bn_mul_recursive(3ssl)

1bn_internal(3)                      OpenSSL                     bn_internal(3)
2
3
4

NAME

6       bn_mul_words, bn_mul_add_words, bn_sqr_words, bn_div_words,
7       bn_add_words, bn_sub_words, bn_mul_comba4, bn_mul_comba8,
8       bn_sqr_comba4, bn_sqr_comba8, bn_cmp_words, bn_mul_normal,
9       bn_mul_low_normal, bn_mul_recursive, bn_mul_part_recursive,
10       bn_mul_low_recursive, bn_mul_high, bn_sqr_normal, bn_sqr_recursive,
11       bn_expand, bn_wexpand, bn_expand2, bn_fix_top, bn_check_top, bn_print,
12       bn_dump, bn_set_max, bn_set_high, bn_set_low - BIGNUM library internal
13       functions
14

SYNOPSIS

16        #include <openssl/bn.h>
17
18        BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w);
19        BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num,
20          BN_ULONG w);
21        void     bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num);
22        BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
23        BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
24          int num);
25        BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
26          int num);
27
28        void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
29        void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
30        void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a);
31        void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a);
32
33        int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n);
34
35        void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b,
36          int nb);
37        void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
38        void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
39          int dna,int dnb,BN_ULONG *tmp);
40        void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
41          int n, int tna,int tnb, BN_ULONG *tmp);
42        void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
43          int n2, BN_ULONG *tmp);
44        void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l,
45          int n2, BN_ULONG *tmp);
46
47        void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp);
48        void bn_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *tmp);
49
50        void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
51        void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
52        void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a);
53
54        BIGNUM *bn_expand(BIGNUM *a, int bits);
55        BIGNUM *bn_wexpand(BIGNUM *a, int n);
56        BIGNUM *bn_expand2(BIGNUM *a, int n);
57        void bn_fix_top(BIGNUM *a);
58
59        void bn_check_top(BIGNUM *a);
60        void bn_print(BIGNUM *a);
61        void bn_dump(BN_ULONG *d, int n);
62        void bn_set_max(BIGNUM *a);
63        void bn_set_high(BIGNUM *r, BIGNUM *a, int n);
64        void bn_set_low(BIGNUM *r, BIGNUM *a, int n);
65

