nn.c

加密算法源代码DES&RSA

#include "rsa_incl.h"
#include "nn.h"

/* internal static functions */

static NN_DIGIT subdigitmult PROTO_LIST
	((NN_DIGIT *, NN_DIGIT *, NN_DIGIT, NN_DIGIT *, unsigned int));

static void dmult PROTO_LIST ((NN_DIGIT, NN_DIGIT, NN_DIGIT *, NN_DIGIT *));

static unsigned int NN_DigitBits PROTO_LIST ((NN_DIGIT));

#ifndef USEASM
/* Decodes character string b into a, where character string is ordered
	 from most to least significant.

	 Lengths: a[digits], b[len].
	 Assumes b[i] = 0 for i < len - digits * NN_DIGIT_LEN. (Otherwise most
	 significant bytes are truncated.)
 */
void NN_Decode (a, digits, b, len)
NN_DIGIT *a;
unsigned char *b;
unsigned int digits, len;
{
  NN_DIGIT t;
  unsigned int i, u;
  int j;
  
            /* @##$ unsigned/signed bug fix added JSAK - Fri  31/05/96 18:09:11 */
  for (i = 0, j = len - 1; i < digits && j >= 0; i++) {
    t = 0;
    for (u = 0; j >= 0 && u < NN_DIGIT_BITS; j--, u += 8)
			t |= ((NN_DIGIT)b[j]) << u;
		a[i] = t;
  }
  
  for (; i < digits; i++)
    a[i] = 0;
}

/* Encodes b into character string a, where character string is ordered
   from most to least significant.

	 Lengths: a[len], b[digits].
	 Assumes NN_Bits (b, digits) <= 8 * len. (Otherwise most significant
	 digits are truncated.)
 */
void NN_Encode (a, len, b, digits)
NN_DIGIT *b;
unsigned char *a;
unsigned int digits, len;
{
	NN_DIGIT t;
    unsigned int i, u;
    int j;

            /* @##$ unsigned/signed bug fix added JSAK - Fri  31/05/96 18:09:11 */
    for (i = 0, j = len - 1; i < digits && j >= 0; i++) {
		t = b[i];
        for (u = 0; j >= 0 && u < NN_DIGIT_BITS; j--, u += 8)
			a[j] = (unsigned char)(t >> u);
	}

    for (; j >= 0; j--)
		a[j] = 0;
}

/* Assigns a = 0. */

void NN_AssignZero (a, digits)
NN_DIGIT *a;
unsigned int digits;
{
	if(digits) {
		do {
			*a++ = 0;
		}while(--digits);
	}
}

#endif

/* Assigns a = 2^b.

   Lengths: a[digits].
	 Requires b < digits * NN_DIGIT_BITS.
 */
void NN_Assign2Exp (a, b, digits)
NN_DIGIT *a;
unsigned int b, digits;
{
  NN_AssignZero (a, digits);

	if (b >= digits * NN_DIGIT_BITS)
    return;

  a[b / NN_DIGIT_BITS] = (NN_DIGIT)1 << (b % NN_DIGIT_BITS);
}

/* Computes a = b - c. Returns borrow.

	 Lengths: a[digits], b[digits], c[digits].
 */
NN_DIGIT NN_Sub (a, b, c, digits)
NN_DIGIT *a, *b, *c;
unsigned int digits;
{
	NN_DIGIT temp, borrow = 0;

	if(digits)
		do {
            /* Bug fix 16/10/95 - JSK, code below removed, caused bug with
               Sun Compiler SC4.

			if((temp = (*b++) - borrow) == MAX_NN_DIGIT)
                temp = MAX_NN_DIGIT - *c++;
            */

            temp = *b - borrow;
            b++;
            if(temp == MAX_NN_DIGIT) {
                temp = MAX_NN_DIGIT - *c;
                c++;
            }else {      /* Patch to prevent bug for Sun CC */
                if((temp -= *c) > (MAX_NN_DIGIT - *c))
					borrow = 1;
				else
					borrow = 0;
                c++;
            }
			*a++ = temp;
		}while(--digits);

	return(borrow);
}

/* Computes a = b * c.

