so for a value of 4, bn.d[0]=4 and bn.top=1. .Fa neg is 1 if the number is negative. When a .Vt BIGNUM is 0, the .Fa d field can be .Dv NULL and .Fa top == 0. .Pp .Fa flags is a bit field of flags which are defined in .In openssl/bn.h . The flags begin with .Dv BN_FLG_ . The macros .Fn BN_set_flags b n and .Fn BN_get_flags b n exist to enable or fetch flag(s) .Fa n from a .Vt BIGNUM structure .Fa b . .Pp Various routines in this library require the use of temporary .Vt BIGNUM variables during their execution. Since dynamic memory allocation to create .Vt BIGNUM Ns s is rather expensive when used in conjunction with repeated subroutine calls, the .Vt BN_CTX structure is used. This structure contains BN_CTX_NUM .Vt BIGNUM Ns s ; see .Xr BN_CTX_start 3 . .Ss Low level arithmetic operations These functions are implemented in C and for several platforms in assembly language: .Pp .Fn bn_mul_words rp ap num w operates on the .Fa num word arrays .Fa rp and .Fa ap . It computes .Fa ap * .Fa w , places the result in .Fa rp , and returns the high word (carry). .Pp .Fn bn_mul_add_words rp ap num w operates on the .Fa num word arrays .Fa rp and .Fa ap . It computes .Fa ap * .Fa w + .Fa rp , places the result in .Fa rp , and returns the high word (carry). .Pp .Fn bn_sqr_words rp ap num operates on the .Fa num word array .Fa ap and the .Pf 2* Fa num word array .Fa ap . It computes .Fa ap * .Fa ap word-wise, and places the low and high bytes of the result in .Fa rp . .Pp .Fn bn_div_words h l d divides the two word number .Pq Fa h , Fa l by .Fa d and returns the result. .Pp .Fn bn_add_words rp ap bp num operates on the .Fa num word arrays .Fa ap , .Fa bp and .Fa rp . It computes .Fa ap + .Fa bp , places the result in .Fa rp , and returns the high word (carry). .Pp .Fn bn_sub_words rp ap bp num operates on the .Fa num word arrays .Fa ap , .Fa bp and .Fa rp . It computes .Fa ap - .Fa bp , places the result in .Fa rp , and returns the carry (1 if .Fa bp \(ra .Fa ap , 0 otherwise). .Pp .Fn bn_mul_comba4 r a b operates on the 4 word arrays .Fa a and .Fa b and the 8-word array .Fa r . It computes .Fa a Ns * Ns Fa b and places the result in .Fa r . .Pp .Fn bn_mul_comba8 r a b operates on the 8-word arrays .Fa a and .Fa b and the 16-word array .Fa r . It computes .Fa a Ns * Ns Fa b and places the result in .Fa r . .Pp .Fn bn_sqr_comba4 r a b operates on the 4-word arrays .Fa a and .Fa b and the 8-word array .Fa r . .Pp .Fn bn_sqr_comba8 r a b operates on the 8-word arrays .Fa a and .Fa b and the 16 word array .Fa r . .Pp The following functions are implemented in C: .Pp .Fn bn_cmp_words a b n operates on the .Fa n word arrays .Fa a and .Fa b . It returns 1, 0 and -1 if .Fa a is greater than, equal and less than .Fa b . .Pp .Fn bn_mul_normal r a na b nb operates on the .Fa na word array .Fa a , the .Fa nb word array .Fa b and the .Fa na Ns + Ns Fa nb word array .Fa r . It computes .Fa a Ns * Ns Fa b and places the result in .Fa r . .Pp .Fn bn_mul_low_normal r a b n operates on the .Fa n word arrays .Fa r , .Fa a and .Fa b . It computes the .Fa n low words of .Fa a Ns * Ns Fa b and places the