#ifndef MIRACL_H
#define MIRACL_H
/*
* main MIRACL header - miracl.h.
*
* Copyright (c) 1988-2001 Shamus Software Ltd.
*/
#include "mirdef.h"
#ifdef __ia64__
#if MIRACL==64
#define MR_ITANIUM
#include
#endif
#endif
#ifdef MR_FP
#include
#endif
#ifndef MR_NO_FILE_IO
#include
#endif
/* error returns */
#define MR_ERR_BASE_TOO_BIG 1
#define MR_ERR_DIV_BY_ZERO 2
#define MR_ERR_OVERFLOW 3
#define MR_ERR_NEG_RESULT 4
#define MR_ERR_BAD_FORMAT 5
#define MR_ERR_BAD_BASE 6
#define MR_ERR_BAD_PARAMETERS 7
#define MR_ERR_OUT_OF_MEMORY 8
#define MR_ERR_NEG_ROOT 9
#define MR_ERR_NEG_POWER 10
#define MR_ERR_BAD_ROOT 11
#define MR_ERR_INT_OP 12
#define MR_ERR_FLASH_OVERFLOW 13
#define MR_ERR_TOO_BIG 14
#define MR_ERR_NEG_LOG 15
#define MR_ERR_DOUBLE_FAIL 16
#define MR_ERR_IO_OVERFLOW 17
#define MR_ERR_NO_MIRSYS 18
#define MR_ERR_BAD_MODULUS 19
#define MR_ERR_NO_MODULUS 20
#define MR_ERR_EXP_TOO_BIG 21
#define MR_ERR_NOT_SUPPORTED 22
#define MR_ERR_NOT_DOUBLE_LEN 23
#define MR_ERR_NOT_IRREDUC 24
#define MR_ERR_NO_ROUNDING 25
/* some useful definitions */
#define forever for(;;)
#ifndef TRUE
#define TRUE 1
#endif
#ifndef FALSE
#define FALSE 0
#endif
#define OFF 0
#define ON 1
#define PLUS 1
#define MINUS (-1)
#define MR_MAXDEPTH 24
/* max routine stack depth */
/* big and flash variables consist of an encoded length, *
* and an array of mr_smalls containing the digits */
typedef int BOOL;
#define MR_BYTE unsigned char
#ifdef MR_BITSINCHAR
#if MR_BITSINCHAR == 8
#define MR_TOBYTE(x) ((MR_BYTE)(x))
#else
#define MR_TOBYTE(x) ((MR_BYTE)((x)&0xFF))
#endif
#else
#define MR_TOBYTE(x) ((MR_BYTE)(x))
#endif
#ifdef MR_FP
typedef mr_utype mr_small;
#ifdef mr_dltype
typedef mr_dltype mr_large;
#endif
#define MR_DIV(a,b) (modf((a)/(b),&dres),dres)
#ifdef MR_FP_ROUNDING
/* slightly dicey - the optimizer might remove the MAGIC ! */
#define MR_LROUND(a) ( ( (a) + MR_MAGIC ) - MR_MAGIC )
#else
#define MR_LROUND(a) (modfl((a),&ldres),ldres)
#endif
#define MR_REMAIN(a,b) ((a)-(b)*MR_DIV((a),(b)))
#else
typedef unsigned mr_utype mr_small;
#ifdef mr_dltype
typedef unsigned mr_dltype mr_large;
#endif
#define MR_DIV(a,b) ((a)/(b))
#define MR_REMAIN(a,b) ((a)%(b))
#define MR_LROUND(a) ((a))
#endif
struct bigtype
{
mr_unsign32 len;
mr_small *w;
};
typedef struct bigtype *big;
typedef big zzn;
/* Macro to create big x on the stack - x_t and x_g must be distinct variables
By convention use like this. See brute.c and identity.c for examples
BIG(x,x_t,x_g,10)
BIG(y,y_t,y_g,10)
*/
#define BIG(x,xt,xg,s) mr_small xg[s]; struct bigtype xt={s,xg}; big x=&xt;
typedef big flash;
#define MR_MSBIT ((mr_unsign32)1<<31)
#define MR_OBITS (MR_MSBIT-1)
#if MIRACL >= MR_IBITS
#define MR_TOOBIG (1<<(MR_IBITS-2))
#else
#define MR_TOOBIG (1<<(MIRACL-1))
#endif
#ifdef MR_FLASH
#define MR_EBITS (8*sizeof(double) - MR_FLASH)