	 Lengths: a[2*digits], b[digits], c[digits].
	 Assumes digits < MAX_NN_DIGITS.
*/

void NN_Mult (a, b, c, digits)
NN_DIGIT *a, *b, *c;
unsigned int digits;
{
	NN_DIGIT t[2*MAX_NN_DIGITS];
	NN_DIGIT dhigh, dlow, carry;
	unsigned int bDigits, cDigits, i, j;

	NN_AssignZero (t, 2 * digits);

	bDigits = NN_Digits (b, digits);
	cDigits = NN_Digits (c, digits);

	for (i = 0; i < bDigits; i++) {
		carry = 0;
		if(*(b+i) != 0) {
			for(j = 0; j < cDigits; j++) {
				dmult(*(b+i), *(c+j), &dhigh, &dlow);
				if((*(t+(i+j)) = *(t+(i+j)) + carry) < carry)
					carry = 1;
				else
					carry = 0;
				if((*(t+(i+j)) += dlow) < dlow)
					carry++;
				carry += dhigh;
			}
		}
		*(t+(i+cDigits)) += carry;
	}


	NN_Assign(a, t, 2 * digits);
}

/* Computes a = b * 2^c (i.e., shifts left c bits), returning carry.

	 Requires c < NN_DIGIT_BITS. */

NN_DIGIT NN_LShift (a, b, c, digits)
NN_DIGIT *a, *b;
unsigned int c, digits;
{
	NN_DIGIT temp, carry = 0;
	unsigned int t;

	if(c < NN_DIGIT_BITS)
		if(digits) {

			t = NN_DIGIT_BITS - c;

			do {
				temp = *b++;
				*a++ = (temp << c) | carry;
				carry = c ? (temp >> t) : 0;
			}while(--digits);
		}

	return (carry);
}

/* Computes a = c div 2^c (i.e., shifts right c bits), returning carry.

	 Requires: c < NN_DIGIT_BITS. */

NN_DIGIT NN_RShift (a, b, c, digits)
NN_DIGIT *a, *b;
unsigned int c, digits;
{
	NN_DIGIT temp, carry = 0;
	unsigned int t;

	if(c < NN_DIGIT_BITS)
		if(digits) {

			t = NN_DIGIT_BITS - c;

			do {
				digits--;
				temp = *(b+digits);
				*(a+digits) = (temp >> c) | carry;
				carry = c ? (temp << t) : 0;
			}while(digits);
		}

	return (carry);
}

/* Computes a = c div d and b = c mod d.

	 Lengths: a[cDigits], b[dDigits], c[cDigits], d[dDigits].
	 Assumes d > 0, cDigits < 2 * MAX_NN_DIGITS,
					 dDigits < MAX_NN_DIGITS.
*/

void NN_Div (a, b, c, cDigits, d, dDigits)
NN_DIGIT *a, *b, *c, *d;
unsigned int cDigits, dDigits;
{
	NN_DIGIT ai, cc[2*MAX_NN_DIGITS+1], dd[MAX_NN_DIGITS], s;
	NN_DIGIT t[2], u, v, *ccptr;
	NN_HALF_DIGIT aHigh, aLow, cHigh, cLow;
	int i;
	unsigned int ddDigits, shift;

	ddDigits = NN_Digits (d, dDigits);
	if(ddDigits == 0)
		return;

	shift = NN_DIGIT_BITS - NN_DigitBits (d[ddDigits-1]);
	NN_AssignZero (cc, ddDigits);
	cc[cDigits] = NN_LShift (cc, c, shift, cDigits);
	NN_LShift (dd, d, shift, ddDigits);
	s = dd[ddDigits-1];

	NN_AssignZero (a, cDigits);

	for (i = cDigits-ddDigits; i >= 0; i--) {
		if (s == MAX_NN_DIGIT)
			ai = cc[i+ddDigits];
		else {
			ccptr = &cc[i+ddDigits-1];

			s++;
			cHigh = (NN_HALF_DIGIT)HIGH_HALF (s);
			cLow = (NN_HALF_DIGIT)LOW_HALF (s);

