/* * Copyright (c) 1995 Colin Plumb. All rights reserved. * For licensing and other legal details, see the file legal.c. * * bn32.c - the high-level bignum interface * * Like lbn32.c, this reserves the string "32" for textual replacement. * The string must not appear anywhere unless it is intended to be replaced * to generate other bignum interface functions. */ #ifndef HAVE_CONFIG_H #define HAVE_CONFIG_H 0 #endif #if HAVE_CONFIG_H #include "bnconfig.h" #endif /* * Some compilers complain about #if FOO if FOO isn't defined, * so do the ANSI-mandated thing explicitly... */ #ifndef NO_ASSERT_H #define NO_ASSERT_H 0 #endif #ifndef NO_STRING_H #define NO_STRING_H 0 #endif #ifndef HAVE_STRINGS_H #define HAVE_STRINGS_H 0 #endif #if !NO_ASSERT_H #include #else #define assert(x) (void)0 #endif #if !NO_STRING_H #include /* for memmove() in bnMakeOdd */ #elif HAVE_STRINGS_H #include #endif /* * This was useful during debugging, so it's left in here. * You can ignore it. DBMALLOC is generally undefined. */ #ifndef DBMALLOC #define DBMALLOC 0 #endif #if DBMALLOC #include "../dbmalloc/malloc.h" #define MALLOCDB malloc_chain_check(1) #else #define MALLOCDB (void)0 #endif #include "lbn.h" #include "lbn32.h" #include "lbnmem.h" #include "bn32.h" #include "bn.h" /* Work-arounds for some particularly broken systems */ #include "kludge.h" /* For memmove() */ /* Functions */ void bnInit_32(void) { bnEnd = bnEnd_32; bnPrealloc = bnPrealloc_32; bnCopy = bnCopy_32; bnNorm = bnNorm_32; bnExtractBigBytes = bnExtractBigBytes_32; bnInsertBigBytes = bnInsertBigBytes_32; bnExtractLittleBytes = bnExtractLittleBytes_32; bnInsertLittleBytes = bnInsertLittleBytes_32; bnLSWord = bnLSWord_32; bnReadBit = bnReadBit_32; bnBits = bnBits_32; bnAdd = bnAdd_32; bnSub = bnSub_32; bnCmpQ = bnCmpQ_32; bnSetQ = bnSetQ_32; bnAddQ = bnAddQ_32; bnSubQ = bnSubQ_32; bnCmp = bnCmp_32; bnSquare = bnSquare_32; bnMul = bnMul_32; bnMulQ = bnMulQ_32; bnDivMod = bnDivMod_32; bnMod = bnMod_32; bnModQ = bnModQ_32; bnExpMod = bnExpMod_32; bnDoubleExpMod = bnDoubleExpMod_32; bnTwoExpMod = bnTwoExpMod_32; bnGcd = bnGcd_32; bnInv = bnInv_32; bnLShift = bnLShift_32; bnRShift = bnRShift_32; bnMakeOdd = bnMakeOdd_32; bnBasePrecompBegin = bnBasePrecompBegin_32; bnBasePrecompEnd = bnBasePrecompEnd_32; bnBasePrecompExpMod = bnBasePrecompExpMod_32; bnDoubleBasePrecompExpMod = bnDoubleBasePrecompExpMod_32; } void bnEnd_32(struct BigNum *bn) { if (bn->ptr) { LBNFREE((BNWORD32 *)bn->ptr, bn->allocated); bn->ptr = 0; } bn->size = 0; bn->allocated = 0; MALLOCDB; } /* Internal function. It operates in words. */ static int bnResize_32(struct BigNum *bn, unsigned len) { void *p; /* Round size up: most mallocs impose 8-byte granularity anyway */ len = (len + (8/sizeof(BNWORD32) - 