DESCRIPTION

67       This page documents the internal functions used by the OpenSSL BIGNUM
68       implementation. They are described here to facilitate debugging and
69       extending the library. They are not to be used by applications.
70
71   The BIGNUM structure
72        typedef struct bignum_st BIGNUM;
73
74        struct bignum_st
75               {
76               BN_ULONG *d;    /* Pointer to an array of 'BN_BITS2' bit chunks. */
77               int top;        /* Index of last used d +1. */
78               /* The next are internal book keeping for bn_expand. */
79               int dmax;       /* Size of the d array. */
80               int neg;        /* one if the number is negative */
81               int flags;
82               };
83
84       The integer value is stored in d, a malloc()ed array of words
85       (BN_ULONG), least significant word first. A BN_ULONG can be either 16,
86       32 or 64 bits in size, depending on the 'number of bits' (BITS2)
87       specified in "openssl/bn.h".
88
89       dmax is the size of the d array that has been allocated.  top is the
90       number of words being used, so for a value of 4, bn.d[0]=4 and
91       bn.top=1.  neg is 1 if the number is negative.  When a BIGNUM is 0, the
92       d field can be NULL and top == 0.
93
94       flags is a bit field of flags which are defined in "openssl/bn.h". The
95       flags begin with BN_FLG_. The macros BN_set_flags(b,n) and
96       BN_get_flags(b,n) exist to enable or fetch flag(s) n from BIGNUM
97       structure b.
98
99       Various routines in this library require the use of temporary BIGNUM
100       variables during their execution.  Since dynamic memory allocation to
101       create BIGNUMs is rather expensive when used in conjunction with
102       repeated subroutine calls, the BN_CTX structure is used.  This
103       structure contains BN_CTX_NUM BIGNUMs, see BN_CTX_start(3).
104
105   Low-level arithmetic operations
106       These functions are implemented in C and for several platforms in
107       assembly language:
108
109       bn_mul_words(rp, ap, num, w) operates on the num word arrays rp and ap.
110       It computes ap * w, places the result in rp, and returns the high word
111       (carry).
112
113       bn_mul_add_words(rp, ap, num, w) operates on the num word arrays rp and
114       ap.  It computes ap * w + rp, places the result in rp, and returns the
115       high word (carry).
116
117       bn_sqr_words(rp, ap, n) operates on the num word array ap and the 2*num
118       word array ap.  It computes ap * ap word-wise, and places the low and
119       high bytes of the result in rp.
120
121       bn_div_words(h, l, d) divides the two word number (h,l) by d and
122       returns the result.
123
124       bn_add_words(rp, ap, bp, num) operates on the num word arrays ap, bp
125       and rp.  It computes ap + bp, places the result in rp, and returns the
126       high word (carry).
127
128       bn_sub_words(rp, ap, bp, num) operates on the num word arrays ap, bp
129       and rp.  It computes ap - bp, places the result in rp, and returns the
130       carry (1 if bp > ap, 0 otherwise).
131
132       bn_mul_comba4(r, a, b) operates on the 4 word arrays a and b and the 8
133       word array r.  It computes a*b and places the result in r.
134
135       bn_mul_comba8(r, a, b) operates on the 8 word arrays a and b and the 16
136       word array r.  It computes a*b and places the result in r.
137
138       bn_sqr_comba4(r, a, b) operates on the 4 word arrays a and b and the 8
139       word array r.
140
141       bn_sqr_comba8(r, a, b) operates on the 8 word arrays a and b and the 16
142       word array r.
143
144       The following functions are implemented in C:
145
146       bn_cmp_words(a, b, n) operates on the n word arrays a and b.  It
147       returns 1, 0 and -1 if a is greater than, equal and less than b.
148
149       bn_mul_normal(r, a, na, b, nb) operates on the na word array a, the nb
150       word array b and the na+nb word array r.  It computes a*b and places
151       the result in r.
152
153       bn_mul_low_normal(r, a, b, n) operates on the n word arrays r, a and b.
154       It computes the n low words of a*b and places the result in r.
155
156       bn_mul_recursive(r, a, b, n2, dna, dnb, t) operates on the word arrays
157       a and b of length n2+dna and n2+dnb (dna and dnb are currently allowed
158       to be 0 or negative) and the 2*n2 word arrays r and t.  n2 must be a
159       power of 2.  It computes a*b and places the result in r.
160
161       bn_mul_part_recursive(r, a, b, n, tna, tnb, tmp) operates on the word
162       arrays a and b of length n+tna and n+tnb and the 4*n word arrays r and
163       tmp.
164
165       bn_mul_low_recursive(r, a, b, n2, tmp) operates on the n2 word arrays r
166       and tmp and the n2/2 word arrays a and b.
167
168       bn_mul_high(r, a, b, l, n2, tmp) operates on the n2 word arrays r, a, b
169       and l (?) and the 3*n2 word array tmp.
170
171       BN_mul() calls bn_mul_normal(), or an optimized implementation if the
172       factors have the same size: bn_mul_comba8() is used if they are 8 words
173       long, bn_mul_recursive() if they are larger than BN_MULL_SIZE_NORMAL
174       and the size is an exact multiple of the word size, and
175       bn_mul_part_recursive() for others that are larger than
176       BN_MULL_SIZE_NORMAL.
177
178       bn_sqr_normal(r, a, n, tmp) operates on the n word array a and the 2*n
179       word arrays tmp and r.
180
181       The implementations use the following macros which, depending on the
182       architecture, may use "long long" C operations or inline assembler.
183       They are defined in "bn_lcl.h".
184
185       mul(r, a, w, c) computes w*a+c and places the low word of the result in
186       r and the high word in c.
187
188       mul_add(r, a, w, c) computes w*a+r+c and places the low word of the
189       result in r and the high word in c.
190
191       sqr(r0, r1, a) computes a*a and places the low word of the result in r0
192       and the high word in r1.
193
194   Size changes
195       bn_expand() ensures that b has enough space for a bits bit number.
196       bn_wexpand() ensures that b has enough space for an n word number.  If
197       the number has to be expanded, both macros call bn_expand2(), which
198       allocates a new d array and copies the data.  They return NULL on
199       error, b otherwise.
200
201       The bn_fix_top() macro reduces a->top to point to the most significant
202       non-zero word plus one when a has shrunk.
203
204   Debugging
205       bn_check_top() verifies that "((a)->top >= 0 && (a)->top <=
206       (a)->dmax)".  A violation will cause the program to abort.
207
208       bn_print() prints a to stderr. bn_dump() prints n words at d (in
209       reverse order, i.e. most significant word first) to stderr.
210
211       bn_set_max() makes a a static number with a dmax of its current size.
212       This is used by bn_set_low() and bn_set_high() to make r a read-only
213       BIGNUM that contains the n low or high words of a.
214
215       If BN_DEBUG is not defined, bn_check_top(), bn_print(), bn_dump() and
216       bn_set_max() are defined as empty macros.
217

NAME

SYNOPSIS

DESCRIPTION

SEE ALSO