			*t = *ccptr;
			*(t+1) = *(ccptr+1);

			if (cHigh == MAX_NN_HALF_DIGIT)
				aHigh = (NN_HALF_DIGIT)HIGH_HALF (*(t+1));
			else
				aHigh = (NN_HALF_DIGIT)(*(t+1) / (cHigh + 1));
			u = (NN_DIGIT)aHigh * (NN_DIGIT)cLow;
			v = (NN_DIGIT)aHigh * (NN_DIGIT)cHigh;
			if ((*t -= TO_HIGH_HALF (u)) > (MAX_NN_DIGIT - TO_HIGH_HALF (u)))
				t[1]--;
			*(t+1) -= HIGH_HALF (u);
			*(t+1) -= v;

			while ((*(t+1) > cHigh) ||
						 ((*(t+1) == cHigh) && (*t >= TO_HIGH_HALF (cLow)))) {
				if ((*t -= TO_HIGH_HALF (cLow)) > MAX_NN_DIGIT - TO_HIGH_HALF (cLow))
					t[1]--;
				*(t+1) -= cHigh;
				aHigh++;
			}

			if (cHigh == MAX_NN_HALF_DIGIT)
				aLow = (NN_HALF_DIGIT)LOW_HALF (*(t+1));
			else
				aLow =
			(NN_HALF_DIGIT)((TO_HIGH_HALF (*(t+1)) + HIGH_HALF (*t)) / (cHigh + 1));
			u = (NN_DIGIT)aLow * (NN_DIGIT)cLow;
			v = (NN_DIGIT)aLow * (NN_DIGIT)cHigh;
			if ((*t -= u) > (MAX_NN_DIGIT - u))
				t[1]--;
			if ((*t -= TO_HIGH_HALF (v)) > (MAX_NN_DIGIT - TO_HIGH_HALF (v)))
				t[1]--;
			*(t+1) -= HIGH_HALF (v);

			while ((*(t+1) > 0) || ((*(t+1) == 0) && *t >= s)) {
				if ((*t -= s) > (MAX_NN_DIGIT - s))
					t[1]--;
				aLow++;
			}

			ai = TO_HIGH_HALF (aHigh) + aLow;
			s--;
		}

		cc[i+ddDigits] -= subdigitmult(&cc[i], &cc[i], ai, dd, ddDigits);

		while (cc[i+ddDigits] || (NN_Cmp (&cc[i], dd, ddDigits) >= 0)) {
			ai++;
			cc[i+ddDigits] -= NN_Sub (&cc[i], &cc[i], dd, ddDigits);
		}

		a[i] = ai;
	}

	NN_AssignZero (b, dDigits);
	NN_RShift (b, cc, shift, ddDigits);
}


/* Computes a = b mod c.

	 Lengths: a[cDigits], b[bDigits], c[cDigits].
	 Assumes c > 0, bDigits < 2 * MAX_NN_DIGITS, cDigits < MAX_NN_DIGITS.
*/
void NN_Mod (a, b, bDigits, c, cDigits)
NN_DIGIT *a, *b, *c;
unsigned int bDigits, cDigits;
{
    NN_DIGIT t[2 * MAX_NN_DIGITS];
  
	NN_Div (t, a, b, bDigits, c, cDigits);
}

/* Computes a = b * c mod d.

   Lengths: a[digits], b[digits], c[digits], d[digits].
   Assumes d > 0, digits < MAX_NN_DIGITS.
 */
void NN_ModMult (a, b, c, d, digits)
NN_DIGIT *a, *b, *c, *d;
unsigned int digits;
{
    NN_DIGIT t[2*MAX_NN_DIGITS];

	NN_Mult (t, b, c, digits);
    NN_Mod (a, t, 2 * digits, d, digits);
}

/* Computes a = b^c mod d.

