Subversion Repositories Kolibri OS

;    mpint.inc - Multi precision integer procedures

;

;    Copyright (C) 2015-2017 Jeffrey Amelynck

;

;    This program is free software: you can redistribute it and/or modify

;    it under the terms of the GNU General Public License as published by

;    the Free Software Foundation, either version 3 of the License, or

;    (at your option) any later version.

;

;    This program is distributed in the hope that it will be useful,

;    but WITHOUT ANY WARRANTY; without even the implied warranty of

;    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

;    GNU General Public License for more details.

;

;    You should have received a copy of the GNU General Public License

;    along with this program.  If not, see .

; Notes:

;

; These procedures work only with positive integers.

; For compatibility reasons, the highest bit must always be 0.

; However, leading 0 bytes MUST at all other times be omitted.

;

; You have been warned!

MPINT_MAX_LEN = MAX_BITS/8

;;===========================================================================;;

proc mpint_to_little_endian uses esi edi ecx ;///////////////////////////////;;

;;---------------------------------------------------------------------------;;

;? Convert big endian MPINT to little endian MPINT.                          ;;

;;---------------------------------------------------------------------------;;

;> esi = pointer to big endian MPINT                                         ;;

;> edi = pointer to buffer for little endian MPINT                           ;;

;;---------------------------------------------------------------------------;;

;< eax = MPINT number length                                                 ;;

;;===========================================================================;;

; Load length dword

        lodsd

; Convert to little endian

        bswap   eax

        stosd

        test    eax, eax

        jz      .zero

; Copy data, convert to little endian meanwhile

        push    eax

        add     esi, eax

        push    esi

        dec     esi

        mov     ecx, eax

        std

  @@:

        lodsb

        mov     byte[edi], al

        inc     edi

        dec     ecx

        jnz     @r

        cld

        pop     esi eax

  .zero:

        ret

endp

;;===========================================================================;;

proc mpint_to_big_endian uses esi edi ecx ;//////////////////////////////////;;

;;---------------------------------------------------------------------------;;

;? Convert little endian MPINT to big endian MPINT.                          ;;

;;---------------------------------------------------------------------------;;

;> esi = pointer to little endian MPINT                                      ;;

;> edi = pointer to buffer for big endian MPINT                              ;;

;;---------------------------------------------------------------------------;;

;< eax = MPINT number length                                                 ;;

;;===========================================================================;;

; Load length dword

        lodsd

        test    eax, eax

        jz      .zero

        mov     ecx, eax

        add     esi, eax

        dec     esi

        push    eax     ; we'll return length to the caller later

        bswap   eax

        stosd

; Copy data, convert to big endian meanwhile

        std

  @@:

        lodsb

        mov     byte[edi], al

        inc     edi

        dec     ecx

        jnz     @r

        cld

        pop     eax

        ret

  .zero:

        stosd           ; Number 0 has 0 data bytes

        ret

endp

;;===========================================================================;;

proc mpint_print uses ecx esi eax, src ;/////////////////////////////////////;;

;;---------------------------------------------------------------------------;;

;? Print MPINT to the debug board.                                           ;;

;;---------------------------------------------------------------------------;;

;> src = pointer to little endian MPINT                                      ;;

;;---------------------------------------------------------------------------;;

;< -                                                                         ;;

;;===========================================================================;;

        DEBUGF  1, "0x"

        mov     esi, [src]

        mov     ecx, [esi]

        test    ecx, ecx

        jz      .zero

        lea     esi, [esi + ecx + 4 - 1]

        pushf

        std

  .loop:

        lodsb

        DEBUGF  1, "%x", eax:2

        dec     ecx

        jnz     .loop

        DEBUGF  1, "\n"

        popf

        ret

  .zero:

        DEBUGF  1, "00\n"

        ret

endp

;;===========================================================================;;

proc mpint_hob uses edi ecx eax, dst ;///////////////////////////////////////;;

;;---------------------------------------------------------------------------;;

;? Return an index number giving the position of the highest order bit.      ;;

;;---------------------------------------------------------------------------;;

;> src = pointer to little endian MPINT                                      ;;

;;---------------------------------------------------------------------------;;

;< eax = highest order bit number                                            ;;

