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SecuDe是一个由安全应用程序接口组成,对验证机制、证件处理、PEM、X.400报文处理和密钥管理提供支持。SecuDe提供DES、 RSA杂凑函数、密钥生成以及数字签名的生成和核实等多种密码机制。

#
#    Copyright (C) 1991, GMD Darmstadt
#
#                         NOTICE
#
#    Acquisition, use, and distribution of this module 
#    and related materials are subject to restrictions 
#    mentioned in each volume of the documentation.
#

Arithmetic Package for Long Integers
====================================

this package implements an arithmetic on long integer numbers. It includes
the following modules:

interface.h:	- interface definitions and useful macros

lnutil.c	- some functions for machine independent conversions between
		  external and internal representations of long numbers.

bool.c		- boolean functions on long integers (XOR)

comp.c		- logical functions on long integers (compare)

modarit.c	- the modulus arithmetic on long integers (madd, msub, mmult,
		  mdiv, mexp, mexp2)

and machine architecture and system dependent directories which implement
the basic interface for the arithmetic on long integers:

std		- standard "C" interface which should work on any computer, (but
		  slow)
mc68apollo	- apollo workstation (SysV, mc68xxx)
mc68munix	- pcs cadmus (SysV, mc68xxx)
mc68sun		- Sun-3 (SunOS, mc68xxx)
sparc		- Sun-4 (SunOS, SPARC)
ms-dos		- ibm-pc (DOS, intel)
sun386		- Sun386 (SunOS, 80386)

representation of long integers:
--------------------------------

external:	the external representation of long integers follows the
		definition of ASN.1 Basic Encoding Rules (ISO8425). I.e.
		integers are represented in either octet or bit strings
		with high order bits/octets first.

internal:	a long integer can be viewed from C program language as
		struct long_integer {
			unsigned int	len;
			unsigned int	val[MAXLGTH];
		};
		len defines the number of words used for representing the
		long integer in the array val[]. The integer value '0' is
		represented as (len==0). The least significant word is stored
		first.


interface.h:
------------
needs the compile definition WLNGxx (xx one of {16,32}) wordsize in bits

MAXLGTH		- const value of the standard long integer size in words.
MAXGENL		- const value of the long integer size for rsa key pair
		  generation
WLNG		- the word size in bits (derived from WLNGxx)
WBYTES		- the number of bytes in a word
SWBYTES		- the shift size to get the number of bytes from number of words
SWBITS		- the shift size to get the number of bits from number of words
HSBIT		- highest significant bit mask
HSBYTE		- highest significant byte mask
L_NUMBER	- typedef struct long integer (s.a.)
LZ_EINS		- long integer value 1
LZ_ZWEI		- long integer value 2
LZ_FERMAT5	- long integer value 5th fermat number (F4=2^2^4)
trans(S,D)	- assignment of long integers (D:=S)
normalize(L)	- normalize long integer (reduce leading zero words)
inttoln(i,L)	- produce long integer from integer
lntoint(L)	- high significant word of L
lngofln(L)	- word count of long integer
lntoINTEGER(L,I)- store long integer in an octetstring
INTEGERtoln(I,L)- load long integer from octetstring



lnutil:
-------

lngtouse(L)	- (int) function which gives the useable bitsize of a long
		  integer

intlog2(L)	- (int) function which gives the integer part of the logarithm
		  base 2 of L

bitstoln(B,L,off,bits) - extracts from a given bitstring B the bits from offset
		  off with size bits and loads it into the long integer L

lntobits(L,B,bits) - appends the contents of the long integer L to the bitstring
		  B with almost size bits and stripping high order bits resp
		  expanding to size bits

octetstoln(O,L,off,octs) - extracts from a given octetstring O the octets from
		  offset off with size octs and loads it into the long integer L

lntoctets(L,O,octs) - appends the contents of the long integer L to the
		  octetstring O with almost size octs and stripping high order
		  octets resp expanding to size octs

lz_eins		- the long integer of value 1
lz_zwei		- the long integer of value 2
lz_fermat5	- the long integer of value F4



bool.c:
-------

xor(A,B,X)	- the logical exclusive or on two long integers A, B gives
		  result long integer X


comp.c:
-------

comp(A,B)	- (int) function signum(ABS(A-B))



modarit.c:
----------

madd(A,B,S,N)	- addition of two long integers A, B modulo long integer N gives
		  result long integer S

msub(A,B,D,N)	- subtraction of two long integers A, B modulo long integer N
		  gives result long integer D

mmult(A,B,P,N)	- multiplication of two long integers A, B modulo long integer N
		  gives result long integer P

mdiv(A,B,Q,N)	- division of two long integers A, B modulo long integer N gives
		  result long integer Q

mexp(B, P, X, N)- exponentiation of long integer base B to the power of long
		  integer P modulo long integer N gives result long integer X

mexp2(P, X, N)	- equivalent procedure as mexp(lz_zwei,P,X,N)



basic arithmetic: (std)
-----------------

add(A,B,S)	- addition of long integers A, B gives result long integer S

sub(A,B,D)	- subtraction of long integers A, B gives result long integer D
		  the result is undefined if B>A

mult(A,B,P)	- multiplication of long integers A, B gives result long integer
		  P

div(A,B,Q,R)	- division of long integers A, B gives long integer quotient Q
		  and residual long integer R; if R is equivalent to Q only
		  the residual is returned

shift(A,s,X)	- shifts long integer A by s bits (left if s>0, right if s<0)
		  and gives result X