   Lengths: a[dDigits], b[dDigits], c[cDigits], d[dDigits].
	 Assumes d > 0, cDigits > 0, dDigits < MAX_NN_DIGITS.
 */
void NN_ModExp (a, b, c, cDigits, d, dDigits)
NN_DIGIT *a, *b, *c, *d;
unsigned int cDigits, dDigits;
{
    NN_DIGIT bPower[3][MAX_NN_DIGITS], ci, t[MAX_NN_DIGITS];
    int i;
	unsigned int ciBits, j, s;

	/* Store b, b^2 mod d, and b^3 mod d.
	 */
	NN_Assign (bPower[0], b, dDigits);
	NN_ModMult (bPower[1], bPower[0], b, d, dDigits);
    NN_ModMult (bPower[2], bPower[1], b, d, dDigits);
  
    NN_ASSIGN_DIGIT (t, 1, dDigits);

	cDigits = NN_Digits (c, cDigits);
    for (i = cDigits - 1; i >= 0; i--) {
		ci = c[i];
		ciBits = NN_DIGIT_BITS;

		/* Scan past leading zero bits of most significant digit.
		 */
		if (i == (int)(cDigits - 1)) {
			while (! DIGIT_2MSB (ci)) {
				ci <<= 2;
				ciBits -= 2;
			}
        }

        for (j = 0; j < ciBits; j += 2, ci <<= 2) {
        /* Compute t = t^4 * b^s mod d, where s = two MSB's of ci. */
            NN_ModMult (t, t, t, d, dDigits);
            NN_ModMult (t, t, t, d, dDigits);
            if ((s = DIGIT_2MSB (ci)) != 0)
            NN_ModMult (t, t, bPower[s-1], d, dDigits);
        }
    }
  
	NN_Assign (a, t, dDigits);
}

/* Compute a = 1/b mod c, assuming inverse exists.
   
   Lengths: a[digits], b[digits], c[digits].
	 Assumes gcd (b, c) = 1, digits < MAX_NN_DIGITS.
 */
void NN_ModInv (a, b, c, digits)
NN_DIGIT *a, *b, *c;
unsigned int digits;
{
    NN_DIGIT q[MAX_NN_DIGITS], t1[MAX_NN_DIGITS], t3[MAX_NN_DIGITS],
		u1[MAX_NN_DIGITS], u3[MAX_NN_DIGITS], v1[MAX_NN_DIGITS],
		v3[MAX_NN_DIGITS], w[2*MAX_NN_DIGITS];
    int u1Sign;

    /* Apply extended Euclidean algorithm, modified to avoid negative
       numbers.
    */
    NN_ASSIGN_DIGIT (u1, 1, digits);
	NN_AssignZero (v1, digits);
    NN_Assign (u3, b, digits);
	NN_Assign (v3, c, digits);
    u1Sign = 1;

	while (! NN_Zero (v3, digits)) {
        NN_Div (q, t3, u3, digits, v3, digits);
        NN_Mult (w, q, v1, digits);
		NN_Add (t1, u1, w, digits);
        NN_Assign (u1, v1, digits);
		NN_Assign (v1, t1, digits);
		NN_Assign (u3, v3, digits);
		NN_Assign (v3, t3, digits);
		u1Sign = -u1Sign;
	}

    /* Negate result if sign is negative. */
	if (u1Sign < 0)
		NN_Sub (a, c, u1, digits);
	else
		NN_Assign (a, u1, digits);
}

/* Computes a = gcd(b, c).

	 Assumes b > c, digits < MAX_NN_DIGITS.
*/

#define iplus1  ( i==2 ? 0 : i+1 )      /* used by Euclid algorithms */
#define iminus1 ( i==0 ? 2 : i-1 )      /* used by Euclid algorithms */
#define g(i) (  &(t[i][0])  )

void NN_Gcd(a ,b ,c, digits)
NN_DIGIT *a, *b, *c;
unsigned int digits;
{
	short i;
	NN_DIGIT t[3][MAX_NN_DIGITS];

	NN_Assign(g(0), c, digits);
	NN_Assign(g(1), b, digits);

	i=1;

	while(!NN_Zero(g(i),digits)) {
		NN_Mod(g(iplus1), g(iminus1), digits, g(i), digits);
		i = iplus1;
	}

	NN_Assign(a , g(iminus1), digits);
}

/* Returns the significant length of a in bits.