1)) & ~(8/sizeof(BNWORD32) - 1); p = LBNREALLOC((BNWORD32 *)bn->ptr, bn->allocated, len); if (!p) return -1; bn->ptr = p; bn->allocated = len; MALLOCDB; return 0; } #define bnSizeCheck(bn, size) \ if (bn->allocated < size && bnResize_32(bn, size) < 0) \ return -1 /* Preallocate enough space in bn to hold "bits" bits. */ int bnPrealloc_32(struct BigNum *bn, unsigned bits) { bits = (bits + 32-1)/32; bnSizeCheck(bn, bits); MALLOCDB; return 0; } int bnCopy_32(struct BigNum *dest, struct BigNum const *src) { bnSizeCheck(dest, src->size); dest->size = src->size; lbnCopy_32((BNWORD32 *)dest->ptr, (BNWORD32 *)src->ptr, src->size); MALLOCDB; return 0; } /* Is this ever needed? Normalize the bn by deleting high-order 0 words */ void bnNorm_32(struct BigNum *bn) { bn->size = lbnNorm_32((BNWORD32 *)bn->ptr, bn->size); } /* * Convert a bignum to big-endian bytes. Returns, in big-endian form, a * substring of the bignum starting from lsbyte and "len" bytes long. * Unused high-order (leading) bytes are filled with 0. */ void bnExtractBigBytes_32(struct BigNum const *bn, unsigned char *dest, unsigned lsbyte, unsigned len) { unsigned s = bn->size * (32 / 8); /* Fill unused leading bytes with 0 */ while (s < lsbyte + len) { *dest++ = 0; len--; } if (len) lbnExtractBigBytes_32((BNWORD32 *)bn->ptr, dest, lsbyte, len); MALLOCDB; } /* The inverse of the above. */ int bnInsertBigBytes_32(struct BigNum *bn, unsigned char const *src, unsigned lsbyte, unsigned len) { unsigned s = bn->size; unsigned words = (len+lsbyte+sizeof(BNWORD32)-1) / sizeof(BNWORD32); /* Pad with zeros as required */ bnSizeCheck(bn, words); if (s < words) { lbnZero_32((BNWORD32 *)bn->ptr BIGLITTLE(-s,+s), words-s); s = words; } lbnInsertBigBytes_32((BNWORD32 *)bn->ptr, src, lsbyte, len); bn->size = lbnNorm_32((BNWORD32 *)bn->ptr, s); MALLOCDB; return 0; } /* * Convert a bignum to little-endian bytes. Returns, in little-endian form, a * substring of the bignum starting from lsbyte and "len" bytes long. * Unused high-order (trailing) bytes are filled with 0. */ void bnExtractLittleBytes_32(struct BigNum const *bn, unsigned char *dest, unsigned lsbyte, unsigned len) { unsigned s = bn->size * (32 / 8); /* Fill unused leading bytes with 0 */ while (s < lsbyte + len) dest[--len] = 0; if (len) lbnExtractLittleBytes_32((BNWORD32 *)bn->ptr, dest, lsbyte, len); MALLOCDB; } /* The inverse of the above */ int bnInsertLittleBytes_32(struct BigNum *bn, unsigned char const *src, unsigned lsbyte, unsigned len) { unsigned s = bn->size; unsigned words = (len+lsbyte+sizeof(BNWORD32)-1) / sizeof(BNWORD32); /* Pad with zeros as required */ bnSizeCheck(bn, words); if (s < words) { lbnZero_32((BNWORD32 *)bn->ptr BIGLITTLE(-s,+s), words-s); s = words; } lbnInsertLittleBytes_32((BNWORD32 *)bn->ptr, src, lsbyte, len); bn->size = lbnNorm_32((BNWORD32 *)bn->ptr, s); MALLOCDB; return 0; } /* Return the least-significant word of the input. */ unsigned bnLSWord_32(struct BigNum const *bn) { return bn->size ? (unsigned)((BNWORD32 *)bn->ptr)[BIGLITTLE(-1,0)]: 0; } /* Return a selected bit of the data */ int bnReadBit_32(struct BigNum const *bn, unsigned bit) { BNWORD32 word; if (bit/32 >= bn->size) return 0; word = ((BNWORD32 *)bn->ptr)[BIGLITTLE(-1-bit/32,bit/32)]; return (int)(word >> (bit % 32) & 1); } /* Count the number of significant bits. */ unsigned bnBits_32(struct BigNum const *bn) { return lbnBits_32((BNWORD32 *)bn->ptr, bn->size); } /* dest += src */ int bnAdd_32(struct BigNum *dest, struct BigNum const *src) { unsigned s = src->size, d = dest->size; BNWORD32 t; if (!s) return 0; bnSizeCheck(dest, s); if (d < s) { lbnZero_32((BNWORD32 *)dest->ptr BIGLITTLE(-d,+d), s-d); dest->size = d = s; MALLOCDB; } t = lbnAddN_32((BNWORD32 *)dest->ptr, (BNWORD32 *)src->ptr, s); MALLOCDB; if (t) { if (d > s) { t = lbnAdd1_32((BNWORD32 *)dest->ptr BIGLITTLE(-s,+s), d-s, t); MALLOCDB; } if (t) { bnSizeCheck(dest, d+1); ((BNWORD32 *)dest->ptr)[BIGLITTLE(-1-d,d)] = t; dest->size = d+1; } } return 0; } /* * dest -= src. * If dest goes negative, this produces the absolute value of * the difference (the negative of the true value) and returns 1. * Otherwise, it returls 0. */ int bnSub_32(struct BigNum *dest, struct BigNum const *src) { unsigned s = src->size, d = dest->size; BNWORD32 t; if (d < s && d < (s = lbnNorm_32((BNWORD32 *)src->ptr, s))) { bnSizeCheck(dest, s); lbnZero_32((BNWORD32 *)dest->ptr BIGLITTLE(-d,+d), s-d); dest->size = d = s; MALLOCDB; } if (!s) return 0; t = lbnSubN_32((BNWORD32 *)dest->ptr, (BNWORD32 *)src->ptr, s); MALLOCDB; if (t) { if (d > s) { t = lbnSub1_32((BNWORD32 *)dest->ptr BIGLITTLE(-s,+s), d-s, t); MALLOCDB; } if (t) { lbnNeg_32((BNWORD32 *)dest->ptr, d); dest->size = lbnNorm_32((BNWORD32 *)dest->ptr, dest->size); MALLOCDB; return 1; } } dest->size = lbnNorm_32((BNWORD32 *)dest->ptr, dest->size); return 0; } /* * Compare the BigNum to the given value, which must be < 65536. * Returns -1. 0 or 1 if ab. * a <=> b --> bnCmpQ(a,b) <=> 0 */ int bnCmpQ_32(struct BigNum const *a, unsigned b) { unsigned t; BNWORD32 v; t = lbnNorm_32((BNWORD32 *)a->ptr, a->size); /* If a is more than one word long or zero, it's easy... */ if (t != 1) return (t > 1) ? 1 : (b ? -1 : 0); v = (unsigned)((BNWORD32 *)a->ptr)[BIGLITTLE(-1,0)]; return (v > b) ? 