+ for (i = 0; i < mlen; i++)
+ m[i] = 0;
+ sfree(m);
+ for (i = 0; i < plen; i++)
+ n[i] = 0;
+ sfree(n);
+}
+
+/*
+ * Decrement a number.
+ */
+void decbn(Bignum bn)
+{
+ int i = 1;
+ while (i < bn[0] && bn[i] == 0)
+ bn[i++] = 0xFFFF;
+ bn[i]--;
+}
+
+Bignum bignum_from_bytes(unsigned char *data, int nbytes)
+{
+ Bignum result;
+ int w, i;
+
+ w = (nbytes + 1) / 2; /* bytes -> words */
+
+ result = newbn(w);
+ for (i = 1; i <= w; i++)
+ result[i] = 0;
+ for (i = nbytes; i--;) {
+ unsigned char byte = *data++;
+ if (i & 1)
+ result[1 + i / 2] |= byte << 8;
+ else
+ result[1 + i / 2] |= byte;
+ }
+
+ while (result[0] > 1 && result[result[0]] == 0)
+ result[0]--;
+ return result;
+}
+
+/*
+ * Read an ssh1-format bignum from a data buffer. Return the number
+ * of bytes consumed.
+ */
+int ssh1_read_bignum(unsigned char *data, Bignum * result)
+{
+ unsigned char *p = data;
+ int i;
+ int w, b;
+
+ w = 0;
+ for (i = 0; i < 2; i++)
+ w = (w << 8) + *p++;
+ b = (w + 7) / 8; /* bits -> bytes */
+
+ if (!result) /* just return length */
+ return b + 2;
+
+ *result = bignum_from_bytes(p, b);
+
+ return p + b - data;
+}
+
+/*
+ * Return the bit count of a bignum, for ssh1 encoding.
+ */
+int bignum_bitcount(Bignum bn)
+{
+ int bitcount = bn[0] * 16 - 1;
+ while (bitcount >= 0
+ && (bn[bitcount / 16 + 1] >> (bitcount % 16)) == 0) bitcount--;
+ return bitcount + 1;
+}
+
+/*
+ * Return the byte length of a bignum when ssh1 encoded.
+ */
+int ssh1_bignum_length(Bignum bn)
+{
+ return 2 + (bignum_bitcount(bn) + 7) / 8;
+}
+
+/*
+ * Return the byte length of a bignum when ssh2 encoded.
+ */
+int ssh2_bignum_length(Bignum bn)
+{
+ return 4 + (bignum_bitcount(bn) + 8) / 8;
+}
+
+/*
+ * Return a byte from a bignum; 0 is least significant, etc.
+ */
+int bignum_byte(Bignum bn, int i)
+{
+ if (i >= 2 * bn[0])
+ return 0; /* beyond the end */
+ else if (i & 1)
+ return (bn[i / 2 + 1] >> 8) & 0xFF;
+ else
+ return (bn[i / 2 + 1]) & 0xFF;
+}
+
+/*
+ * Return a bit from a bignum; 0 is least significant, etc.
+ */
+int bignum_bit(Bignum bn, int i)
+{
+ if (i >= 16 * bn[0])
+ return 0; /* beyond the end */
+ else
+ return (bn[i / 16 + 1] >> (i % 16)) & 1;
+}
+
+/*
+ * Set a bit in a bignum; 0 is least significant, etc.
+ */
+void bignum_set_bit(Bignum bn, int bitnum, int value)
+{
+ if (bitnum >= 16 * bn[0])
+ abort(); /* beyond the end */
+ else {
+ int v = bitnum / 16 + 1;
+ int mask = 1 << (bitnum % 16);
+ if (value)
+ bn[v] |= mask;
+ else
+ bn[v] &= ~mask;
+ }
+}
+
+/*
+ * Write a ssh1-format bignum into a buffer. It is assumed the
+ * buffer is big enough. Returns the number of bytes used.
