--- /dev/null
+/* NN.C - natural numbers routines
+ */
+
+/* Copyright (C) RSA Laboratories, a division of RSA Data Security,
+ Inc., created 1991. All rights reserved.
+ */
+
+#include "global.h"
+#include "rsaref.h"
+#include "nn.h"
+#include "digit.h"
+
+static NN_DIGIT NN_AddDigitMult PROTO_LIST
+ ((NN_DIGIT *, NN_DIGIT *, NN_DIGIT, NN_DIGIT *, unsigned int));
+static NN_DIGIT NN_SubDigitMult PROTO_LIST
+ ((NN_DIGIT *, NN_DIGIT *, NN_DIGIT, NN_DIGIT *, unsigned int));
+
+static unsigned int NN_DigitBits PROTO_LIST ((NN_DIGIT));
+
+/* 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;
+ int j;
+ unsigned int i, u;
+
+ 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;
+ int j;
+ unsigned int i, u;
+
+ 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 = b.
+
+ Lengths: a[digits], b[digits].
+ */
+void NN_Assign (a, b, digits)
+NN_DIGIT *a, *b;
+unsigned int digits;
+{
+ unsigned int i;
+
+ for (i = 0; i < digits; i++)
+ a[i] = b[i];
+}
+
+/* Assigns a = 0.
+
+ Lengths: a[digits].
+ */
+void NN_AssignZero (a, digits)
+NN_DIGIT *a;
+unsigned int digits;
+{
+ unsigned int i;
+
+ for (i = 0; i < digits; i++)
+ a[i] = 0;
+}
+
+/* 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 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 ai, carry;
+ unsigned int i;
+
+ carry = 0;
+
+ for (i = 0; i < digits; i++) {
+ if ((ai = b[i] + carry) < carry)
+ ai = c[i];
+ else if ((ai += c[i]) < c[i])
+ carry = 1;
+ else
+ carry = 0;
+ a[i] = ai;
+ }
+
+ return (carry);
+}
+
+/* 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 ai, borrow;
+ unsigned int i;
+
+ borrow = 0;
+
+ for (i = 0; i < digits; i++) {
+ if ((ai = b[i] - borrow) > (MAX_NN_DIGIT - borrow))
+ ai = MAX_NN_DIGIT - c[i];
+ else if ((ai -= c[i]) > (MAX_NN_DIGIT - c[i]))
+ borrow = 1;
+ else
+ borrow = 0;
+ a[i] = ai;
+ }
+
+ 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];
+ unsigned int bDigits, cDigits, i;
+
+ NN_AssignZero (t, 2 * digits);
+
+ bDigits = NN_Digits (b, digits);
+ cDigits = NN_Digits (c, digits);
+
+ for (i = 0; i < bDigits; i++)
+ t[i+cDigits] += NN_AddDigitMult (&t[i], &t[i], b[i], c, cDigits);
+
+ NN_Assign (a, t, 2 * digits);
+
+ /* Zeroize potentially sensitive information.
+ */
+ R_memset ((POINTER)t, 0, sizeof (t));
+}
+
+/* Computes a = b * 2^c (i.e., shifts left c bits), returning carry.
+
+ Lengths: a[digits], b[digits].
+ Requires c < NN_DIGIT_BITS.
+ */
+NN_DIGIT NN_LShift (a, b, c, digits)
+NN_DIGIT *a, *b;
+unsigned int c, digits;
+{
+ NN_DIGIT bi, carry;
+ unsigned int i, t;
+
+ if (c >= NN_DIGIT_BITS)
+ return (0);
+
+ t = NN_DIGIT_BITS - c;
+
+ carry = 0;
+
+ for (i = 0; i < digits; i++) {
+ bi = b[i];
+ a[i] = (bi << c) | carry;
+ carry = c ? (bi >> t) : 0;
+ }
+
+ return (carry);
+}
+
+/* Computes a = c div 2^c (i.e., shifts right c bits), returning carry.
+
+ Lengths: a[digits], b[digits].
+ Requires: c < NN_DIGIT_BITS.
+ */
+NN_DIGIT NN_RShift (a, b, c, digits)
+NN_DIGIT *a, *b;
+unsigned int c, digits;
+{
+ NN_DIGIT bi, carry;
+ int i;
+ unsigned int t;
+
+ if (c >= NN_DIGIT_BITS)
+ return (0);
+
+ t = NN_DIGIT_BITS - c;
+
+ carry = 0;
+
+ for (i = digits - 1; i >= 0; i--) {
+ bi = b[i];
+ a[i] = (bi >> c) | carry;
+ carry = c ? (bi << t) : 0;
+ }
+
+ 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], t;
+ int i;
+ unsigned int ddDigits, shift;
+
+ ddDigits = NN_Digits (d, dDigits);
+ if (ddDigits == 0)
+ return;
+
+ /* Normalize operands.
+ */
+ 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);
+ t = dd[ddDigits-1];
+
+ NN_AssignZero (a, cDigits);
+
+ for (i = cDigits-ddDigits; i >= 0; i--) {
+ /* Underestimate quotient digit and subtract.
+ */
+ if (t == MAX_NN_DIGIT)
+ ai = cc[i+ddDigits];
+ else
+ NN_DigitDiv (&ai, &cc[i+ddDigits-1], t + 1);
+ cc[i+ddDigits] -= NN_SubDigitMult (&cc[i], &cc[i], ai, dd, ddDigits);
+
+ /* Correct estimate.
+ */
+ 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;
+ }
+
+ /* Restore result.