;;===========================================================================;;

        mov     edi, [dst]

        lodsd

        dec     eax                     ; total length minus one

        mov     cl, [edi+eax]           ; load the highest order byte

        shl     eax, 3                  ; multiply eax by 8 to get nr of bits

; Now shift bits of the highest order byte right, until the byte reaches zero, counting bits meanwhile

        test    cl, cl

        jz      .end

  @@:

        inc     eax

        shr     cl, 1

        jnz     @r

  .end:

        ret

endp

;;===========================================================================;;

proc mpint_cmp uses esi edi ecx eax, dst, src ;//////////////////////////////;;

;;---------------------------------------------------------------------------;;

;? Compare two mpints.                                                       ;;

;;---------------------------------------------------------------------------;;

;> dst = pointer to little endian MPINT                                      ;;

;> src = pointer to little endian MPINT                                      ;;

;;---------------------------------------------------------------------------;;

;< flags are set as for single precision CMP instruction                     ;;

;;===========================================================================;;

; First, check if number of significant bytes is the same

; If not, number with more bytes is bigger

        mov     esi, [src]

        mov     edi, [dst]

        mov     ecx, [esi]

        cmp     ecx, [edi]

        jne     .got_answer

; Numbers have equal amount of bytes, compare starting from the high order byte

        add     edi, ecx

        add     esi, ecx

        std

  .do_byte:

        test    ecx, 11b

        jz      .do_dword

        dec     esi

        dec     edi

        cmpsb

        jne     .got_answer

        dec     ecx

        jmp     .do_byte

  .do_dword:

        shr     ecx, 2

        jz      .got_answer

        sub     esi, 4

        sub     edi, 4

        repe cmpsd

  .got_answer:

        cld

        ret

endp

;;===========================================================================;;

proc mpint_mov uses esi edi ecx, dst, src ;//////////////////////////////////;;

;;---------------------------------------------------------------------------;;

;? Copy mpint.                                                               ;;

;;---------------------------------------------------------------------------;;

;> dst = pointer to buffer for little endian MPINT                           ;;

;> src = pointer to little endian MPINT                                      ;;

;;---------------------------------------------------------------------------;;

;< dst = src                                                                 ;;

;;===========================================================================;;

        mov     esi, [src]

        mov     edi, [dst]

        mov     ecx, [esi]

        push    ecx

        shr     ecx, 2

        inc     ecx             ; for length dword

        rep movsd

        pop     ecx

        and     ecx, 11b

        jz      @f

        rep movsb

  @@:

        ret

endp

;;===========================================================================;;

proc mpint_shl1 uses esi ecx, dst ;//////////////////////////////////////////;;

;;---------------------------------------------------------------------------;;

;? Shift little endian MPINT one bit to the left.                            ;;

;;---------------------------------------------------------------------------;;

;> dst = pointer to little endian MPINT                                      ;;

;;---------------------------------------------------------------------------;;

;< dst = dst SHL 1                                                           ;;

;;===========================================================================;;

        mov     esi, [dst]

        mov     ecx, [esi]

        test    ecx, ecx

        jz      .done

; Test if high order byte will overflow

; Remember: highest bit must never be set for positive numbers!

        test    byte[esi+ecx+3], 11000000b

        jz      @f

; We must grow a byte in size!

; TODO: check for overflow

        inc     ecx

        mov     [esi], ecx

        mov     byte[esi+ecx+3], 0        ; Add the new MSB

  @@:

        add     esi, 4

; Do the lowest order byte first

        shl     byte[esi], 1

        dec     ecx

        jz      .done

; And the remaining bytes

  @@:

        inc     esi

        rcl     byte[esi], 1

        dec     ecx

        jnz     @r

  .done:

        ret

endp

;;===========================================================================;;

proc mpint_shr1 uses edi ecx, dst ;//////////////////////////////////////////;;

;;---------------------------------------------------------------------------;;

;? Shift little endian MPINT one bit to the right.                           ;;

;;---------------------------------------------------------------------------;;

;> dst = pointer to little endian MPINT                                      ;;

;;---------------------------------------------------------------------------;;

;< dst = dst SHR 1                                                           ;;

;;===========================================================================;;

        mov     edi, [dst]

        mov     ecx, [edi]

        test    ecx, ecx

        jz      .done

; Do the highest order byte first

        dec     ecx

        shr     byte[edi+ecx+3], 1

; Was it 0? If so, we must decrement total length

        jnz     @f

        jc      @f

        mov     [edi], ecx

  @@:

        test    ecx, ecx

        jz      .done

; Now do the trailing bytes

        add     edi, 4

        add     edi, ecx

  @@:

        dec     edi

        rcr     byte[edi], 1

        dec     ecx             ; does not affect carry flag, hooray!