result in .Fa r . .Pp .Fn bn_mul_recursive r a b n2 dna dnb t operates on the word arrays .Fa a and .Fa b of length .Fa n2 Ns + Ns Fa dna and .Fa n2 Ns + Ns Fa dnb .Pf ( Fa dna and .Fa dnb are currently allowed to be 0 or negative) and the .Pf 2* Fa n2 word arrays .Fa r and .Sy t . .Fa n2 must be a power of 2. It computes .Fa a Ns * Ns Fa b and places the result in .Fa r . .Pp .Fn bn_mul_part_recursive r a b n tna tnb tmp operates on the word arrays .Fa a and .Fa b of length .Fa n Ns + Ns Fa tna and .Fa n Ns + Ns Fa tnb and the .Pf 4* Fa n word arrays .Fa r and .Fa tmp . .Pp .Fn bn_mul_low_recursive r a b n2 tmp operates on the .Fa n2 word arrays .Fa r and .Fa tmp and the .Fa n2 Ns /2 word arrays .Fa a and .Fa b . .Pp .Fn bn_mul_high r a b l n2 tmp operates on the .Fa n2 word arrays .Fa r , .Fa a , .Fa b and .Fa l (?) and the .Pf 3* Fa n2 word array .Fa tmp . .Pp .Xr BN_mul 3 calls .Fn bn_mul_normal , or an optimized implementation if the factors have the same size: .Fn bn_mul_comba8 is used if they are 8 words long, .Fn bn_mul_recursive if they are larger than .Dv BN_MULL_SIZE_NORMAL and the size is an exact multiple of the word size, and .Fn bn_mul_part_recursive for others that are larger than .Dv BN_MULL_SIZE_NORMAL . .Pp .Fn bn_sqr_normal r a n tmp operates on the .Fa n word array .Fa a and the .Pf 2* Fa n word arrays .Fa tmp and .Fa r . .Pp The implementations use the following macros which, depending on the architecture, may use .Vt long long C operations or inline assembler. They are defined in .Pa bn_lcl.h . .Pp .Fn mul r a w c computes .Fa w Ns * Ns Fa a Ns + Ns Fa c and places the low word of the result in .Fa r and the high word in .Fa c . .Pp .Fn mul_add r a w c computes .Fa w Ns * Ns Fa a Ns + Ns Fa r Ns + Ns Fa c and places the low word of the result in .Fa r and the high word in .Fa c . .Pp .Fn sqr r0 r1 a computes .Fa a Ns * Ns Fa a and places the low word of the result in .Fa r0 and the high word in .Fa r1 . .Ss Size changes .Fn bn_expand ensures that .Fa b has enough space for a .Fa bits bit number. .Fn bn_wexpand ensures that .Fa b has enough space for an .Fa n word number. If the number has to be expanded, both macros call .Fn bn_expand2 , which allocates a new .Fa d array and copies the data. They return .Dv NULL on error, .Fa b otherwise. .Pp The .Fn bn_fix_top macro reduces .Fa a Ns -> Ns Fa top to point to the most significant non-zero word plus one when .Fa a has shrunk. .Ss Debugging .Fn bn_check_top verifies that .Ql ((a)-\(ratop \(ra= 0 && (a)-\(ratop \(la= (a)-\(radmax) . A violation will cause the program to abort. .Pp .Fn bn_print prints .Fa a to .Dv stderr . .Fn bn_dump prints .Fa n words at .Fa d (in reverse order, i.e.\& most significant word first) to .Dv stderr . .Pp .Fn bn_set_max makes .Fa a a static number with a .Fa dmax of its current size. This is used by .Fn bn_set_low and .Fn bn_set_high to make .Fa r a read-only .Vt BIGNUM that contains the .Fa n low or high words of .Fa a . .Pp If .Dv BN_DEBUG is not defined, .Fn bn_check_top , .Fn bn_print , .Fn bn_dump and .Fn bn_set_max are defined as empty macros. .Sh SEE ALSO .Xr BN_new 3