/* no of Bits per double exponent */
#define MR_BTS 16
#define MR_MSK 0xFFFF
#endif
#define MR_HASH_BYTES 20
/* Marsaglia & Zaman Random number generator */
/* constants alternatives */
#define NK 37 /* 21 */
#define NJ 24 /* 6 */
#define NV 14 /* 8 */
#ifdef MR_LITTLE_ENDIAN
#define MR_TOP(x) (*(((mr_small *)&(x))+1))
#define MR_BOT(x) (*(((mr_small *)&(x))))
#endif
#ifdef MR_BIG_ENDIAN
#define MR_TOP(x) (*(((mr_small *)&(x))))
#define MR_BOT(x) (*(((mr_small *)&(x))+1))
#endif
/* chinese remainder theorem structures */
typedef struct {
big *C;
big *V;
big *M;
int NP;
} big_chinese;
typedef struct {
mr_utype *C;
mr_utype *V;
mr_utype *M;
int NP;
} small_chinese;
/* Cryptographically strong pseudo-random number generator */
typedef struct {
mr_unsign32 ira[NK]; /* random number... */
int rndptr; /* ...array & pointer */
mr_unsign32 borrow;
int pool_ptr;
char pool[MR_HASH_BYTES]; /* random pool */
} csprng;
/* secure hash Algorithm structure */
typedef struct {
mr_unsign32 length[2];
mr_unsign32 h[8];
mr_unsign32 w[80];
} sha256;
typedef sha256 sha;
#ifdef mr_unsign64
typedef struct {
mr_unsign64 length[2];
mr_unsign64 h[8];
mr_unsign64 w[80];
} sha512;
typedef sha512 sha384;
#endif
/* advanced encryption algorithm structure */
#define MR_ECB 0
#define MR_CBC 1
#define MR_CFB1 2
#define MR_CFB2 3
#define MR_CFB4 5
#define MR_PCFB1 10
#define MR_PCFB2 11
#define MR_PCFB4 13
#define MR_OFB1 14
#define MR_OFB2 15
#define MR_OFB4 17
#define MR_OFB8 21
#define MR_OFB16 29
typedef struct {
int Nk,Nr;
int mode;
mr_unsign32 fkey[60];
mr_unsign32 rkey[60];
char f[16];
} aes;
/* Elliptic curve point status */
#define MR_EPOINT_GENERAL 0
#define MR_EPOINT_NORMALIZED 1
#define MR_EPOINT_INFINITY 2
#define MR_PROJECTIVE 0
#define MR_AFFINE 1
/* Elliptic Curve epoint structure. Uses projective (X,Y,Z) co-ordinates */
typedef struct {
big X;
big Y;
big Z;
int marker;
} epoint;
/* Structure for Brickell method for finite *
field exponentiation with precomputation */
typedef struct {
big *table;
big n;
int base;
int store;
} brick;
/* Structure for Brickell method for elliptic *
curve exponentiation with precomputation */
typedef struct {
epoint **table;
big a,b,n;
int base;
int store;
} ebrick;
typedef struct {
epoint **table;
big a6,a2;
int m,a,b,c;
int base;
int store;
} ebrick2;
/* main MIRACL instance structure */
typedef struct {
mr_small base; /* number base */
mr_small apbase; /* apparent base */
int pack; /* packing density */
int lg2b; /* bits in base */
mr_small base2; /* 2^mr_lg2b */
BOOL (*user)(void); /* pointer to user supplied function */
int nib; /* length of bigs */
int depth; /* error tracing ..*/
int trace[MR_MAXDEPTH]; /* .. mechanism */
BOOL check; /* overflow check */
BOOL fout; /* Output to file */
BOOL fin; /* Input from file */
BOOL active;
#ifndef MR_NO_FILE_IO