        jnz     @r

  .done:

        ret

endp

;;===========================================================================;;

proc mpint_shl uses eax ebx ecx edx esi edi, dst, shift ;////////////////////;;

;;---------------------------------------------------------------------------;;

;? Left shift little endian MPINT by x bits.                                 ;;

;;---------------------------------------------------------------------------;;

;> dst = pointer to little endian MPINT                                      ;;

;> shift = number of bits to shift the MPINT                                 ;;

;;---------------------------------------------------------------------------;;

;< -                                                                         ;;

;;===========================================================================;;

        mov     ecx, [shift]

        shr     ecx, 3                  ; 8 bits in one byte

        cmp     ecx, MPINT_MAX_LEN

        jge     .zero

        mov     esi, [dst]

        add     esi, MPINT_MAX_LEN+4-4

        mov     edi, esi

        and     ecx, not 11b

        sub     esi, ecx

        mov     edx, MPINT_MAX_LEN/4-1

        shr     ecx, 2                  ; 4 bytes in one dword

        push    ecx

        sub     edx, ecx

        mov     ecx, [shift]

        and     ecx, 11111b

        std

  .loop:

        lodsd

        mov     ebx, [esi]

        shld    eax, ebx, cl

        stosd

        dec     edx

        jnz     .loop

        lodsd

        shl     eax, cl

        stosd

        ; fill the lsb bytes with zeros

        pop     ecx

        test    ecx, ecx

        jz      @f

        xor     eax, eax

        rep stosd

  @@:

        cld

        ret

  .zero:

        mov     eax, [dst]

        mov     dword[eax], 0

        ret

endp

;;===========================================================================;;

proc mpint_shlmov uses eax ebx ecx edx esi edi, dst, src, shift ;////////////;;

;;---------------------------------------------------------------------------;;

;? Left shift by x bits and copy little endian MPINT.                        ;;

;;---------------------------------------------------------------------------;;

;> src = pointer to little endian MPINT                                      ;;

;> dst = pointer to little endian MPINT                                      ;;

;> shift = number of bits to shift the MPINT to the left                     ;;

;;---------------------------------------------------------------------------;;

;< dst = src SHL shift                                                       ;;

;;===========================================================================;;

        mov     ecx, [shift]

        shr     ecx, 3                  ; 8 bits in one byte

        cmp     ecx, MPINT_MAX_LEN

        jge     .zero

        mov     esi, [src]

        add     esi, MPINT_MAX_LEN+4-4

        mov     edi, [dst]

        add     edi, MPINT_MAX_LEN+4-4

        and     ecx, not 11b

        sub     esi, ecx

        mov     edx, MPINT_MAX_LEN/4-1

        shr     ecx, 2                  ; 4 bytes in one dword

        push    ecx

        sub     edx, ecx

        mov     ecx, [shift]

        and     ecx, 11111b

        std

  .loop:

        lodsd

        mov     ebx, [esi]

        shld    eax, ebx, cl

        stosd

        dec     edx

        jnz     .loop

        lodsd

        shl     eax, cl

        stosd

        ; fill the lsb bytes with zeros

        pop     ecx

        test    ecx, ecx

        jz      @f

        xor     eax, eax

        rep stosd

  @@:

        cld

        ret

  .zero:

        mov     eax, [dst]

        mov     dword[eax], 0

        ret

endp

;;===========================================================================;;

proc mpint_add uses esi edi ecx eax, dst, src ;//////////////////////////////;;

;;---------------------------------------------------------------------------;;

;? Add a little endian MPINT to another little endian MPINT.                 ;;

;;---------------------------------------------------------------------------;;

;> src = pointer to little endian MPINT                                      ;;

;> dst = pointer to little endian MPINT                                      ;;

;;---------------------------------------------------------------------------;;

;< dst = dst + src                                                           ;;