+ */
+int ssh1_write_bignum(void *data, Bignum bn)
+{
+ unsigned char *p = data;
+ int len = ssh1_bignum_length(bn);
+ int i;
+ int bitc = bignum_bitcount(bn);
+
+ *p++ = (bitc >> 8) & 0xFF;
+ *p++ = (bitc) & 0xFF;
+ for (i = len - 2; i--;)
+ *p++ = bignum_byte(bn, i);
+ return len;
+}
+
+/*
+ * Compare two bignums. Returns like strcmp.
+ */
+int bignum_cmp(Bignum a, Bignum b)
+{
+ int amax = a[0], bmax = b[0];
+ int i = (amax > bmax ? amax : bmax);
+ while (i) {
+ unsigned short aval = (i > amax ? 0 : a[i]);
+ unsigned short bval = (i > bmax ? 0 : b[i]);
+ if (aval < bval)
+ return -1;
+ if (aval > bval)
+ return +1;
+ i--;
+ }
+ return 0;
+}
+
+/*
+ * Right-shift one bignum to form another.
+ */
+Bignum bignum_rshift(Bignum a, int shift)
+{
+ Bignum ret;
+ int i, shiftw, shiftb, shiftbb, bits;
+ unsigned short ai, ai1;
+
+ bits = bignum_bitcount(a) - shift;
+ ret = newbn((bits + 15) / 16);
+
+ if (ret) {
+ shiftw = shift / 16;
+ shiftb = shift % 16;
+ shiftbb = 16 - shiftb;
+
+ ai1 = a[shiftw + 1];
+ for (i = 1; i <= ret[0]; i++) {
+ ai = ai1;
+ ai1 = (i + shiftw + 1 <= a[0] ? a[i + shiftw + 1] : 0);
+ ret[i] = ((ai >> shiftb) | (ai1 << shiftbb)) & 0xFFFF;
+ }
+ }
+
+ return ret;
+}
+
+/*
+ * Non-modular multiplication and addition.
+ */
+Bignum bigmuladd(Bignum a, Bignum b, Bignum addend)
+{
+ int alen = a[0], blen = b[0];
+ int mlen = (alen > blen ? alen : blen);
+ int rlen, i, maxspot;
+ unsigned short *workspace;
+ Bignum ret;
+
+ /* mlen space for a, mlen space for b, 2*mlen for result */
+ workspace = smalloc(mlen * 4 * sizeof(unsigned short));
+ for (i = 0; i < mlen; i++) {
+ workspace[0 * mlen + i] = (mlen - i <= a[0] ? a[mlen - i] : 0);
+ workspace[1 * mlen + i] = (mlen - i <= b[0] ? b[mlen - i] : 0);
+ }
+
+ internal_mul(workspace + 0 * mlen, workspace + 1 * mlen,
+ workspace + 2 * mlen, mlen);
+
+ /* now just copy the result back */
+ rlen = alen + blen + 1;
+ if (addend && rlen <= addend[0])
+ rlen = addend[0] + 1;
+ ret = newbn(rlen);
+ maxspot = 0;
+ for (i = 1; i <= ret[0]; i++) {
+ ret[i] = (i <= 2 * mlen ? workspace[4 * mlen - i] : 0);
+ if (ret[i] != 0)
+ maxspot = i;
+ }
+ ret[0] = maxspot;
+
+ /* now add in the addend, if any */
+ if (addend) {
+ unsigned long carry = 0;
+ for (i = 1; i <= rlen; i++) {
+ carry += (i <= ret[0] ? ret[i] : 0);
+ carry += (i <= addend[0] ? addend[i] : 0);
+ ret[i] = (unsigned short) carry & 0xFFFF;
+ carry >>= 16;
+ if (ret[i] != 0 && i > maxspot)
+ maxspot = i;
+ }
+ }
+ ret[0] = maxspot;
+
+ return ret;
+}
+
+/*
+ * Non-modular multiplication.
+ */
+Bignum bigmul(Bignum a, Bignum b)
+{
+ return bigmuladd(a, b, NULL);
+}
+
+/*
+ * Create a bignum which is the bitmask covering another one. That
+ * is, the smallest integer which is >= N and is also one less than
+ * a power of two.