FILE *infile; /* Input file */
FILE *otfile; /* Output file */
#endif
mr_unsign32 ira[NK]; /* random number... */
int rndptr; /* ...array & pointer */
mr_unsign32 borrow;
/* Montgomery constants */
mr_small ndash;
big modulus;
BOOL ACTIVE;
BOOL MONTY;
/* Elliptic Curve details */
BOOL SS; /* True for Super-Singular */
big A,B,C;
int coord,Asize,Bsize;
int M,AA,BB,CC; /* for GF(2^m) curves */
int logN; /* constants for fast fourier fft multiplication */
int nprimes,degree;
mr_utype *prime,*cr;
mr_utype *inverse,**roots;
small_chinese chin;
mr_utype const1,const2,const3;
mr_small msw,lsw;
mr_utype **s1,**s2; /* pre-computed tables for polynomial reduction */
mr_utype **t; /* workspace */
mr_utype *wa;
mr_utype *wb;
mr_utype *wc;
BOOL same;
BOOL first_one;
BOOL debug;
big w0; /* workspace bigs */
big w1,w2,w3,w4;
big w5,w6,w7;
big w8,w9,w10,w11;
big w12,w13,w14,w15;
big w16,w17,w18;
/* User modifiables */
char *IOBUFF; /* i/o buffer */
int IOBSIZ; /* size of i/o buffer */
BOOL ERCON; /* error control */
int ERNUM; /* last error code */
int NTRY; /* no. of tries for probablistic primality testing */
int IOBASE; /* base for input and output */
BOOL EXACT; /* exact flag */
BOOL RPOINT; /* =ON for radix point, =OFF for fractions in output */
BOOL TRACER; /* turns trace tracker on/off */
int INPLEN; /* input length */
int *PRIMES; /* small primes array */
#ifdef MR_FLASH
int workprec;
int stprec; /* start precision */
int RS,RD;
double D;
double db,n,p;
int a,b,c,d,r,q,oldn,ndig;
mr_small u,v,ku,kv;
BOOL last,carryon;
flash pi;
#endif
#ifdef MR_KCM
big big_ndash;
big ws;
#endif
#ifdef MR_FP_ROUNDING
mr_large inverse_base;
#endif
int size;
char *workspace;
} miracl;
#ifndef MR_GENERIC_MT
#ifdef MR_WINDOWS_MT
#define MR_OS_THREADS
#endif
#ifdef MR_UNIX_MT
#define MR_OS_THREADS
#endif
#ifndef MR_OS_THREADS
extern miracl *mr_mip; /* pointer to MIRACL's only global variable */
#endif
#endif
#ifdef MR_GENERIC_MT
#define _MIPT_ miracl *,
#define _MIPTO_ miracl *
#define _MIPD_ miracl *mr_mip,
#define _MIPDO_ miracl *mr_mip
#define _MIPP_ mr_mip,
#define _MIPPO_ mr_mip
#else
#define _MIPT_
#define _MIPTO_ void
#define _MIPD_
#define _MIPDO_ void
#define _MIPP_
#define _MIPPO_
#endif
/* Preamble and exit code for MIRACL routines. *
* Not used if MR_STRIPPED_DOWN is defined */
#ifdef MR_STRIPPED_DOWN
#define MR_OUT
#define MR_IN(N)
#else
#define MR_OUT mr_mip->depth--;
#define MR_IN(N) mr_mip->depth++; if (mr_mip->depthtrace[mr_mip->depth]=(N); if (mr_mip->TRACER) mr_track(_MIPPO_); }
#endif
/* Function definitions */
/* Group 0 - Internal routines */
extern void mr_berror(_MIPT_ int);
extern mr_small mr_shiftbits(mr_small,int);
extern mr_small mr_setbase(_MIPT_ mr_small);
extern void mr_track(_MIPTO_ );
extern void mr_lzero(big);
extern BOOL mr_notint(flash);
extern int mr_lent(flash);
