| bn_internal.3 (206048) | bn_internal.3 (215698) |
|---|---|
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| 68.\" Accent mark definitions (@(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2). 69.\" Fear. Run. Save yourself. No user-serviceable parts. 70. \" fudge factors for nroff and troff 71.if n \{\ 72. ds #H 0 73. ds #V .8m 74. ds #F .3m 75. ds #[ \f1 --- 48 unchanged lines hidden (view full) --- 124. ds Th \o'LP' 125. ds ae ae 126. ds Ae AE 127.\} 128.rm #[ #] #H #V #F C 129.\" ======================================================================== 130.\" 131.IX Title "bn_internal 3" | 63.\" Accent mark definitions (@(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2). 64.\" Fear. Run. Save yourself. No user-serviceable parts. 65. \" fudge factors for nroff and troff 66.if n \{\ 67. ds #H 0 68. ds #V .8m 69. ds #F .3m 70. ds #[ \f1 --- 48 unchanged lines hidden (view full) --- 119. ds Th \o'LP' 120. ds ae ae 121. ds Ae AE 122.\} 123.rm #[ #] #H #V #F C 124.\" ======================================================================== 125.\" 126.IX Title "bn_internal 3" |
| 132.TH bn_internal 3 "2010-03-24" "0.9.8n" "OpenSSL" | 127.TH bn_internal 3 "2010-11-16" "0.9.8p" "OpenSSL" 128.\" For nroff, turn off justification. Always turn off hyphenation; it makes 129.\" way too many mistakes in technical documents. 130.if n .ad l 131.nh |
| 133.SH "NAME" 134bn_mul_words, bn_mul_add_words, bn_sqr_words, bn_div_words, 135bn_add_words, bn_sub_words, bn_mul_comba4, bn_mul_comba8, 136bn_sqr_comba4, bn_sqr_comba8, bn_cmp_words, bn_mul_normal, 137bn_mul_low_normal, bn_mul_recursive, bn_mul_part_recursive, 138bn_mul_low_recursive, bn_mul_high, bn_sqr_normal, bn_sqr_recursive, 139bn_expand, bn_wexpand, bn_expand2, bn_fix_top, bn_check_top, 140bn_print, bn_dump, bn_set_max, bn_set_high, bn_set_low \- BIGNUM 141library internal functions 142.SH "SYNOPSIS" 143.IX Header "SYNOPSIS" | 132.SH "NAME" 133bn_mul_words, bn_mul_add_words, bn_sqr_words, bn_div_words, 134bn_add_words, bn_sub_words, bn_mul_comba4, bn_mul_comba8, 135bn_sqr_comba4, bn_sqr_comba8, bn_cmp_words, bn_mul_normal, 136bn_mul_low_normal, bn_mul_recursive, bn_mul_part_recursive, 137bn_mul_low_recursive, bn_mul_high, bn_sqr_normal, bn_sqr_recursive, 138bn_expand, bn_wexpand, bn_expand2, bn_fix_top, bn_check_top, 139bn_print, bn_dump, bn_set_max, bn_set_high, bn_set_low \- BIGNUM 140library internal functions 141.SH "SYNOPSIS" 142.IX Header "SYNOPSIS" |
| 144.Vb 9 | 143.Vb 1 144\& #include <openssl/bn.h> 145\& |
| 145\& BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w); 146\& BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num, 147\& BN_ULONG w); 148\& void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num); 149\& BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d); 150\& BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp, 151\& int num); 152\& BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp, 153\& int num); | 146\& BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w); 147\& BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num, 148\& BN_ULONG w); 149\& void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num); 150\& BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d); 151\& BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp, 152\& int num); 153\& BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp, 154\& int num); |
| 154.Ve 155.PP 156.Vb 4 | 155\& |
| 157\& void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); 158\& void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); 159\& void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a); 160\& void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a); | 156\& void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); 157\& void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); 158\& void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a); 159\& void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a); |
| 161.Ve 162.PP 163.Vb 1 | 160\& |
