MirOS Manual: bn_add_words(3), bn_check_top(3), bn_cmp_words(3), bn_div_words(3), bn_dump(3), bn_expand(3), bn_expand2(3), bn_fix_top(3), bn_internal(3), bn_mul_add_words(3), bn_mul_comba4(3), bn_mul_comba8(3), bn_mul_high(3), bn_mul_low_normal(3), bn_mul_low_recursive(3), bn_mul_normal(3), bn_mul_part_recursive(3), bn_mul_recursive(3), bn_mul_words(3), bn_print(3), bn_set_high(3), bn_set_low(3), bn_set_max(3), bn_sqr_comba4(3), bn_sqr_comba8(3), bn_sqr_normal(3), bn_sqr_recursive(3), bn_sqr_words(3), bn_sub_words(3), bn_wexpand(3), mul(3), mul_add(3), sqr(3)


BN_INTERNAL(3)               OpenSSL               BN_INTERNAL(3)

NAME

     bn_mul_words, bn_mul_add_words, bn_sqr_words, bn_div_words,
     bn_add_words, bn_sub_words, bn_mul_comba4, bn_mul_comba8,
     bn_sqr_comba4, bn_sqr_comba8, bn_cmp_words, bn_mul_normal,
     bn_mul_low_normal, bn_mul_recursive, bn_mul_part_recursive,
     bn_mul_low_recursive, bn_mul_high, bn_sqr_normal,
     bn_sqr_recursive, bn_expand, bn_wexpand, bn_expand2,
     bn_fix_top, bn_check_top, bn_print, bn_dump, bn_set_max,
     bn_set_high, bn_set_low - BIGNUM library internal functions

SYNOPSIS

      BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w);
      BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num,
        BN_ULONG w);
      void     bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num);
      BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
      BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
        int num);
      BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
        int num);

      void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
      void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
      void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a);
      void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a);

      int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n);

      void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b,
        int nb);
      void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
      void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
        int dna,int dnb,BN_ULONG *tmp);
      void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
        int n, int tna,int tnb, BN_ULONG *tmp);
      void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
        int n2, BN_ULONG *tmp);
      void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l,
        int n2, BN_ULONG *tmp);

      void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp);
      void bn_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *tmp);

      void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
      void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
      void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a);

      BIGNUM *bn_expand(BIGNUM *a, int bits);
      BIGNUM *bn_wexpand(BIGNUM *a, int n);
      BIGNUM *bn_expand2(BIGNUM *a, int n);
      void bn_fix_top(BIGNUM *a);

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BN_INTERNAL(3)               OpenSSL               BN_INTERNAL(3)

      void bn_check_top(BIGNUM *a);
      void bn_print(BIGNUM *a);
      void bn_dump(BN_ULONG *d, int n);
      void bn_set_max(BIGNUM *a);
      void bn_set_high(BIGNUM *r, BIGNUM *a, int n);
      void bn_set_low(BIGNUM *r, BIGNUM *a, int n);

DESCRIPTION

     This page documents the internal functions used by the
     OpenSSL BIGNUM implementation. They are described here to
     facilitate debugging and extending the library. They are not
     to be used by applications.

     The BIGNUM structure

      typedef struct bignum_st
             {
             int top;      /* index of last used d (most significant word) */
             BN_ULONG *d;  /* pointer to an array of 'BITS2' bit chunks */
             int max;      /* size of the d array */
             int neg;      /* sign */
             } BIGNUM;

     The big number is stored in d, a malloc()ed array of
     BN_ULONGs, least significant first. A BN_ULONG can be either
     16, 32 or 64 bits in size (BITS2), depending on the 'number
     of bits' specified in "openssl/bn.h".

     max is the size of the d array that has been allocated.  top
     is the 'last' entry being used, so for a value of 4,
     bn.d[0]=4 and bn.top=1.  neg is 1 if the number is negative.
     When a BIGNUM is 0, the d field can be NULL and top == 0.

     Various routines in this library require the use of tem-
     porary BIGNUM variables during their execution.  Since
     dynamic memory allocation to create BIGNUMs is rather expen-
     sive when used in conjunction with repeated subroutine
     calls, the BN_CTX structure is used.  This structure con-
     tains BN_CTX_NUM BIGNUMs, see BN_CTX_start(3).

     Low-level arithmetic operations

     These functions are implemented in C and for several plat-
     forms in assembly language:

     bn_mul_words(rp, ap, num, w) operates on the num word arrays
     rp and ap.  It computes ap * w, places the result in rp, and
     returns the high word (carry).

     bn_mul_add_words(rp, ap, num, w) operates on the num word
     arrays rp and ap.  It computes ap * w + rp, places the
     result in rp, and returns the high word (carry).