extern void mr_padd(_MIPT_ big,big,big);
extern void mr_psub(_MIPT_ big,big,big);
extern void mr_pmul(_MIPT_ big,mr_small,big);
#ifdef MR_FP_ROUNDING
extern mr_large mr_invert(mr_small);
extern mr_small imuldiv(mr_small,mr_small,mr_small,mr_small,mr_large,mr_small *);
extern mr_small mr_sdiv(_MIPT_ big,mr_small,mr_large,big);
#else
extern mr_small mr_sdiv(_MIPT_ big,mr_small,big);
#endif
extern void mr_shift(_MIPT_ big,int,big);
extern miracl *mr_first_alloc(void);
extern void *mr_alloc(_MIPT_ int,int);
extern void mr_free(void *);
extern void set_user_function(_MIPT_ BOOL (*)(void));
extern void set_io_buffer_size(_MIPT_ int);
extern int mr_testbit(_MIPT_ big,int);
extern int mr_window(_MIPT_ big,int,int *,int *);
extern int mr_window2(_MIPT_ big,big,int,int *,int *);
extern int mr_naf_window(_MIPT_ big,big,int,int *,int *);
extern int mr_fft_init(_MIPT_ int,big,big,BOOL);
extern void mr_dif_fft(_MIPT_ int,int,mr_utype *);
extern void mr_dit_fft(_MIPT_ int,int,mr_utype *);
extern void fft_reset(_MIPTO_);
extern int mr_poly_mul(_MIPT_ int,big*,int,big*,big*);
extern int mr_poly_sqr(_MIPT_ int,big*,big*);
extern void mr_polymod_set(_MIPT_ int,big*,big*);
extern int mr_poly_rem(_MIPT_ int,big *,big *);
extern int mr_ps_big_mul(_MIPT_ int,big *,big *,big *);
extern int mr_ps_zzn_mul(_MIPT_ int,big *,big *,big *);
extern mr_small muldiv(mr_small,mr_small,mr_small,mr_small,mr_small *);
extern mr_small muldvm(mr_small,mr_small,mr_small,mr_small *);
extern mr_small muldvd(mr_small,mr_small,mr_small,mr_small *);
extern void muldvd2(mr_small,mr_small,mr_small *,mr_small *);
/* Group 1 - General purpose, I/O and basic arithmetic routines */
/*
function: 返回两个整数的最大公约数
*/
extern int igcd(int x,int y);
extern mr_small sgcd(mr_small,mr_small);
extern int isqrt(int,int);
extern void irand(_MIPT_ mr_unsign32);
extern mr_small brand(_MIPTO_ );
extern void zero(flash);
/*
function: 将一个整数n转换成一个大数x
*/
extern void convert(_MIPT_ int n,big x);
extern void lgconv(_MIPT_ long,big);
/*
function: 释放内存大数所占的内存
*/
extern flash mirvar(_MIPT_ int);
extern flash mirvar_mem(_MIPT_ char *,int);
/*
function: 释放内存大数所占的内存
*/
extern void mirkill(big x);
extern void *memalloc(_MIPT_ int);
extern void memkill(_MIPT_ char *,int);
extern void mr_init_threading(void);
extern void mr_end_threading(void);
extern miracl *get_mip(_MIPTO_ );
/*
function:初始化MIRACL系统，该函数必须在调用MIRACL库函数之前先执行
Example: miracl *mip=mirsys(500,10);//初始化500位的10进行制数
*/
extern miracl *mirsys(int nd,mr_small nb);
/*
function: 清除MIRACL系统，释放所有内部变量
*/
extern void mirexit(_MIPTO_ );
extern int exsign(flash);
extern void insign(int,flash);
extern int getdig(_MIPT_ big,int);
/*
function:返回大数x中数字的个数
*/
extern int numdig(_MIPT_ big);
extern void putdig(_MIPT_ int,big,int);
/*
function: 将一个大数赋值给另一个大数，y=x
*/
extern void copy(flash x,flash y);
/*
function: 大数取负号，y=-x.