+ */
+ NN_AssignZero (b, dDigits);
+ NN_RShift (b, cc, shift, ddDigits);
+
+ /* Zeroize potentially sensitive information.
+ */
+ R_memset ((POINTER)cc, 0, sizeof (cc));
+ R_memset ((POINTER)dd, 0, sizeof (dd));
+}
+
+/* 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);
+
+ /* Zeroize potentially sensitive information.
+ */
+ R_memset ((POINTER)t, 0, sizeof (t));
+}
+
+/* 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);
+
+ /* Zeroize potentially sensitive information.
+ */
+ R_memset ((POINTER)t, 0, sizeof (t));
+}
+
+/* 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);
+
+ /* Zeroize potentially sensitive information.
+ */
+ R_memset ((POINTER)bPower, 0, sizeof (bPower));
+ R_memset ((POINTER)t, 0, sizeof (t));
+}
+
+/* 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);
+
+ /* Zeroize potentially sensitive information.
+ */
+ R_memset ((POINTER)q, 0, sizeof (q));
+ R_memset ((POINTER)t1, 0, sizeof (t1));
+ R_memset ((POINTER)t3, 0, sizeof (t3));
+ R_memset ((POINTER)u1, 0, sizeof (u1));
+ R_memset ((POINTER)u3, 0, sizeof (u3));
+ R_memset ((POINTER)v1, 0, sizeof (v1));
+ R_memset ((POINTER)v3, 0, sizeof (v3));
+ R_memset ((POINTER)w, 0, sizeof (w));
+}
+
+/* Computes a = gcd(b, c).
+
+ Lengths: a[digits], b[digits], c[digits].
+ Assumes b > c, digits < MAX_NN_DIGITS.
+ */
+void NN_Gcd (a, b, c, digits)
+NN_DIGIT *a, *b, *c;
+unsigned int digits;
+{
+ NN_DIGIT t[MAX_NN_DIGITS], u[MAX_NN_DIGITS], v[MAX_NN_DIGITS];
+
+ NN_Assign (u, b, digits);
+ NN_Assign (v, c, digits);
+
+ while (! NN_Zero (v, digits)) {
+ NN_Mod (t, u, digits, v, digits);
+ NN_Assign (u, v, digits);
+ NN_Assign (v, t, digits);
+ }
+
+ NN_Assign (a, u, digits);
+
+ /* Zeroize potentially sensitive information.
+ */
+ R_memset ((POINTER)t, 0, sizeof (t));
+ R_memset ((POINTER)u, 0, sizeof (u));
+ R_memset ((POINTER)v, 0, sizeof (v));
+}
+
+/* Returns sign of a - b.
+
+ Lengths: a[digits], b[digits].
+ */
+int NN_Cmp (a, b, digits)
+NN_DIGIT *a, *b;
+unsigned int digits;
+{
+ int i;
+
+ for (i = digits - 1; i >= 0; i--) {
+ if (a[i] > b[i])
+ return (1);
+ if (a[i] < b[i])
+ return (-1);
+ }
+
+ return (0);
+}
+
+/* Returns nonzero iff a is zero.
+
+ Lengths: a[digits].
+ */
+int NN_Zero (a, digits)
+NN_DIGIT *a;
+unsigned int digits;
+{
+ unsigned int i;
+
+ for (i = 0; i < digits; i++)
+ if (a[i])
+ return (0);
+
+ return (1);
+}
+
+/* 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]));
+}
+
+/* Returns the significant length of a in digits.
+
+ Lengths: a[digits].
+ */
+unsigned int NN_Digits (a, digits)
+NN_DIGIT *a;
+unsigned int digits;
+{
+ int i;
+
+ for (i = digits - 1; i >= 0; i--)
+ if (a[i])
+ break;
+
+ return (i + 1);
+}
+
+/* Computes a = b + c*d, where c is a digit. Returns carry.
+
+ Lengths: a[digits], b[digits], d[digits].
+ */
+static NN_DIGIT NN_AddDigitMult (a, b, c, d, digits)
+NN_DIGIT *a, *b, c, *d;
+unsigned int digits;
+{
+ NN_DIGIT carry, t[2];
+ unsigned int i;
+
+ if (c == 0)
+ return (0);
+
+ carry = 0;
+ for (i = 0; i < digits; i++) {
+ NN_DigitMult (t, c, d[i]);
+ if ((a[i] = b[i] + carry) < carry)
+ carry = 1;
+ else
+ carry = 0;
+ if ((a[i] += t[0]) < t[0])
+ carry++;
+ carry += t[1];
+ }
+
+ return (carry);
+}
+
+/* Computes a = b - c*d, where c is a digit. Returns borrow.
+
+ Lengths: a[digits], b[digits], d[digits].
+ */
+static NN_DIGIT NN_SubDigitMult (a, b, c, d, digits)
+NN_DIGIT *a, *b, c, *d;
+unsigned int digits;
+{
+ NN_DIGIT borrow, t[2];
+ unsigned int i;
+
+ if (c == 0)
+ return (0);
+
+ borrow = 0;
+ for (i = 0; i < digits; i++) {
+ NN_DigitMult (t, c, d[i]);
+ if ((a[i] = b[i] - borrow) > (MAX_NN_DIGIT - borrow))
+ borrow = 1;
+ else
+ borrow = 0;
+ if ((a[i] -= t[0]) > (MAX_NN_DIGIT - t[0]))
+ borrow++;
+ borrow += t[1];
+ }
+
+ 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);
+}
andersk / moira.git / blobdiff