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1.\" $OpenBSD: bn_dump.3,v 1.9 2023/11/16 18:10:19 schwarze Exp $
2.\" full merge up to:
3.\" OpenSSL crypto/bn/README.pod aebb9aac Jul 19 09:27:53 2016 -0400
4.\"
5.\" This file was written by Ulf Moeller <ulf@openssl.org>.
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53.Dd $Mdocdate: November 16 2023 $
54.Dt BN_DUMP 3
55.Os
56.Sh NAME
57.Nm bn_mul_words ,
58.Nm bn_mul_add_words ,
59.Nm bn_sqr_words ,
60.Nm bn_div_words ,
61.Nm bn_add_words ,
62.Nm bn_sub_words ,
63.Nm bn_mul_comba4 ,
64.Nm bn_mul_comba8 ,
65.Nm bn_sqr_comba4 ,
66.Nm bn_sqr_comba8 ,
67.Nm bn_mul_normal ,
68.Nm bn_expand ,
69.Nm bn_wexpand
70.Nd BIGNUM library internal functions
71.Sh SYNOPSIS
72.Fd #include "bn_local.h"
73.Ft BN_ULONG
74.Fo bn_mul_words
75.Fa "BN_ULONG *rp"
76.Fa "BN_ULONG *ap"
77.Fa "int num"
78.Fa "BN_ULONG w"
79.Fc
80.Ft BN_ULONG
81.Fo bn_mul_add_words
82.Fa "BN_ULONG *rp"
83.Fa "BN_ULONG *ap"
84.Fa "int num"
85.Fa "BN_ULONG w"
86.Fc
87.Ft void
88.Fo bn_sqr_words
89.Fa "BN_ULONG *rp"
90.Fa "BN_ULONG *ap"
91.Fa "int num"
92.Fc
93.Ft BN_ULONG
94.Fo bn_div_words
95.Fa "BN_ULONG h"
96.Fa "BN_ULONG l"
97.Fa "BN_ULONG d"
98.Fc
99.Ft BN_ULONG
100.Fo bn_add_words
101.Fa "BN_ULONG *rp"
102.Fa "BN_ULONG *ap"
103.Fa "BN_ULONG *bp"
104.Fa "int num"
105.Fc
106.Ft BN_ULONG
107.Fo bn_sub_words
108.Fa "BN_ULONG *rp"
109.Fa "BN_ULONG *ap"
110.Fa "BN_ULONG *bp"
111.Fa "int num"
112.Fc
113.Ft void
114.Fo bn_mul_comba4
115.Fa "BN_ULONG *r"
116.Fa "BN_ULONG *a"
117.Fa "BN_ULONG *b"
118.Fc
119.Ft void
120.Fo bn_mul_comba8
121.Fa "BN_ULONG *r"
122.Fa "BN_ULONG *a"
123.Fa "BN_ULONG *b"
124.Fc
125.Ft void
126.Fo bn_sqr_comba4
127.Fa "BN_ULONG *r"
128.Fa "BN_ULONG *a"
129.Fc
130.Ft void
131.Fo bn_sqr_comba8
132.Fa "BN_ULONG *r"
133.Fa "BN_ULONG *a"
134.Fc
135.Ft void
136.Fo bn_mul_normal
137.Fa "BN_ULONG *r"
138.Fa "BN_ULONG *a"
139.Fa "int na"
140.Fa "BN_ULONG *b"
141.Fa "int nb"
142.Fc
143.Ft BIGNUM *
144.Fo bn_expand
145.Fa "BIGNUM *a"
146.Fa "int bits"
147.Fc
148.Ft BIGNUM *
149.Fo bn_wexpand
150.Fa "BIGNUM *a"
151.Fa "int n"
152.Fc
153.Sh DESCRIPTION
154This page documents some internal functions used by the
155.Vt BIGNUM
156implementation.
157They are described here to facilitate debugging and extending the
158library.
159They are
160.Em not
161to be used by applications.
162.Ss The BIGNUM structure
163.Bd -literal
164typedef struct bignum_st BIGNUM;
165
166struct bignum_st {
167 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */
168 int top; /* Index of last used d +1. */
169 /* The next are internal book keeping for bn_expand. */
170 int dmax; /* Size of the d array. */
171 int neg; /* one if the number is negative */
172 int flags;
173};
174.Ed
175.Pp
176The integer value is stored in
177.Fa d ,
178a
179.Xr malloc 3 Ap ed
180array of words
181.Pq Vt BN_ULONG ,
182least significant word first.
183.Vt BN_ULONG
184is a macro that expands to
185.Vt unsigned long Pq = Vt uint64_t
186on
187.Dv _LP64
188platforms and
189.Vt unsigned int Pq = Vt uint32_t
190elsewhere.
191.Pp
192.Fa dmax
193is the size of the
194.Fa d
195array that has been allocated.
196.Fa top
197is the number of words being used, so for a value of 4, bn.d[0]=4 and
198bn.top=1.