+ */
+Bignum bignum_bitmask(Bignum n)
+{
+ Bignum ret = copybn(n);
+ int i;
+ unsigned short j;
+
+ i = ret[0];
+ while (n[i] == 0 && i > 0)
+ i--;
+ if (i <= 0)
+ return ret; /* input was zero */
+ j = 1;
+ while (j < n[i])
+ j = 2 * j + 1;
+ ret[i] = j;
+ while (--i > 0)
+ ret[i] = 0xFFFF;
+ return ret;
+}
+
+/*
+ * Convert a (max 32-bit) long into a bignum.
+ */
+Bignum bignum_from_long(unsigned long n)
+{
+ Bignum ret;
+
+ ret = newbn(3);
+ ret[1] = (unsigned short)(n & 0xFFFF);
+ ret[2] = (unsigned short)((n >> 16) & 0xFFFF);
+ ret[3] = 0;
+ ret[0] = (ret[2] ? 2 : 1);
+ return ret;
+}
+
+/*
+ * Add a long to a bignum.
+ */
+Bignum bignum_add_long(Bignum number, unsigned long addend)
+{
+ Bignum ret = newbn(number[0] + 1);
+ int i, maxspot = 0;
+ unsigned long carry = 0;
+
+ for (i = 1; i <= ret[0]; i++) {
+ carry += addend & 0xFFFF;
+ carry += (i <= number[0] ? number[i] : 0);
+ addend >>= 16;
+ ret[i] = (unsigned short) carry & 0xFFFF;
+ carry >>= 16;
+ if (ret[i] != 0)
+ maxspot = i;
+ }
+ ret[0] = maxspot;
+ return ret;
+}
+
+/*
+ * Compute the residue of a bignum, modulo a (max 16-bit) short.
+ */
+unsigned short bignum_mod_short(Bignum number, unsigned short modulus)
+{
+ unsigned long mod, r;
+ int i;
+
+ r = 0;
+ mod = modulus;
+ for (i = number[0]; i > 0; i--)
+ r = (r * 65536 + number[i]) % mod;
+ return (unsigned short) r;
+}
+
+void diagbn(char *prefix, Bignum md)
+{
+ int i, nibbles, morenibbles;
+ static const char hex[] = "0123456789ABCDEF";
+
+ debug(("%s0x", prefix ? prefix : ""));
+
+ nibbles = (3 + bignum_bitcount(md)) / 4;
+ if (nibbles < 1)
+ nibbles = 1;
+ morenibbles = 4 * md[0] - nibbles;
+ for (i = 0; i < morenibbles; i++)
+ debug(("-"));
+ for (i = nibbles; i--;)
+ debug(("%c",
+ hex[(bignum_byte(md, i / 2) >> (4 * (i % 2))) & 0xF]));
+
+ if (prefix)
+ debug(("\n"));
+}
+
+/*
+ * Simple division.
+ */
+Bignum bigdiv(Bignum a, Bignum b)
+{
+ Bignum q = newbn(a[0]);
+ bigdivmod(a, b, NULL, q);
+ return q;
+}
+
+/*
+ * Simple remainder.
+ */
+Bignum bigmod(Bignum a, Bignum b)
+{
+ Bignum r = newbn(b[0]);
+ bigdivmod(a, b, r, NULL);
+ return r;
+}
+
+/*
+ * Greatest common divisor.
+ */
+Bignum biggcd(Bignum av, Bignum bv)
+{
+ Bignum a = copybn(av);
+ Bignum b = copybn(bv);
+
+ while (bignum_cmp(b, Zero) != 0) {
+ Bignum t = newbn(b[0]);
+ bigdivmod(a, b, t, NULL);
+ while (t[0] > 1 && t[t[0]] == 0)
+ t[0]--;
+ freebn(a);
+ a = b;
+ b = t;
+ }
+
+ freebn(b);
+ return a;
+}
+
+/*
+ * Modular inverse, using Euclid's extended algorithm.
