X-Git-Url: https://git.distorted.org.uk/u/mdw/putty/blobdiff_plain/01c034ad857128c51482a563befb374e38ebe668..32874aeac8dacbca26663777b39a79efc5d8dc4b:/sshbn.c diff --git a/sshbn.c b/sshbn.c index 2fd98f91..0d0fce34 100644 --- a/sshbn.c +++ b/sshbn.c @@ -6,7 +6,7 @@ #include #include -#if 0 // use PuTTY main debugging for diagbn() +#if 0 // use PuTTY main debugging for diagbn() #include #include "putty.h" #define debugprint debug @@ -38,28 +38,33 @@ unsigned short bnOne[2] = { 1, 1 }; Bignum Zero = bnZero, One = bnOne; -static Bignum newbn(int length) { - Bignum b = smalloc((length+1)*sizeof(unsigned short)); +static Bignum newbn(int length) +{ + Bignum b = smalloc((length + 1) * sizeof(unsigned short)); if (!b) abort(); /* FIXME */ - memset(b, 0, (length+1)*sizeof(*b)); + memset(b, 0, (length + 1) * sizeof(*b)); b[0] = length; return b; } -void bn_restore_invariant(Bignum b) { - while (b[0] > 1 && b[b[0]] == 0) b[0]--; +void bn_restore_invariant(Bignum b) +{ + while (b[0] > 1 && b[b[0]] == 0) + b[0]--; } -Bignum copybn(Bignum orig) { - Bignum b = smalloc((orig[0]+1)*sizeof(unsigned short)); +Bignum copybn(Bignum orig) +{ + Bignum b = smalloc((orig[0] + 1) * sizeof(unsigned short)); if (!b) abort(); /* FIXME */ - memcpy(b, orig, (orig[0]+1)*sizeof(*b)); + memcpy(b, orig, (orig[0] + 1) * sizeof(*b)); return b; } -void freebn(Bignum b) { +void freebn(Bignum b) +{ /* * Burn the evidence, just in case. */ @@ -67,8 +72,9 @@ void freebn(Bignum b) { sfree(b); } -Bignum bn_power_2(int n) { - Bignum ret = newbn(n/16+1); +Bignum bn_power_2(int n) +{ + Bignum ret = newbn(n / 16 + 1); bignum_set_bit(ret, n, 1); return ret; } @@ -79,12 +85,12 @@ Bignum bn_power_2(int n) { * Result is returned in the first 2*len words of c. */ static void internal_mul(unsigned short *a, unsigned short *b, - unsigned short *c, int len) + unsigned short *c, int len) { int i, j; unsigned long ai, t; - for (j = 0; j < 2*len; j++) + for (j = 0; j < 2 * len; j++) c[j] = 0; for (i = len - 1; i >= 0; i--) { @@ -92,16 +98,17 @@ static void internal_mul(unsigned short *a, unsigned short *b, t = 0; for (j = len - 1; j >= 0; j--) { t += ai * (unsigned long) b[j]; - t += (unsigned long) c[i+j+1]; - c[i+j+1] = (unsigned short)t; + t += (unsigned long) c[i + j + 1]; + c[i + j + 1] = (unsigned short) t; t = t >> 16; } - c[i] = (unsigned short)t; + c[i] = (unsigned short) t; } } static void internal_add_shifted(unsigned short *number, - unsigned n, int shift) { + unsigned n, int shift) +{ int word = 1 + (shift / 16); int bshift = shift % 16; unsigned long addend; @@ -109,10 +116,10 @@ static void internal_add_shifted(unsigned short *number, addend = n << bshift; while (addend) { - addend += number[word]; - number[word] = (unsigned short) addend & 0xFFFF; - addend >>= 16; - word++; + addend += number[word]; + number[word] = (unsigned short) addend & 0xFFFF; + addend >>= 16; + word++; } } @@ -127,8 +134,8 @@ static void internal_add_shifted(unsigned short *number, * left by `qshift' before adding into quot. */ static void internal_mod(unsigned short *a, int alen, - unsigned short *m, int mlen, - unsigned