1 : ((v < b) ? -1 : 0); } /* Set dest to a small value */ int bnSetQ_32(struct BigNum *dest, unsigned src) { if (src) { bnSizeCheck(dest, 1); ((BNWORD32 *)dest->ptr)[BIGLITTLE(-1,0)] = (BNWORD32)src; dest->size = 1; } else { dest->size = 0; } return 0; } /* dest += src */ int bnAddQ_32(struct BigNum *dest, unsigned src) { BNWORD32 t; if (!dest->size) return bnSetQ(dest, src); t = lbnAdd1_32((BNWORD32 *)dest->ptr, dest->size, (BNWORD32)src); MALLOCDB; if (t) { src = dest->size; bnSizeCheck(dest, src+1); ((BNWORD32 *)dest->ptr)[BIGLITTLE(-1-src,src)] = t; dest->size = src+1; } return 0; } /* * Return value as for bnSub: 1 if subtract underflowed, in which * case the return is the negative of the computed value. */ int bnSubQ_32(struct BigNum *dest, unsigned src) { BNWORD32 t; if (!dest->size) return bnSetQ(dest, src) < 0 ? -1 : (src != 0); t = lbnSub1_32((BNWORD32 *)dest->ptr, dest->size, src); MALLOCDB; if (t) { /* Underflow. <= 1 word, so do it simply. */ lbnNeg_32((BNWORD32 *)dest->ptr, 1); dest->size = 1; return 1; } /* Try to normalize? Needing this is going to be pretty damn rare. */ /* dest->size = lbnNorm_32((BNWORD32 *)dest->ptr, dest->size); */ return 0; } /* * Compare two BigNums. Returns -1. 0 or 1 if ab. * a <=> b --> bnCmp(a,b) <=> 0 */ int bnCmp_32(struct BigNum const *a, struct BigNum const *b) { unsigned s, t; s = lbnNorm_32((BNWORD32 *)a->ptr, a->size); t = lbnNorm_32((BNWORD32 *)b->ptr, b->size); if (s != t) return s > t ? 1 : -1; return lbnCmp_32((BNWORD32 *)a->ptr, (BNWORD32 *)b->ptr, s); } /* dest = src*src. This is more efficient than bnMul. */ int bnSquare_32(struct BigNum *dest, struct BigNum const *src) { unsigned s; BNWORD32 *srcbuf; s = lbnNorm_32((BNWORD32 *)src->ptr, src->size); if (!s) { dest->size = 0; return 0; } bnSizeCheck(dest, 2*s); if (src == dest) { LBNALLOC(srcbuf, BNWORD32, s); if (!srcbuf) return -1; lbnCopy_32(srcbuf, (BNWORD32 *)src->ptr, s); lbnSquare_32((BNWORD32 *)dest->ptr, (BNWORD32 *)srcbuf, s); LBNFREE(srcbuf, s); } else { lbnSquare_32((BNWORD32 *)dest->ptr, (BNWORD32 *)src->ptr, s); } dest->size = lbnNorm_32((BNWORD32 *)dest->ptr, 2*s); MALLOCDB; return 0; } /* dest = a * b. Any overlap between operands is allowed. */ int bnMul_32(struct BigNum *dest, struct BigNum const *a, struct BigNum const *b) { unsigned s, t; BNWORD32 *srcbuf; s = lbnNorm_32((BNWORD32 *)a->ptr, a->size); t = lbnNorm_32((BNWORD32 *)b->ptr, b->size); if (!s || !t) { dest->size = 0; return 0; } if (a == b) return bnSquare_32(dest, a); bnSizeCheck(dest, s+t); if (dest == a) { LBNALLOC(srcbuf, BNWORD32, s); if (!srcbuf) return -1; lbnCopy_32(srcbuf, (BNWORD32 *)a->ptr, s); lbnMul_32((BNWORD32 *)dest->ptr, srcbuf, s, (BNWORD32 *)b->ptr, t); LBNFREE(srcbuf, s); } else if (dest == b) { LBNALLOC(srcbuf, BNWORD32, t); if (!srcbuf) return -1; lbnCopy_32(srcbuf, (BNWORD32 *)b->ptr, t); lbnMul_32((BNWORD32 *)dest->ptr, (BNWORD32 *)a->ptr, s, srcbuf, t); LBNFREE(srcbuf, t); } else { lbnMul_32((BNWORD32 *)dest->ptr, (BNWORD32 *)a->ptr, s, (BNWORD32 *)b->ptr, t); } dest->size = lbnNorm_32((BNWORD32 *)dest->ptr, s+t); MALLOCDB; return 0; } /* dest = a * b */ int bnMulQ_32(struct BigNum *dest, struct BigNum const *a, unsigned b) { unsigned s; s = lbnNorm_32((BNWORD32 *)a->ptr, a->size); if (!s || !b) { dest->size = 0; return 0; } if (b == 1) return bnCopy_32(dest, a); bnSizeCheck(dest, s+1); lbnMulN1_32((BNWORD32 *)dest->ptr, (BNWORD32 *)a->ptr, s, b); dest->size = lbnNorm_32((BNWORD32 *)dest->ptr, s+1); MALLOCDB; return 0; } /* q = n/d, r = n % d */ int bnDivMod_32(struct BigNum *q, struct BigNum *r, struct BigNum const *n, struct BigNum const *d) { unsigned dsize, nsize; BNWORD32 qhigh; dsize = lbnNorm_32((BNWORD32 *)d->ptr, d->size); nsize = lbnNorm_32((BNWORD32 *)n->ptr, n->size); if (nsize < dsize) { q->size = 0; /* No quotient */ r->size = nsize; return 0; /* Success */ } bnSizeCheck(q, nsize-dsize); if (r != n) { /* You are allowed to reduce in place */ bnSizeCheck(r, nsize); lbnCopy_32((BNWORD32 *)r->ptr, (BNWORD32 *)n->ptr, nsize); } qhigh = lbnDiv_32((BNWORD32 *)q->ptr, (BNWORD32 *)r->ptr, nsize, (BNWORD32 *)d->ptr, dsize); nsize -= dsize; if (qhigh) { bnSizeCheck(q, nsize+1); *((BNWORD32 *)q->ptr BIGLITTLE(-nsize-1,+nsize)) = qhigh; q->size = nsize+1; } else { q->size = lbnNorm_32((BNWORD32 *)q->ptr, nsize); } r->size = lbnNorm_32((BNWORD32 *)r->ptr, dsize); MALLOCDB; return 0; } /* det = src % d */ int bnMod_32(struct BigNum *dest, struct BigNum const *src, struct BigNum const *d) { unsigned dsize, nsize; nsize = lbnNorm_32((BNWORD32 *)src->ptr, src->size); dsize = lbnNorm_32((BNWORD32 *)d->ptr, d->size); if (dest != src) { bnSizeCheck(dest, nsize); lbnCopy_32((BNWORD32 *)dest->ptr, (BNWORD32 *)src->ptr, nsize); } if (nsize < dsize) { dest->size = nsize; /* No quotient */ return 0; } (void)lbnDiv_32((BNWORD32 *)dest->ptr BIGLITTLE(-dsize,+dsize), (BNWORD32 *)dest->ptr, nsize, (BNWORD32 *)d->ptr, dsize); dest->size = lbnNorm_32((BNWORD32 *)dest->ptr, dsize); MALLOCDB; return 0; } /* return src % d. */ unsigned bnModQ_32(struct BigNum const *src, unsigned d) { unsigned s; s = lbnNorm_32((BNWORD32 *)src->ptr, src->size); if (!s) return 0; if (d & (d-1)) /* Not a power of 2 */ d = lbnModQ_32((BNWORD32 *)src->ptr, s, d); else d = (unsigned)((BNWORD32 *)src->ptr)[BIGLITTLE(-1,0)] & (d-1); return d; } /* dest = n^exp (mod mod) */ int bnExpMod_32(struct BigNum *dest, struct BigNum const *n, struct BigNum const *exp, struct BigNum const *mod) { unsigned nsize, esize, msize; nsize = lbnNorm_32((BNWORD32 *)n->ptr, n->size); esize = lbnNorm_32((BNWORD32 *)exp->ptr, exp->size); msize = lbnNorm_32((BNWORD32 *)mod->ptr, mod->size); if (!msize || (((BNWORD32 *)mod->ptr)[BIGLITTLE(-1,0)] & 1) == 0) return -1; /* Illegal modulus! */ bnSizeCheck(dest, msize); /* Special-case