+ */
+Bignum modinv(Bignum number, Bignum modulus)
+{
+ Bignum a = copybn(modulus);
+ Bignum b = copybn(number);
+ Bignum xp = copybn(Zero);
+ Bignum x = copybn(One);
+ int sign = +1;
+
+ while (bignum_cmp(b, One) != 0) {
+ Bignum t = newbn(b[0]);
+ Bignum q = newbn(a[0]);
+ bigdivmod(a, b, t, q);
+ while (t[0] > 1 && t[t[0]] == 0)
+ t[0]--;
+ freebn(a);
+ a = b;
+ b = t;
+ t = xp;
+ xp = x;
+ x = bigmuladd(q, xp, t);
+ sign = -sign;
+ freebn(t);
+ }
+
+ freebn(b);
+ freebn(a);
+ freebn(xp);
+
+ /* now we know that sign * x == 1, and that x < modulus */
+ if (sign < 0) {
+ /* set a new x to be modulus - x */
+ Bignum newx = newbn(modulus[0]);
+ unsigned short carry = 0;
+ int maxspot = 1;
+ int i;
+
+ for (i = 1; i <= newx[0]; i++) {
+ unsigned short aword = (i <= modulus[0] ? modulus[i] : 0);
+ unsigned short bword = (i <= x[0] ? x[i] : 0);
+ newx[i] = aword - bword - carry;
+ bword = ~bword;
+ carry = carry ? (newx[i] >= bword) : (newx[i] > bword);
+ if (newx[i] != 0)
+ maxspot = i;
+ }
+ newx[0] = maxspot;
+ freebn(x);
+ x = newx;
+ }
+
+ /* and return. */
+ return x;
+}
+
+/*
+ * Render a bignum into decimal. Return a malloced string holding
+ * the decimal representation.
+ */
+char *bignum_decimal(Bignum x)
+{
+ int ndigits, ndigit;
+ int i, iszero;
+ unsigned long carry;
+ char *ret;
+ unsigned short *workspace;
+
+ /*
+ * First, estimate the number of digits. Since log(10)/log(2)
+ * is just greater than 93/28 (the joys of continued fraction
+ * approximations...) we know that for every 93 bits, we need
+ * at most 28 digits. This will tell us how much to malloc.
+ *
+ * Formally: if x has i bits, that means x is strictly less
+ * than 2^i. Since 2 is less than 10^(28/93), this is less than
+ * 10^(28i/93). We need an integer power of ten, so we must
+ * round up (rounding down might make it less than x again).
+ * Therefore if we multiply the bit count by 28/93, rounding
+ * up, we will have enough digits.
+ */
+ i = bignum_bitcount(x);
+ ndigits = (28 * i + 92) / 93; /* multiply by 28/93 and round up */
+ ndigits++; /* allow for trailing \0 */
+ ret = smalloc(ndigits);
+
+ /*
+ * Now allocate some workspace to hold the binary form as we
+ * repeatedly divide it by ten. Initialise this to the
+ * big-endian form of the number.
+ */
+ workspace = smalloc(sizeof(unsigned short) * x[0]);
+ for (i = 0; i < x[0]; i++)
+ workspace[i] = x[x[0] - i];
+
+ /*
+ * Next, write the decimal number starting with the last digit.
+ * We use ordinary short division, dividing 10 into the
+ * workspace.
+ */
+ ndigit = ndigits - 1;
+ ret[ndigit] = '\0';
+ do {
+ iszero = 1;
+ carry = 0;
+ for (i = 0; i < x[0]; i++) {
+ carry = (carry << 16) + workspace[i];
+ workspace[i] = (unsigned short) (carry / 10);
+ if (workspace[i])
+ iszero = 0;
+ carry %= 10;
+ }
+ ret[--ndigit] = (char) (carry + '0');
+ } while (!iszero);
+
+ /*
+ * There's a chance we've fallen short of the start of the
+ * string. Correct if so.
+ */
+ if (ndigit > 0)
+ memmove(ret, ret + ndigit, ndigits - ndigit);
+
+ /*
+ * Done.
+ */
+ return ret;