short *quot, int qshift) + unsigned short *m, int mlen, + unsigned short *quot, int qshift) { unsigned short m0, m1; unsigned int h; @@ -136,25 +143,25 @@ static void internal_mod(unsigned short *a, int alen, m0 = m[0]; if (mlen > 1) - m1 = m[1]; + m1 = m[1]; else - m1 = 0; + m1 = 0; - for (i = 0; i <= alen-mlen; i++) { + for (i = 0; i <= alen - mlen; i++) { unsigned long t; unsigned int q, r, c, ai1; if (i == 0) { h = 0; } else { - h = a[i-1]; - a[i-1] = 0; + h = a[i - 1]; + a[i - 1] = 0; } - if (i == alen-1) - ai1 = 0; - else - ai1 = a[i+1]; + if (i == alen - 1) + ai1 = 0; + else + ai1 = a[i + 1]; /* Find q = h:a[i] / m0 */ t = ((unsigned long) h << 16) + a[i]; @@ -162,25 +169,25 @@ static void internal_mod(unsigned short *a, int alen, r = t % m0; /* Refine our estimate of q by looking at - h:a[i]:a[i+1] / m0:m1 */ - t = (long) m1 * (long) q; + h:a[i]:a[i+1] / m0:m1 */ + t = (long) m1 *(long) q; if (t > ((unsigned long) r << 16) + ai1) { q--; t -= m1; - r = (r + m0) & 0xffff; /* overflow? */ - if (r >= (unsigned long)m0 && - t > ((unsigned long) r << 16) + ai1) - q--; + r = (r + m0) & 0xffff; /* overflow? */ + if (r >= (unsigned long) m0 && + t > ((unsigned long) r << 16) + ai1) q--; } /* Subtract q * m from a[i...] */ c = 0; for (k = mlen - 1; k >= 0; k--) { - t = (long) q * (long) m[k]; + t = (long) q *(long) m[k]; t += c; c = t >> 16; - if ((unsigned short) t > a[i+k]) c++; - a[i+k] -= (unsigned short) t; + if ((unsigned short) t > a[i + k]) + c++; + a[i + k] -= (unsigned short) t; } /* Add back m in case of borrow */ @@ -188,14 +195,14 @@ static void internal_mod(unsigned short *a, int alen, t = 0; for (k = mlen - 1; k >= 0; k--) { t += m[k]; - t += a[i+k]; - a[i+k] = (unsigned short)t; + t += a[i + k]; + a[i + k] = (unsigned short) t; t = t >> 16; } - q--; + q--; } - if (quot) - internal_add_shifted(quot, q, qshift + 16 * (alen-mlen-i)); + if (quot) + internal_add_shifted(quot, q, qshift + 16 * (alen - mlen - i)); } } @@ -216,74 +223,95 @@ Bignum modpow(Bignum base, Bignum exp, Bignum mod) /* We use big endian internally */ mlen = mod[0]; m = smalloc(mlen * sizeof(unsigned short)); - for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; + for (j = 0; j < mlen; j++) + m[j] = mod[mod[0] - j]; /* Shift m left to make msb bit set */ for (mshift = 0; mshift < 15; mshift++) - if ((m[0] << mshift) & 0x8000) break; + if ((m[0] << mshift) & 0x8000) + break; if (mshift) { for (i = 0; i < mlen - 1; i++) - m[i] = (m[i] << mshift) | (m[i+1] >> (16-mshift)); - m[mlen-1] = m[mlen-1] << mshift; + m[i] = (m[i] << mshift) | (m[i + 1] >> (16 - mshift)); + m[mlen - 1] = m[mlen - 1] << mshift; } /* Allocate n of size mlen, copy base to n */ n = smalloc(mlen * sizeof(unsigned short)); i = mlen - base[0]; - for (j = 0; j < i; j++) n[j] = 0; - for (j = 0; j < base[0]; j++) n[i+j] = base[base[0] - j]; + for (j = 0; j < i; j++) + n[j] = 0; + for (j = 0; j < base[0]; j++) + n[i + j] = base[base[0] - j]; /* Allocate a and b of size 2*mlen. Set a = 1 */ a = smalloc(2 * mlen * sizeof(unsigned short)); b = smalloc(2 * mlen * sizeof(unsigned short)); - for (i = 0; i < 2*mlen; i++) a[i] = 0; - a[2*mlen-1] = 1; + for (i = 0; i < 2 * mlen; i++) + a[i] = 0; + a[2 * mlen - 1] = 1; /* Skip leading zero bits of exp. */ - i = 0; j = 15; + i = 0; + j = 15; while (i < exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) { j--; - if (j < 0) { i++; j = 15; } + if (j < 0) { + i++; + j = 15; + } } /* Main computation */ while (i < exp[0]) { while (j >= 0) { internal_mul(a + mlen, a + mlen, b, mlen); - internal_mod(b, mlen*2, m, mlen, NULL, 0); + internal_mod(b, mlen * 2, m, mlen, NULL, 0); if ((exp[exp[0] - i] & (1 << j)) != 0) { internal_mul(b + mlen, n, a, mlen); - internal_mod(a, mlen*2, m, mlen, NULL, 0); + internal_mod(a, mlen * 2, m, mlen, NULL, 0); } else { unsigned short *t; - t = a; a = b; b = t; + t = a; + a = b; + b = t; } j--; } - i++; j = 15; + i++; + j = 15; } /* Fixup result in case the modulus was shifted */ if (mshift) { - for (i = mlen - 1; i < 2*mlen - 1; i++) - a[i] = (a[i] << mshift) | (a[i+1] >> (16-mshift)); - a[2*mlen-1] = a[2*mlen-1] << mshift; - internal_mod(a, mlen*2, m, mlen, NULL, 0); - for (i = 2*mlen - 1; i >= mlen; i--) - a[i] = (a[i] >> mshift) | (a[i-1] << (16-mshift)); + for (i = mlen - 1; i < 2 * mlen - 1; i++) + a[i] = (a[i] << mshift) | (a[i + 1] >> (16 - mshift)); + a[2 * mlen - 1] = a[2 * mlen - 1] << mshift; + internal_mod(a, mlen * 2, m, mlen, NULL, 0); + for (i = 2 * mlen - 1; i >= mlen; i--) + a[i] = (a[i] >> mshift) | (a[i - 1] << (16 - mshift)); } /* Copy result to buffer */ result = newbn(mod[0]); for (i = 0; i < mlen; i++) - result[result[0] - i] = a[i+mlen]; - while (result[0] > 1 && result[result[0]] == 0) result[0]--; + result[result[0] - i] = a[i + mlen]; + while (result[0] > 1 && result[result[0]] == 0) + result[0]--; /* Free temporary arrays */ - for (i = 0; i < 2*mlen; i++) a[i] = 0; sfree(a); - for (i = 0; i < 2*mlen; i++) b[i] = 0; sfree(b); - for (i = 0; i < mlen; i++) m[i] = 0; sfree(m); - for (i = 0; i < mlen; i++) n[i] = 0; sfree(n); + for (i = 0; i < 2 * mlen; i++) + a[i] = 0; + sfree(a); + for (i = 0; i < 2 * mlen; i++) + b[i] = 0; + sfree(b); + for (i = 0; i < mlen; i++) + m[i] = 0; + sfree(m); + for (i = 0; i < mlen; i++) + n[i] = 0; + sfree(n); return result; } @@ -304,15 +332,17 @@ Bignum modmul(Bignum p, Bignum q, Bignum mod) /* We use big endian internally */ mlen = mod[0]; m = smalloc(mlen * sizeof(unsigned short)); - for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; + for (j = 0; j < mlen; j++) + m[j] = mod[mod[0] - j]; /* Shift m left to make msb bit set */ for (mshift = 0; mshift < 15; mshift++) - if ((m[0] << mshift) & 0x8000) break; + if ((m[0] << mshift) & 0x8000) + break; if (mshift) { for (i = 0; i < mlen - 1; i++) - m[i] = (m[i] << mshift) | (m[i+1] >> (16-mshift)); - m[mlen-1] = m[mlen-1] << mshift; + m[i] = (m[i] << mshift) | (m[i + 1] >> (16 - mshift)); + m[mlen - 1] = m[mlen - 1] << mshift; } pqlen = (p[0] > q[0] ? p[0] : q[0]); @@ -320,44 +350,57 @@ Bignum modmul(Bignum p, Bignum q, Bignum mod) /* Allocate n of size pqlen, copy p to n */ n = smalloc(pqlen * sizeof(unsigned short)); i = pqlen - p[0]; - for (j = 0; j < i; j++) n[j] = 0; - for (j = 0; j < p[0]; j++) n[i+j] = p[p[0] - j]; + for (j = 0; j < i; j++) + n[j] = 0; + for (j = 0; j < p[0]; j++) + n[i + j] = p[p[0] - j]; /* Allocate o of size pqlen, copy q to o */ o = smalloc(pqlen * sizeof(unsigned short)); i = pqlen - q[0]; - for (j = 0; j < i; j++) o[j] = 0; - for (j = 0; j < q[0]; j++) o[i+j] = q[q[0] - j]; + for (j = 0; j < i; j++) + o[j] = 0; + for (j = 0; j < q[0]; j++) + o[i + j] = q[q[0] - j]; /* Allocate a of size 2*pqlen for result */ a = smalloc(2 * pqlen * sizeof(unsigned short)); /* Main computation */ internal_mul(n, o, a, pqlen); - internal_mod(a, pqlen*2, m, mlen, NULL, 0); + internal_mod(a, pqlen * 2, m, mlen, NULL, 0); /* Fixup result in case the modulus was shifted */ if (mshift) { - for (i = 2*pqlen - mlen - 1; i < 2*pqlen - 1; i++) - a[i] = (a[i] << mshift) | (a[i+1] >> (16-mshift)); - a[2*pqlen-1] = a[2*pqlen-1] << mshift; - internal_mod(a, pqlen*2, m, mlen, NULL, 0); - for (i = 2*pqlen - 1; i >= 2*pqlen - mlen; i--) - a[i] = (a[i] >> mshift) | (a[i-1] << (16-mshift)); + for (i = 2 * pqlen - mlen - 1; i < 2 * pqlen - 1; i++) + a[i] = (a[i] << mshift) | (a[i + 1] >> (16 - mshift)); + a[2 * pqlen - 1] = a[2 * pqlen - 1] << mshift; + internal_mod(a, pqlen * 2, m, mlen, NULL, 0); + for (i = 2 * pqlen - 1; i >= 2 * pqlen - mlen; i--) + a[i] = (a[i] >> mshift) | (a[i - 1] << (16 - mshift)); } /* Copy result to buffer */ - rlen = (mlen < pqlen*2 ? mlen : pqlen*2); + rlen = (mlen < pqlen * 2 ? mlen : pqlen * 2); result = newbn(rlen); for (i = 0; i < rlen; i++) - result[result[0] - i] = a[i+2*pqlen-rlen]; - while (result[0] > 1 && result[result[0]] == 0) result[0]--; + result[result[0] - i] = a[i + 2 * pqlen - rlen]; + while (result[0] > 1 && result[result[0]] == 0) + result[0]--; /* Free temporary arrays */ - for (i = 0; i < 2*pqlen; i++) a[i] = 0; sfree(a); - for (i = 0; i < mlen; i++) m[i] = 0; sfree(m); - for (i = 0; i < pqlen; i++) n[i] = 0; sfree(n); - for (i = 0; i < pqlen; i++) o[i] = 0; sfree(o); + for (i = 0; i < 2 * pqlen; i++) + a[i] = 0; + sfree(a); + for (i = 0; i < mlen; i++) + m[i] = 0; + sfree(m); + for (i = 0; i < pqlen; i++) + n[i] = 0; + sfree(n); + for (i = 0; i < pqlen; i++) + o[i] = 0; + sfree(o); return result; } @@ -378,25 +421,30 @@ void bigmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) /* We use big endian internally */ mlen = mod[0]; m = smalloc(mlen * sizeof(unsigned short)); - for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; + for (j = 0; j < mlen; j++) + m[j] = mod[mod[0] - j]; /* Shift m left to make msb bit set */ for (mshift = 0; mshift < 15; mshift++) - if ((m[0] << mshift) & 0x8000) break; + if ((m[0] << mshift) & 0x8000) + break; if (mshift) { for (i = 0; i < mlen - 1; i++) - m[i] = (m[i] << mshift) | (m[i+1] >> (16-mshift)); - m[mlen-1] = m[mlen-1] << mshift; + m[i] = (m[i] << mshift) | (m[i + 1] >> (16 - mshift)); + m[mlen - 1] = m[mlen - 1] << mshift; } plen = p[0]; /* Ensure plen > mlen */ - if (plen <= mlen) plen = mlen+1; + if (plen <= mlen) + plen = mlen + 1; /* Allocate n of size plen, copy p to n */ n = smalloc(plen * sizeof(unsigned