	 Lengths: a[digits]. */

unsigned int NN_Bits (a, digits)
NN_DIGIT *a;
unsigned int digits;
{
	if ((digits = NN_Digits (a, digits)) == 0)
		return (0);

	return ((digits - 1) * NN_DIGIT_BITS + NN_DigitBits (a[digits-1]));
}

#ifndef USEASM

/* Returns sign of a - b. */

int NN_Cmp (a, b, digits)
NN_DIGIT *a, *b;
unsigned int digits;
{

	if(digits) {
		do {
			digits--;
			if(*(a+digits) > *(b+digits))
				return(1);
			if(*(a+digits) < *(b+digits))
				return(-1);
		}while(digits);
	}

	return (0);
}

/* Returns nonzero iff a is zero. */

int NN_Zero (a, digits)
NN_DIGIT *a;
unsigned int digits;
{
	if(digits) {
		do {
			if(*a++)
				return(0);
		}while(--digits);
	}

	return (1);
}

/* Assigns a = b. */

void NN_Assign (a, b, digits)
NN_DIGIT *a, *b;
unsigned int digits;
{
	if(digits) {
		do {
			*a++ = *b++;
		}while(--digits);
	}
}

/* Returns the significant length of a in digits. */

unsigned int NN_Digits (a, digits)
NN_DIGIT *a;
unsigned int digits;
{

	if(digits) {
		digits--;

		do {
			if(*(a+digits))
				break;
		}while(digits--);

		return(digits + 1);
	}

	return(digits);
}

/* Computes a = b + c. Returns carry.

	 Lengths: a[digits], b[digits], c[digits].
 */
NN_DIGIT NN_Add (a, b, c, digits)
NN_DIGIT *a, *b, *c;
unsigned int digits;
{
	NN_DIGIT temp, carry = 0;

	if(digits)
		do {
			if((temp = (*b++) + carry) < carry)
				temp = *c++;
            else {      /* Patch to prevent bug for Sun CC */
                if((temp += *c) < *c)
					carry = 1;
				else
					carry = 0;
                c++;
            }
			*a++ = temp;
		}while(--digits);

	return (carry);
}

#endif

static NN_DIGIT subdigitmult(a, b, c, d, digits)
NN_DIGIT *a, *b, c, *d;
unsigned int digits;
{
	NN_DIGIT borrow, thigh, tlow;
	unsigned int i;

	borrow = 0;

	if(c != 0) {
		for(i = 0; i < digits; i++) {
			dmult(c, d[i], &thigh, &tlow);
			if((a[i] = b[i] - borrow) > (MAX_NN_DIGIT - borrow))
				borrow = 1;
			else
				borrow = 0;
			if((a[i] -= tlow) > (MAX_NN_DIGIT - tlow))
				borrow++;
			borrow += thigh;
		}
	}

	return (borrow);
}

/* Returns the significant length of a in bits, where a is a digit. */

static unsigned int NN_DigitBits (a)
NN_DIGIT a;
{
	unsigned int i;

	for (i = 0; i < NN_DIGIT_BITS; i++, a >>= 1)
		if (a == 0)
			break;

	return (i);
}

/* Computes a * b, result stored in high and low. */
 
static void dmult( a, b, high, low)
NN_DIGIT          a, b;
NN_DIGIT         *high;
NN_DIGIT         *low;
{
	NN_HALF_DIGIT al, ah, bl, bh;
	NN_DIGIT m1, m2, m, ml, mh, carry = 0;

	al = (NN_HALF_DIGIT)LOW_HALF(a);
	ah = (NN_HALF_DIGIT)HIGH_HALF(a);
	bl = (NN_HALF_DIGIT)LOW_HALF(b);
	bh = (NN_HALF_DIGIT)HIGH_HALF(b);

	*low = (NN_DIGIT) al*bl;
	*high = (NN_DIGIT) ah*bh;

	m1 = (NN_DIGIT) al*bh;
	m2 = (NN_DIGIT) ah*bl;
	m = m1 + m2;

	if(m < m1)
        carry = 1L << (NN_DIGIT_BITS / 2);

	ml = (m & MAX_NN_HALF_DIGIT) << (NN_DIGIT_BITS / 2);
	mh = m >> (NN_DIGIT_BITS / 2);

	*low += ml;

	if(*low < ml)
		carry++;

	*high += carry + mh;
}