| 164\& int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n); | 161\& int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n); |
| 165.Ve 166.PP 167.Vb 11 | 162\& |
| 168\& void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, 169\& int nb); 170\& void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n); 171\& void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, 172\& int dna,int dnb,BN_ULONG *tmp); 173\& void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, 174\& int n, int tna,int tnb, BN_ULONG *tmp); 175\& void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, 176\& int n2, BN_ULONG *tmp); 177\& void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, 178\& int n2, BN_ULONG *tmp); | 163\& void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, 164\& int nb); 165\& void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n); 166\& void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, 167\& int dna,int dnb,BN_ULONG *tmp); 168\& void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, 169\& int n, int tna,int tnb, BN_ULONG *tmp); 170\& void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, 171\& int n2, BN_ULONG *tmp); 172\& void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, 173\& int n2, BN_ULONG *tmp); |
| 179.Ve 180.PP 181.Vb 2 | 174\& |
| 182\& void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp); 183\& void bn_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *tmp); | 175\& void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp); 176\& void bn_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *tmp); |
| 184.Ve 185.PP 186.Vb 3 | 177\& |
| 187\& void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c); 188\& void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c); 189\& void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a); | 178\& void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c); 179\& void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c); 180\& void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a); |
| 190.Ve 191.PP 192.Vb 4 | 181\& |
| 193\& BIGNUM *bn_expand(BIGNUM *a, int bits); 194\& BIGNUM *bn_wexpand(BIGNUM *a, int n); 195\& BIGNUM *bn_expand2(BIGNUM *a, int n); 196\& void bn_fix_top(BIGNUM *a); | 182\& BIGNUM *bn_expand(BIGNUM *a, int bits); 183\& BIGNUM *bn_wexpand(BIGNUM *a, int n); 184\& BIGNUM *bn_expand2(BIGNUM *a, int n); 185\& void bn_fix_top(BIGNUM *a); |
| 197.Ve 198.PP 199.Vb 6 | 186\& |
| 200\& void bn_check_top(BIGNUM *a); 201\& void bn_print(BIGNUM *a); 202\& void bn_dump(BN_ULONG *d, int n); 203\& void bn_set_max(BIGNUM *a); 204\& void bn_set_high(BIGNUM *r, BIGNUM *a, int n); 205\& void bn_set_low(BIGNUM *r, BIGNUM *a, int n); 206.Ve 207.SH "DESCRIPTION" 208.IX Header "DESCRIPTION" 209This page documents the internal functions used by the OpenSSL 210\&\fB\s-1BIGNUM\s0\fR implementation. They are described here to facilitate 211debugging and extending the library. They are \fInot\fR to be used by 212applications. | 187\& void bn_check_top(BIGNUM *a); 188\& void bn_print(BIGNUM *a); 189\& void bn_dump(BN_ULONG *d, int n); 190\& void bn_set_max(BIGNUM *a); 191\& void bn_set_high(BIGNUM *r, BIGNUM *a, int n); 192\& void bn_set_low(BIGNUM *r, BIGNUM *a, int n); 193.Ve 194.SH "DESCRIPTION" 195.IX Header "DESCRIPTION" 196This page documents the internal functions used by the OpenSSL 197\&\fB\s-1BIGNUM\s0\fR implementation. They are described here to facilitate 198debugging and extending the library. They are \fInot\fR to be used by 199applications. |
| 213.Sh "The \s-1BIGNUM\s0 structure" | 200.SS "The \s-1BIGNUM\s0 structure" |
| 214.IX Subsection "The BIGNUM structure" 215.Vb 1 216\& typedef struct bignum_st BIGNUM; | 201.IX Subsection "The BIGNUM structure" 202.Vb 1 203\& typedef struct bignum_st BIGNUM; |
| 217.Ve 218.PP 219.Vb 9 | 204\& |
| 220\& struct bignum_st 221\& { | 205\& struct bignum_st 206\& { |