short)); - for (j = 0; j < plen; j++) n[j] = 0; - for (j = 1; j <= p[0]; j++) n[plen-j] = p[j]; + for (j = 0; j < plen; j++) + n[j] = 0; + for (j = 1; j <= p[0]; j++) + n[plen - j] = p[j]; /* Main computation */ internal_mod(n, plen, m, mlen, quotient, mshift); @@ -404,52 +452,59 @@ void bigmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) /* Fixup result in case the modulus was shifted */ if (mshift) { for (i = plen - mlen - 1; i < plen - 1; i++) - n[i] = (n[i] << mshift) | (n[i+1] >> (16-mshift)); - n[plen-1] = n[plen-1] << mshift; + n[i] = (n[i] << mshift) | (n[i + 1] >> (16 - mshift)); + n[plen - 1] = n[plen - 1] << mshift; internal_mod(n, plen, m, mlen, quotient, 0); for (i = plen - 1; i >= plen - mlen; i--) - n[i] = (n[i] >> mshift) | (n[i-1] << (16-mshift)); + n[i] = (n[i] >> mshift) | (n[i - 1] << (16 - mshift)); } /* Copy result to buffer */ for (i = 1; i <= result[0]; i++) { - int j = plen-i; - result[i] = j>=0 ? n[j] : 0; + int j = plen - i; + result[i] = j >= 0 ? n[j] : 0; } /* Free temporary arrays */ - for (i = 0; i < mlen; i++) m[i] = 0; sfree(m); - for (i = 0; i < plen; i++) n[i] = 0; sfree(n); + 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) { +void decbn(Bignum bn) +{ int i = 1; while (i < bn[0] && bn[i] == 0) - bn[i++] = 0xFFFF; + bn[i++] = 0xFFFF; bn[i]--; } -Bignum bignum_from_bytes(unsigned char *data, int nbytes) { +Bignum bignum_from_bytes(unsigned char *data, int nbytes) +{ Bignum result; int w, i; - w = (nbytes+1)/2; /* bytes -> words */ + 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; + 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]--; + while (result[0] > 1 && result[result[0]] == 0) + result[0]--; return result; } @@ -457,18 +512,19 @@ Bignum bignum_from_bytes(unsigned char *data, int nbytes) { * Read an ssh1-format bignum from a data buffer. Return the number * of bytes consumed. */ -int ssh1_read_bignum(unsigned char *data, Bignum *result) { +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 */ + for (i = 0; i < 2; i++) + w = (w << 8) + *p++; + b = (w + 7) / 8; /* bits -> bytes */ - if (!result) /* just return length */ - return b + 2; + if (!result) /* just return length */ + return b + 2; *result = bignum_from_bytes(p, b); @@ -478,62 +534,68 @@ int ssh1_read_bignum(unsigned char *data, Bignum *result) { /* * Return the bit count of a bignum, for ssh1 encoding. */ -int bignum_bitcount(Bignum bn) { +int bignum_bitcount(Bignum bn) +{ int bitcount = bn[0] * 16 - 1; - while (bitcount >= 0 && (bn[bitcount/16+1] >> (bitcount % 16)) == 0) - bitcount--; + 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; +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; +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 */ +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; + return (bn[i / 2 + 1] >> 8) & 0xFF; else - return (bn[i/2+1] ) & 0xFF; + 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 */ +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; + 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 */ +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; + int v = bitnum / 16 + 1; + int mask = 1 << (bitnum % 16); + if (value) + bn[v] |= mask; + else + bn[v] &= ~mask; } } @@ -541,31 +603,35 @@ void bignum_set_bit(Bignum bn, int bitnum, int value) { * 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) { +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); + *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 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--; + 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; } @@ -573,25 +639,26 @@ int bignum_cmp(Bignum a, Bignum b) { /* * Right-shift one bignum to form another. */ -Bignum bignum_rshift(Bignum a, int shift) { +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); + 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; - } + 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; @@ -600,7 +667,8 @@ Bignum bignum_rshift(Bignum a, int shift) { /* * Non-modular multiplication and addition. */ -Bignum bigmuladd(Bignum a, Bignum b, Bignum addend) { +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; @@ -610,36 +678,37 @@ Bignum bigmuladd(Bignum a, Bignum b, Bignum addend) { /* 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); + 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); + 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; + 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[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; - } + 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; @@ -649,7 +718,8 @@ Bignum bigmuladd(Bignum a, Bignum b, Bignum addend) { /* * Non-modular multiplication. */ -Bignum bigmul(Bignum a, Bignum b) { +Bignum bigmul(Bignum a, Bignum b) +{ return bigmuladd(a, b, NULL); } @@ -658,54 +728,57 @@ Bignum bigmul(Bignum a, Bignum b) { * is, the smallest integer which is >= N and is also one less than * a power of two. */ -Bignum bignum_bitmask(Bignum n) { +Bignum bignum_bitmask(Bignum n) +{ Bignum ret = copybn(n); int i; unsigned short j; i = ret[0]; while (n[i] == 0 && i > 0) - i--; + i--; if (i <= 0) - return ret; /* input was zero */ + return ret; /* input was zero */ j = 1; while (j < n[i]) - j = 2*j+1; + j = 2 * j + 1; ret[i] = j; while (--i > 0) - ret[i] = 0xFFFF; + ret[i] = 0xFFFF; return ret; } /* * Convert a (max 16-bit) short into a bignum. */ -Bignum bignum_from_short(unsigned short n) { +Bignum bignum_from_short(unsigned short n) +{ Bignum ret; ret = newbn(2); ret[1] = n & 0xFFFF; ret[2] = (n >> 16) & 0xFFFF; ret[0] = (ret[2] ? 2 : 1); - return ret; + return ret; } /* * Add a long to a bignum. */ -Bignum bignum_add_long(Bignum number, unsigned long addend) { - Bignum ret = newbn(number[0]+1); +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; + 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; @@ -714,49 +787,59 @@ Bignum bignum_add_long(Bignum number, unsigned long addend) { /* * Compute the residue of a bignum, modulo a (max 16-bit) short. */ -unsigned short bignum_mod_short(Bignum number, unsigned short modulus) { +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; + r = (r * 65536 + number[i]) % mod; return (unsigned short) r; } -void diagbn(char *prefix, Bignum