;;===========================================================================;;

        mov     esi, [src]

        mov     edi, [dst]

        mov     ecx, [esi]      ; source number length

        sub     ecx, [dst]

        jbe     .length_ok

; Length of the destination is currently smaller then the source, pad with 0 bytes

        add     edi, [edi]

        add     edi, 4

        mov     al, 0

        rep stosb

  .length_ok:

        mov     ecx, [esi]

        mov     edi, [dst]

        add     esi, 4

        add     edi, 4

; Add the first byte

        lodsb

        add     byte[edi], al

        dec     ecx

        jz      .done

; Add the other bytes

  @@:

        inc     edi

        lodsb

        adc     byte[edi], al

        dec     ecx

        jnz     @r

  .done:

; check if highest bit OR carry flag is set

; if so, add a byte if we have the buffer space

; TODO: check if we have the buffer space

        jc      .carry

        cmp     byte[edi], 0x80

        jnz     .high_bit_set

        ret

  .carry:

        inc     edi

        mov     byte[edi], 1

        mov     eax, [dst]

        inc     dword[eax]

        ret

  .high_bit_set:

        inc     edi

        mov     byte[edi], 0

        mov     eax, [dst]

        inc     dword[eax]

        ret

endp

;;===========================================================================;;

proc mpint_sub uses eax esi edi ecx, dst, src ;//////////////////////////////;;

;;---------------------------------------------------------------------------;;

;? Subtract a little endian MPINT to another little endian MPINT.            ;;

;;---------------------------------------------------------------------------;;

;> src = pointer to little endian MPINT                                      ;;

;> dst = pointer to little endian MPINT                                      ;;

;;---------------------------------------------------------------------------;;

;< dst = dst - src                                                           ;;

;;===========================================================================;;

        mov     esi, [src]

        mov     edi, [dst]

        mov     ecx, [esi]      ; destination number length

        cmp     ecx, [edi]

        ja      .overflow

        add     esi, 4

        add     edi, 4

; Subtract the first byte

        lodsb

        sub     byte[edi], al

        dec     ecx

        jz      .done

; Subtract the other bytes

  @@:

        inc     edi

        lodsb

        sbb     byte[edi], al

        dec     ecx

        jnz     @r

  .done:

        stdcall mpint_shrink, [dst]

        ret

  .overflow:

        mov     dword[edi], 0

        stc

        ret

endp

;;===========================================================================;;

proc mpint_shrink uses eax edi ecx, dst ;////////////////////////////////////;;

;;---------------------------------------------------------------------------;;

;? Get rid of leading zeroes on a little endian MPINT.                       ;;

;;---------------------------------------------------------------------------;;

;> src = pointer to little endian MPINT                                      ;;

;;---------------------------------------------------------------------------;;

;<                                                                           ;;

;;===========================================================================;;

        mov     edi, [dst]

        lodsd

        std

        mov     ecx, eax

        dec     eax             ; total length minus one

        add     edi, eax

        xor     al, al

        repe cmpsb

        inc     ecx

        mov     edi, [dst]

        mov     [edi], ecx

        cld

        ret

endp

;;===========================================================================;;

proc mpint_mul uses esi edi ecx ebx eax, dst, A, B ;/////////////////////////;;

;;---------------------------------------------------------------------------;;

;? Multiply to little endian MPINTS and store them in a new one.             ;;

;;---------------------------------------------------------------------------;;

;> A = pointer to little endian MPINT                                        ;;

;> B = pointer to little endian MPINT                                        ;;

;> dst = pointer to buffer for little endian MPINT                           ;;

;;---------------------------------------------------------------------------;;

;< dst = A * B                                                               ;;

;;===========================================================================;;

        ; Set result to zero

        mov     eax, [dst]

        mov     dword[eax], 0

        ; first, find the byte in A containing the highest order bit

        mov     edi, [A]

        mov     eax, [edi]

        test    eax, eax

        jz      .zero

        add     edi, eax

        mov     al, [edi+1]

        mov     esi, edi

        mov     bl, 8

  @@:

        shl     al, 1

        jc      .first_hit

        dec     bl

        jnz     @r

        ; Then, starting from this byte, iterate through the bits in A,

        ; starting from the highest order bit down to the lowest order bit.