| 222\& BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */ | 207\& BN_ULONG *d; /* Pointer to an array of \*(AqBN_BITS2\*(Aq bit chunks. */ |
| 223\& int top; /* Index of last used d +1. */ 224\& /* The next are internal book keeping for bn_expand. */ 225\& int dmax; /* Size of the d array. */ 226\& int neg; /* one if the number is negative */ 227\& int flags; 228\& }; 229.Ve 230.PP --- 13 unchanged lines hidden (view full) --- 244structure \fBb\fR. 245.PP 246Various routines in this library require the use of temporary 247\&\fB\s-1BIGNUM\s0\fR variables during their execution. Since dynamic memory 248allocation to create \fB\s-1BIGNUM\s0\fRs is rather expensive when used in 249conjunction with repeated subroutine calls, the \fB\s-1BN_CTX\s0\fR structure is 250used. This structure contains \fB\s-1BN_CTX_NUM\s0\fR \fB\s-1BIGNUM\s0\fRs, see 251\&\fIBN_CTX_start\fR\|(3). | 208\& int top; /* Index of last used d +1. */ 209\& /* The next are internal book keeping for bn_expand. */ 210\& int dmax; /* Size of the d array. */ 211\& int neg; /* one if the number is negative */ 212\& int flags; 213\& }; 214.Ve 215.PP --- 13 unchanged lines hidden (view full) --- 229structure \fBb\fR. 230.PP 231Various routines in this library require the use of temporary 232\&\fB\s-1BIGNUM\s0\fR variables during their execution. Since dynamic memory 233allocation to create \fB\s-1BIGNUM\s0\fRs is rather expensive when used in 234conjunction with repeated subroutine calls, the \fB\s-1BN_CTX\s0\fR structure is 235used. This structure contains \fB\s-1BN_CTX_NUM\s0\fR \fB\s-1BIGNUM\s0\fRs, see 236\&\fIBN_CTX_start\fR\|(3). |
| 252.Sh "Low-level arithmetic operations" | 237.SS "Low-level arithmetic operations" |
| 253.IX Subsection "Low-level arithmetic operations" 254These functions are implemented in C and for several platforms in 255assembly language: 256.PP 257bn_mul_words(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR word 258arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR, places the result 259in \fBrp\fR, and returns the high word (carry). 260.PP 261bn_mul_add_words(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR 262word arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR + \fBrp\fR, places 263the result in \fBrp\fR, and returns the high word (carry). 264.PP 265bn_sqr_words(\fBrp\fR, \fBap\fR, \fBn\fR) operates on the \fBnum\fR word array 266\&\fBap\fR and the 2*\fBnum\fR word array \fBap\fR. It computes \fBap\fR * \fBap\fR | 238.IX Subsection "Low-level arithmetic operations" 239These functions are implemented in C and for several platforms in 240assembly language: 241.PP 242bn_mul_words(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR word 243arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR, places the result 244in \fBrp\fR, and returns the high word (carry). 245.PP 246bn_mul_add_words(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR 247word arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR + \fBrp\fR, places 248the result in \fBrp\fR, and returns the high word (carry). 249.PP 250bn_sqr_words(\fBrp\fR, \fBap\fR, \fBn\fR) operates on the \fBnum\fR word array 251\&\fBap\fR and the 2*\fBnum\fR word array \fBap\fR. It computes \fBap\fR * \fBap\fR |
| 267word\-wise, and places the low and high bytes of the result in \fBrp\fR. | 252word-wise, and places the low and high bytes of the result in \fBrp\fR. |
| 268.PP 269bn_div_words(\fBh\fR, \fBl\fR, \fBd\fR) divides the two word number (\fBh\fR,\fBl\fR) 270by \fBd\fR and returns the result. 271.PP 272bn_add_words(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word 273arrays \fBap\fR, \fBbp\fR and \fBrp\fR. It computes \fBap\fR + \fBbp\fR, places the 274result in \fBrp\fR, and returns the high word (carry). 