md) { +void diagbn(char *prefix, Bignum md) +{ int i, nibbles, morenibbles; static const char hex[] = "0123456789ABCDEF"; debugprint(("%s0x", prefix ? prefix : "")); - nibbles = (3 + bignum_bitcount(md))/4; if (nibbles<1) nibbles=1; - morenibbles = 4*md[0] - nibbles; - for (i=0; i> (4*(i%2))) & 0xF])); + nibbles = (3 + bignum_bitcount(md)) / 4; + if (nibbles < 1) + nibbles = 1; + morenibbles = 4 * md[0] - nibbles; + for (i = 0; i < morenibbles; i++) + debugprint(("-")); + for (i = nibbles; i--;) + debugprint( + ("%c", + hex[(bignum_byte(md, i / 2) >> (4 * (i % 2))) & 0xF])); - if (prefix) debugprint(("\n")); + if (prefix) + debugprint(("\n")); } /* * Greatest common divisor. */ -Bignum biggcd(Bignum av, Bignum bv) { +Bignum biggcd(Bignum av, Bignum bv) +{ Bignum a = copybn(av); Bignum b = copybn(bv); diagbn("a = ", a); diagbn("b = ", b); while (bignum_cmp(b, Zero) != 0) { - Bignum t = newbn(b[0]); - bigmod(a, b, t, NULL); - diagbn("t = ", t); - while (t[0] > 1 && t[t[0]] == 0) t[0]--; - freebn(a); - a = b; - b = t; + Bignum t = newbn(b[0]); + bigmod(a, b, t, NULL); + diagbn("t = ", t); + while (t[0] > 1 && t[t[0]] == 0) + t[0]--; + freebn(a); + a = b; + b = t; } freebn(b); @@ -766,7 +849,8 @@ Bignum biggcd(Bignum av, Bignum bv) { /* * Modular inverse, using Euclid's extended algorithm. */ -Bignum modinv(Bignum number, Bignum modulus) { +Bignum modinv(Bignum number, Bignum modulus) +{ Bignum a = copybn(modulus); Bignum b = copybn(number); Bignum xp = copybn(Zero); @@ -774,18 +858,19 @@ Bignum modinv(Bignum number, Bignum modulus) { int sign = +1; while (bignum_cmp(b, One) != 0) { - Bignum t = newbn(b[0]); - Bignum q = newbn(a[0]); - bigmod(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); + Bignum t = newbn(b[0]); + Bignum q = newbn(a[0]); + bigmod(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); @@ -794,24 +879,24 @@ Bignum modinv(Bignum number, Bignum modulus) { /* 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; + /* 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. */ @@ -822,7 +907,8 @@ Bignum modinv(Bignum number, Bignum modulus) { * Render a bignum into decimal. Return a malloced string holding * the decimal representation. */ -char *bignum_decimal(Bignum x) { +char *bignum_decimal(Bignum x) +{ int ndigits, ndigit; int i, iszero; unsigned long carry; @@ -843,8 +929,8 @@ char *bignum_decimal(Bignum x) { * 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 */ + ndigits = (28 * i + 92) / 93; /* multiply by 28/93 and round up */ + ndigits++; /* allow for trailing \0 */ ret = smalloc(ndigits); /* @@ -854,26 +940,26 @@ char *bignum_decimal(Bignum x) { */ workspace = smalloc(sizeof(unsigned short) * x[0]); for (i = 0; i < x[0]; i++) - workspace[i] = x[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; + 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'); + 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); /* @@ -881,7 +967,7 @@ char *bignum_decimal(Bignum x) { * string. Correct if so. */ if (ndigit > 0) - memmove(ret, ret+ndigit, ndigits-ndigit); + memmove(ret, ret + ndigit, ndigits - ndigit); /* * Done.