  .next_byte:

        mov     al, [edi]

        dec     edi

        mov     bl, 8

  .next_bit:

        stdcall mpint_shl1, [dst]

        shl     al, 1

        jnc     .zero_bit

  .first_hit:

        stdcall mpint_add, [dst], [B]

  .zero_bit:

        dec     bl

        jnz     .next_bit

        dec     ecx

        jnz     .next_byte

  .zero:

        ret

endp

;;===========================================================================;;

proc mpint_mod uses eax ebx ecx, dst, mod ;//////////////////////////////////;;

;;---------------------------------------------------------------------------;;

;? Find the modulo (remainder after division) of dst by mod.                 ;;

;;---------------------------------------------------------------------------;;

;> dst = pointer to little endian MPINT                                      ;;

;> mod = pointer to little endian MPINT                                      ;;

;;---------------------------------------------------------------------------;;

;< dst = dst MOD mod                                                         ;;

;;===========================================================================;;

locals

        mpint_tmp       rb MPINT_MAX_LEN+4

endl

        ; if mod is zero, return

        mov     eax, [mod]

        cmp     dword[eax], 0

        je      .zero

        stdcall mpint_cmp, eax, [dst]

        jb      .done                           ; if dst < mod, dst = dst

        je      .zero                           ; if dst == mod, dst = 0

        lea     ebx, [mpint_tmp]

        ; left shift mod until the high order bits of mod and dst are aligned

        stdcall mpint_hob, [dst]

        mov     ecx, eax

        stdcall mpint_hob, [mod]

        sub     ecx, eax

        stdcall mpint_shlmov, ebx, [mod], ecx

        inc     ecx

        ; For every bit in dst (starting from the high order bit):

  .loop:

        ;   determine if dst is bigger than mpint_tmp

        stdcall mpint_cmp, [dst], ebx

        ja      @f

        ;   if so, subtract mpint_tmp from dst

        stdcall mpint_sub, [dst], ebx

  @@:

        dec     ecx

        jz      .done

        ;   shift mpint_tmp right by 1

        stdcall mpint_shr1, ebx

        jmp     .loop

  .zero:

        mov     eax, [dst]

        mov     dword[eax], 0

  .done:

        ret

endp

;;===========================================================================;;

proc mpint_modexp uses edi eax ebx ecx edx, dst, base, exp, mod ;////////////;;

;;---------------------------------------------------------------------------;;

;? Find the modulo (remainder after division) of dst by mod.                 ;;

;;---------------------------------------------------------------------------;;

;> dst = pointer to buffer for little endian MPINT                           ;;

;> base = pointer to little endian MPINT                                     ;;

;> exp = pointer to little endian MPINT                                      ;;

;> mod = pointer to little endian MPINT                                      ;;

;;---------------------------------------------------------------------------;;

;< dst = base ** exp MOD mod                                                 ;;

;;===========================================================================;;

locals

        mpint_tmp       rb MPINT_MAX_LEN+4

endl

        ; If mod is zero, return

        mov     eax, [mod]

        cmp     dword[eax], 0

        je      .mod_zero

        ; Find the highest order byte in exponent

        mov     edi, [exp]

        mov     ecx, [edi]

        lea     edi, [edi + 4 + ecx - 1]

        ; Find the highest order bit in this byte

        mov     al, [edi]

        test    al, al

        jz      .invalid

        mov     bl, 9

  @@:

        dec     bl

        shl     al, 1

        jnc     @r

        lea     edx, [mpint_tmp]

        ; Initialise result to base, to take care of the highest order bit

        stdcall mpint_mov, [dst], [base]

        dec     bl

        jz      .next_byte

  .bit_loop:

        ; For each bit, square result

        stdcall mpint_mov, edx, [dst]

        stdcall mpint_mul, [dst], edx, edx

        stdcall mpint_mod, [dst], [mod]

        ; If the bit is set, multiply result by the base

        shl     al, 1

        jnc     .next_bit

        stdcall mpint_mov, edx, [dst]

        stdcall mpint_mul, [dst], [base], edx

        stdcall mpint_mod, [dst], [mod]

  .next_bit:

        dec     bl

        jnz     .bit_loop

  .next_byte:

        dec     ecx

        jz      .done

        dec     edi

        mov     al, [edi]

        mov     bl, 8

        jmp     .bit_loop

  .done:

        ret

  .mod_zero:

        DEBUGF  3, "modexp with modulo 0\n"

        ; if mod is zero, result = 0

        mov     eax, [dst]

        mov     dword[eax], 0

        ret

  .exp_zero:

        DEBUGF  3, "modexp with exponent 0\n"

        ; if exponent is zero, result = 1

        mov     eax, [dst]

        mov     dword[eax], 1

        mov     byte[eax+4], 1

        ret

  .invalid:

        DEBUGF  3, "modexp: Invalid input!\n"

        ret

endp