275.PP --- 65 unchanged lines hidden (view full) --- 341mul(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBc\fR and places the 342low word of the result in \fBr\fR and the high word in \fBc\fR. 343.PP 344mul_add(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBr\fR+\fBc\fR and 345places the low word of the result in \fBr\fR and the high word in \fBc\fR. 346.PP 347sqr(\fBr0\fR, \fBr1\fR, \fBa\fR) computes \fBa\fR*\fBa\fR and places the low word 348of the result in \fBr0\fR and the high word in \fBr1\fR. | 253.PP 254bn_div_words(\fBh\fR, \fBl\fR, \fBd\fR) divides the two word number (\fBh\fR,\fBl\fR) 255by \fBd\fR and returns the result. 256.PP 257bn_add_words(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word 258arrays \fBap\fR, \fBbp\fR and \fBrp\fR. It computes \fBap\fR + \fBbp\fR, places the 259result in \fBrp\fR, and returns the high word (carry). 260.PP --- 65 unchanged lines hidden (view full) --- 326mul(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBc\fR and places the 327low word of the result in \fBr\fR and the high word in \fBc\fR. 328.PP 329mul_add(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBr\fR+\fBc\fR and 330places the low word of the result in \fBr\fR and the high word in \fBc\fR. 331.PP 332sqr(\fBr0\fR, \fBr1\fR, \fBa\fR) computes \fBa\fR*\fBa\fR and places the low word 333of the result in \fBr0\fR and the high word in \fBr1\fR. |
| 349.Sh "Size changes" | 334.SS "Size changes" |
| 350.IX Subsection "Size changes" 351\&\fIbn_expand()\fR ensures that \fBb\fR has enough space for a \fBbits\fR bit 352number. \fIbn_wexpand()\fR ensures that \fBb\fR has enough space for an 353\&\fBn\fR word number. If the number has to be expanded, both macros 354call \fIbn_expand2()\fR, which allocates a new \fBd\fR array and copies the 355data. They return \fB\s-1NULL\s0\fR on error, \fBb\fR otherwise. 356.PP 357The \fIbn_fix_top()\fR macro reduces \fBa\->top\fR to point to the most 358significant non-zero word plus one when \fBa\fR has shrunk. | 335.IX Subsection "Size changes" 336\&\fIbn_expand()\fR ensures that \fBb\fR has enough space for a \fBbits\fR bit 337number. \fIbn_wexpand()\fR ensures that \fBb\fR has enough space for an 338\&\fBn\fR word number. If the number has to be expanded, both macros 339call \fIbn_expand2()\fR, which allocates a new \fBd\fR array and copies the 340data. They return \fB\s-1NULL\s0\fR on error, \fBb\fR otherwise. 341.PP 342The \fIbn_fix_top()\fR macro reduces \fBa\->top\fR to point to the most 343significant non-zero word plus one when \fBa\fR has shrunk. |
| 359.Sh "Debugging" | 344.SS "Debugging" |
| 360.IX Subsection "Debugging" 361\&\fIbn_check_top()\fR verifies that \f(CW\*(C`((a)\->top >= 0 && (a)\->top 362<= (a)\->dmax)\*(C'\fR. A violation will cause the program to abort. 363.PP 364\&\fIbn_print()\fR prints \fBa\fR to stderr. \fIbn_dump()\fR prints \fBn\fR words at \fBd\fR 365(in reverse order, i.e. most significant word first) to stderr. 366.PP 367\&\fIbn_set_max()\fR makes \fBa\fR a static number with a \fBdmax\fR of its current size. 368This is used by \fIbn_set_low()\fR and \fIbn_set_high()\fR to make \fBr\fR a read-only 369\&\fB\s-1BIGNUM\s0\fR that contains the \fBn\fR low or high words of \fBa\fR. 370.PP 371If \fB\s-1BN_DEBUG\s0\fR is not defined, \fIbn_check_top()\fR, \fIbn_print()\fR, \fIbn_dump()\fR 372and \fIbn_set_max()\fR are defined as empty macros. 373.SH "SEE ALSO" 374.IX Header "SEE ALSO" 375\&\fIbn\fR\|(3) | 345.IX Subsection "Debugging" 346\&\fIbn_check_top()\fR verifies that \f(CW\*(C`((a)\->top >= 0 && (a)\->top 347<= (a)\->dmax)\*(C'\fR. A violation will cause the program to abort. 348.PP 349\&\fIbn_print()\fR prints \fBa\fR to stderr. \fIbn_dump()\fR prints \fBn\fR words at \fBd\fR 350(in reverse order, i.e. most significant word first) to stderr. 351.PP 352\&\fIbn_set_max()\fR makes \fBa\fR a static number with a \fBdmax\fR of its current size. 353This is used by \fIbn_set_low()\fR and \fIbn_set_high()\fR to make \fBr\fR a read-only 354\&\fB\s-1BIGNUM\s0\fR that contains the \fBn\fR low or high words of \fBa\fR. 355.PP 356If \fB\s-1BN_DEBUG\s0\fR is not defined, \fIbn_check_top()\fR, \fIbn_print()\fR, \fIbn_dump()\fR 357and \fIbn_set_max()\fR are defined as empty macros. 358.SH "SEE ALSO" 359.IX Header "SEE ALSO" 360\&\fIbn\fR\|(3) |