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BN_INTERNAL(3)               OpenSSL               BN_INTERNAL(3)

     bn_sqr_words(rp, ap, n) operates on the num word array ap
     and the 2*num word array ap.  It computes ap * ap word-wise,
     and places the low and high bytes of the result in rp.

     bn_div_words(h, l, d) divides the two word number (h,l) by d
     and returns the result.

     bn_add_words(rp, ap, bp, num) operates on the num word
     arrays ap, bp and rp.  It computes ap + bp, places the
     result in rp, and returns the high word (carry).

     bn_sub_words(rp, ap, bp, num) operates on the num word
     arrays ap, bp and rp.  It computes ap - bp, places the
     result in rp, and returns the carry (1 if bp > ap, 0 other-
     wise).

     bn_mul_comba4(r, a, b) operates on the 4 word arrays a and b
     and the 8 word array r.  It computes a*b and places the
     result in r.

     bn_mul_comba8(r, a, b) operates on the 8 word arrays a and b
     and the 16 word array r.  It computes a*b and places the
     result in r.

     bn_sqr_comba4(r, a, b) operates on the 4 word arrays a and b
     and the 8 word array r.

     bn_sqr_comba8(r, a, b) operates on the 8 word arrays a and b
     and the 16 word array r.

     The following functions are implemented in C:

     bn_cmp_words(a, b, n) operates on the n word arrays a and b.
     It returns 1, 0 and -1 if a is greater than, equal and less
     than b.

     bn_mul_normal(r, a, na, b, nb) operates on the na word array
     a, the nb word array b and the na+nb word array r.  It com-
     putes a*b and places the result in r.

     bn_mul_low_normal(r, a, b, n) operates on the n word arrays
     r, a and b.  It computes the n low words of a*b and places
     the result in r.

     bn_mul_recursive(r, a, b, n2, dna, dnb, t) operates on the
     word arrays a and b of length n2+dna and n2+dnb (dna and dnb
     are currently allowed to be 0 or negative) and the 2*n2 word
     arrays r and t.  n2 must be a power of 2.  It computes a*b
     and places the result in r.

     bn_mul_part_recursive(r, a, b, n, tna, tnb, tmp) operates on
     the word arrays a and b of length n+tna and n+tnb and the

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BN_INTERNAL(3)               OpenSSL               BN_INTERNAL(3)

     4*n word arrays r and tmp.

     bn_mul_low_recursive(r, a, b, n2, tmp) operates on the n2
     word arrays r and tmp and the n2/2 word arrays a and b.

     bn_mul_high(r, a, b, l, n2, tmp) operates on the n2 word
     arrays r, a, b and l (?) and the 3*n2 word array tmp.

     BN_mul() calls bn_mul_normal(), or an optimized implementa-
     tion if the factors have the same size: bn_mul_comba8() is
     used if they are 8 words long, bn_mul_recursive() if they
     are larger than BN_MULL_SIZE_NORMAL and the size is an exact
     multiple of the word size, and bn_mul_part_recursive() for
     others that are larger than BN_MULL_SIZE_NORMAL.

     bn_sqr_normal(r, a, n, tmp) operates on the n word array a
     and the 2*n word arrays tmp and r.

     The implementations use the following macros which, depend-
     ing on the architecture, may use "long long" C operations or
     inline assembler. They are defined in "bn_lcl.h".

     mul(r, a, w, c) computes w*a+c and places the low word of
     the result in r and the high word in c.

     mul_add(r, a, w, c) computes w*a+r+c and places the low word
     of the result in r and the high word in c.

     sqr(r0, r1, a) computes a*a and places the low word of the
     result in r0 and the high word in r1.

     Size changes

     bn_expand() ensures that b has enough space for a bits bit
     number.  bn_wexpand() ensures that b has enough space for an
     n word number.  If the number has to be expanded, both mac-
     ros call bn_expand2(), which allocates a new d array and
     copies the data.  They return NULL on error, b otherwise.

     The bn_fix_top() macro reduces a->top to point to the most
     significant non-zero word when a has shrunk.

     Debugging

     bn_check_top() verifies that "((a)->top >= 0 && (a)->top <=
     (a)->max)".  A violation will cause the program to abort.

     bn_print() prints a to stderr. bn_dump() prints n words at d
     (in reverse order, i.e. most significant word first) to
     stderr.

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BN_INTERNAL(3)               OpenSSL               BN_INTERNAL(3)

     bn_set_max() makes a a static number with a max of its
     current size. This is used by bn_set_low() and bn_set_high()
     to make r a read-only BIGNUM that contains the n low or high
     words of a.

     If BN_DEBUG is not defined, bn_check_top(), bn_print(),
     bn_dump() and bn_set_max() are defined as empty macros.

SEE ALSO

     bn(3)

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