*/
extern void negify(flash x,flash y);
/*
function: 取x的绝对值，y=|x|
*/
extern void absol(flash x,flash y);
extern int size(big);
/*
function: 比较两个大数的大小
return: x>y时返回+1
x=y时返回0
xIOBASE=16;
cinstr(x,"AF12398065BFE4C96DB723A");
*/
extern int cinstr(_MIPT_ flash x,char *s);
/*
function: 将一个大数根据其进制转换成一个字符串
return: 字符串长度
*/
extern int cotstr(_MIPT_ flash,char *);
#ifndef MR_NO_FILE_IO
extern int innum(_MIPT_ flash,FILE *);
extern int otnum(_MIPT_ flash,FILE *);
extern int cinnum(_MIPT_ flash,FILE *);
/*
function: 输出到屏幕
exapmle: std::cout<<"d=";
cotnum(d, stdout);
*/
extern int cotnum(_MIPT_ flash,FILE *);
#endif
/* Group 2 - Advanced arithmetic routines */
extern mr_small smul(mr_small,mr_small,mr_small);
extern mr_small spmd(mr_small,mr_small,mr_small);
/*
function: 计算两个无符号整数（要求互素）的模逆，返回[x^(-1) mod y]
return: 字符串长度
*/
extern mr_small invers(mr_small x,mr_small y);
extern mr_small sqrmp(mr_small,mr_small);
extern int jac(mr_small,mr_small);
extern void gprime(_MIPT_ int);
extern int jack(_MIPT_ big,big);
/*
function: 计算两个大数的最大公约数，z=gcd(x,y)
*/
extern int egcd(_MIPT_ big x,big y,big z);
/*
function: 计算两个大数的扩展最大公约数，也可以用来计算模逆，这个函数比mad 函数运算速度稍慢。z=gcd(x,y)=x.xd+y.yd
Example: xgcd(x,p,x,x,x); //计算x^-1 mod p
x = 1/x mod p (p is prime)
*/
extern int xgcd(_MIPT_ big x,big y,big xd,big yd,big z);
extern int logb2(_MIPT_ big);
/*
function: 计算2的n次方的大数
Example: expb2(1398269,x); //2^1398269
decr(x,1,x); //x = x - 1
mip->IOBASE=10; //使用10进制
cotnum(x,stdout); //输出到屏幕
This calculates and prints out the largest known primenumber (on a true 32-bit computer with lots of memory!)
*/
extern void expb2(int n, big x);
/*
function:计算b的n次方的大数
*/
extern void expint(_MIPT_ int b,int n,big x);
/*
function:将一个大数左移或右移n位，n为正数时左移，负数时右移
*/
extern void sftbit(_MIPT_ big x,int n,big z);
extern void power(_MIPT_ big,long,big,big);
/*
模幂运算，w=x^y mod z
*/
extern void powmod(_MIPT_ big x,big y,big z,big w);
extern void powmod2(_MIPT_ big,big,big,big,big,big);
extern void powmodn(_MIPT_ int,big *,big *,big,big);
extern int powltr(_MIPT_ int,big,big,big);
extern BOOL double_inverse(_MIPT_ big,big,big,big,big);
extern BOOL multi_inverse(_MIPT_ int,big*,big,big*);
extern void lucas(_MIPT_ big,big,big,big,big);
extern BOOL nroot(_MIPT_ big,int,big);
extern BOOL sqroot(_MIPT_ big,big,big);
/*
function: 使用内置的随机数发生器，产生一个小于w的大数随机数，x generates 8086 inline assembly
#define INLINE_ASM 2 -> generates mixed 8086 & 80386 inline assembly,
so you can get some benefit while running in a
16-bit environment on 32-bit hardware (DOS, Windows
3.1...)