199.Fa neg
200is 1 if the number is negative.
201When a
202.Vt BIGNUM
203is 0, the
204.Fa d
205field can be
206.Dv NULL
207and
208.Fa top
209== 0.
210.Pp
211.Fa flags
212is a bit field of flags which are defined in
213.In openssl/bn.h .
214The flags begin with
215.Dv BN_FLG_ .
216The functions
217.Xr BN_set_flags 3
218and
219.Xr BN_get_flags 3
220enable or inspect
221.Fa flags .
222.Pp
223Various routines in this library require the use of temporary
224.Vt BIGNUM
225variables during their execution.
226Since dynamic memory allocation to create
227.Vt BIGNUM Ns s
228is rather expensive when used in conjunction with repeated subroutine
229calls, the
230.Vt BN_CTX
231structure is used.
232This structure contains BN_CTX_NUM
233.Vt BIGNUM Ns s ;
234see
235.Xr BN_CTX_start 3 .
236.Ss Low level arithmetic operations
237These functions are implemented in C and for several platforms in
238assembly language:
239.Pp
240.Fn bn_mul_words rp ap num w
241operates on the
242.Fa num
243word arrays
244.Fa rp
245and
246.Fa ap .
247It computes
248.Fa ap
249*
250.Fa w ,
251places the result in
252.Fa rp ,
253and returns the high word (carry).
254.Pp
255.Fn bn_mul_add_words rp ap num w
256operates on the
257.Fa num
258word arrays
259.Fa rp
260and
261.Fa ap .
262It computes
263.Fa ap
264*
265.Fa w
266+
267.Fa rp ,
268places the result in
269.Fa rp ,
270and returns the high word (carry).
271.Pp
272.Fn bn_sqr_words rp ap num
273operates on the
274.Fa num
275word array
276.Fa ap
277and the
278.Pf 2* Fa num
279word array
280.Fa ap .
281It computes
282.Fa ap
283*
284.Fa ap
285word-wise, and places the low and high bytes of the result in
286.Fa rp .
287.Pp
288.Fn bn_div_words h l d
289divides the two word number
290.Pq Fa h , Fa l
291by
292.Fa d
293and returns the result.
294.Pp
295.Fn bn_add_words rp ap bp num
296operates on the
297.Fa num
298word arrays
299.Fa ap ,
300.Fa bp
301and
302.Fa rp .
303It computes
304.Fa ap
305+
306.Fa bp ,
307places the result in
308.Fa rp ,
309and returns the high word (carry).
310.Pp
311.Fn bn_sub_words rp ap bp num
312operates on the
313.Fa num
314word arrays
315.Fa ap ,
316.Fa bp
317and
318.Fa rp .
319It computes
320.Fa ap
321-
322.Fa bp ,
323places the result in
324.Fa rp ,
325and returns the carry (1 if
326.Fa bp
327\(ra
328.Fa ap ,
3290 otherwise).
330.Pp
331.Fn bn_mul_comba4 r a b
332operates on the 4 word arrays
333.Fa a
334and
335.Fa b
336and the 8-word array
337.Fa r .
338It computes
339.Fa a Ns * Ns Fa b
340and places the result in
341.Fa r .
342.Pp
343.Fn bn_mul_comba8 r a b
344operates on the 8-word arrays
345.Fa a
346and
347.Fa b
348and the 16-word array
349.Fa r .
350It computes
351.Fa a Ns * Ns Fa b
352and places the result in
353.Fa r .
354.Pp
355.Fn bn_sqr_comba4 r a b
356operates on the 4-word arrays
357.Fa a
358and
359.Fa b
360and the 8-word array
361.Fa r .
362.Pp
363.Fn bn_sqr_comba8 r a b
364operates on the 8-word arrays
365.Fa a
366and
367.Fa b
368and the 16 word array
369.Fa r .
370.Pp
371The following functions are implemented in C:
372.Pp
373.Fn bn_mul_normal r a na b nb
374operates on the
375.Fa na
376word array
377.Fa a ,
378the
379.Fa nb
380word array
381.Fa b
382and the
383.Fa na Ns + Ns Fa nb
384word array
385.Fa r .
386It computes
387.Fa a Ns * Ns Fa b
388and places the result in
389.Fa r .
390.Pp
391.Xr BN_mul 3
392calls
393.Fn bn_mul_comba4
394if both factors are 4 words long,
395.Fn bn_mul_comba8
396if both factors are 8 words long,
397or
398.Fn bn_mul_normal
399otherwise.
400.Ss Size changes
401.Fn bn_expand
402ensures that
403.Fa b
404has enough space for a
405.Fa bits
406bit number.
407.Fn bn_wexpand
408ensures that
409.Fa b
410has enough space for an
411.Fa n
412word number.
413They return 0 on error or 1 otherwise.
414.Sh SEE ALSO
415.Xr BN_new 3
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