#define INLINE_ASM 3 -> generate true 80386 inline assembly - (Using DOS
extender, Windows '95/Windows NT)
Actually optimised for Pentium
#define INLINE_ASM 4 -> 80386 code in the GNU style (for (DJGPP)
Small, medium, compact and large memory models are supported for the
first two of the above.
*/
#ifndef MR_NOASM
/* Itanium - inline the time-critical functions */
#ifdef MR_ITANIUM
#define muldvd(a,b,c,rp) (tm=_m64_xmahu((a),(b),(c)),*(rp)=_m64_xmalu((a),(b),(c)),tm)
#define muldvd2(a,b,c,rp) (tm=_m64_xmalu((a),(b),(*(c))),*(c)=_m64_xmahu((a),(b),(*(c))),tm+=*(rp),*(c)+=(tm<*(rp)),*(rp)=tm)
#endif
/* Borland C/Turbo C */
#ifdef __TURBOC__
#ifndef __HUGE__
#define ASM asm
#if defined(__COMPACT__) || defined(__LARGE__)
#define MR_LMM
#endif
#if MIRACL==16
#define INLINE_ASM 1
#endif
#if __TURBOC__>=0x410
#if MIRACL==32
#if defined(__SMALL__) || defined(__MEDIUM__) || defined(__LARGE__) || defined(__COMPACT__)
#define INLINE_ASM 2
#else
#define INLINE_ASM 3
#endif
#endif
#endif
#endif
#endif
/* Microsoft C */
#ifdef _MSC_VER
#ifndef M_I86HM
#define ASM _asm
#if defined(M_I86CM) || defined(M_I86LM)
#define MR_LMM
#endif
#if _MSC_VER>=600
#if MIRACL==16
#define INLINE_ASM 1
#endif
#endif
#if _MSC_VER>=1000
#if MIRACL==32
#define INLINE_ASM 3
#endif
#endif
#endif
#endif
/* DJGPP GNU C */
#ifdef __GNUC__
#ifdef i386
#define ASM __asm__ __volatile__
#if MIRACL==32
#define INLINE_ASM 4
#endif
#endif
#endif
#endif
/*
The following contribution is from Tielo Jongmans, Netherlands
These inline assembler routines are suitable for Watcom 10.0 and up
Added into miracl.h. Notice the override of the original declarations
of these routines, which should be removed.
The following pragma is optional, it is dangerous, but it saves a
calling sequence
*/
/*
#pragma off (check_stack);
extern unsigned int muldiv(unsigned int, unsigned int, unsigned int, unsigned int, unsigned int *);
#pragma aux muldiv= \
"mul edx" \
"add eax,ebx" \
"adc edx,0" \
"div ecx" \
"mov [esi],edx" \
parm [eax] [edx] [ebx] [ecx] [esi] \
value [eax] \
modify [eax edx];
extern unsigned int muldvm(unsigned int, unsigned int, unsigned int, unsigned int *);
#pragma aux muldvm= \
"div ebx" \
"mov [ecx],edx" \
parm [edx] [eax] [ebx] [ecx] \
value [eax] \
modify [eax edx];
extern unsigned int muldvd(unsigned int, unsigned int, unsigned int, unsigned int *);
#pragma aux muldvd= \
"mul edx" \
"add eax,ebx" \
"adc edx,0" \
"mov [ecx],eax" \
"mov eax,edx" \
parm [eax] [edx] [ebx] [ecx] \
value [eax] \
modify [eax edx];
*/
#endif