base of 2 */ if (nsize == 1 && ((BNWORD32 *)n->ptr)[BIGLITTLE(-1,0)] == 2) { if (lbnTwoExpMod_32((BNWORD32 *)dest->ptr, (BNWORD32 *)exp->ptr, esize, (BNWORD32 *)mod->ptr, msize) < 0) return -1; } else { if (lbnExpMod_32((BNWORD32 *)dest->ptr, (BNWORD32 *)n->ptr, nsize, (BNWORD32 *)exp->ptr, esize, (BNWORD32 *)mod->ptr, msize) < 0) return -1; } dest->size = lbnNorm_32((BNWORD32 *)dest->ptr, msize); MALLOCDB; return 0; } /* * dest = n1^e1 * n2^e2 (mod mod). This is more efficient than two * separate modular exponentiations, and in fact asymptotically approaches * the cost of one. */ int bnDoubleExpMod_32(struct BigNum *dest, struct BigNum const *n1, struct BigNum const *e1, struct BigNum const *n2, struct BigNum const *e2, struct BigNum const *mod) { unsigned n1size, e1size, n2size, e2size, msize; n1size = lbnNorm_32((BNWORD32 *)n1->ptr, n1->size); e1size = lbnNorm_32((BNWORD32 *)e1->ptr, e1->size); n2size = lbnNorm_32((BNWORD32 *)n2->ptr, n2->size); e2size = lbnNorm_32((BNWORD32 *)e2->ptr, e2->size); msize = lbnNorm_32((BNWORD32 *)mod->ptr, mod->size); if (!msize || (((BNWORD32 *)mod->ptr)[BIGLITTLE(-1,0)] & 1) == 0) return -1; /* Illegal modulus! */ bnSizeCheck(dest, msize); if (lbnDoubleExpMod_32((BNWORD32 *)dest->ptr, (BNWORD32 *)n1->ptr, n1size, (BNWORD32 *)e1->ptr, e1size, (BNWORD32 *)n2->ptr, n2size, (BNWORD32 *)e2->ptr, e2size, (BNWORD32 *)mod->ptr, msize) < 0) return -1; dest->size = lbnNorm_32((BNWORD32 *)dest->ptr, msize); MALLOCDB; return 0; } /* n = 2^exp (mod mod) */ int bnTwoExpMod_32(struct BigNum *n, struct BigNum const *exp, struct BigNum const *mod) { unsigned esize, msize; esize = lbnNorm_32((BNWORD32 *)exp->ptr, exp->size); msize = lbnNorm_32((BNWORD32 *)mod->ptr, mod->size); if (!msize || (((BNWORD32 *)mod->ptr)[BIGLITTLE(-1,0)] & 1) == 0) return -1; /* Illegal modulus! */ bnSizeCheck(n, msize); if (lbnTwoExpMod_32((BNWORD32 *)n->ptr, (BNWORD32 *)exp->ptr, esize, (BNWORD32 *)mod->ptr, msize) < 0) return -1; n->size = lbnNorm_32((BNWORD32 *)n->ptr, msize); MALLOCDB; return 0; } /* dest = gcd(a, b) */ int bnGcd_32(struct BigNum *dest, struct BigNum const *a, struct BigNum const *b) { BNWORD32 *tmp; unsigned asize, bsize; int i; /* Kind of silly, but we might as well permit it... */ if (a == b) return dest == a ? 0 : bnCopy(dest, a); /* Ensure a is not the same as "dest" */ if (a == dest) { a = b; b = dest; } asize = lbnNorm_32((BNWORD32 *)a->ptr, a->size); bsize = lbnNorm_32((BNWORD32 *)b->ptr, b->size); bnSizeCheck(dest, bsize+1); /* Copy a to tmp */ LBNALLOC(tmp, BNWORD32, asize+1); if (!tmp) return -1; lbnCopy_32(tmp, (BNWORD32 *)a->ptr, asize); /* Copy b to dest, if necessary */ if (dest != b) lbnCopy_32((BNWORD32 *)dest->ptr, (BNWORD32 *)b->ptr, bsize); if (bsize > asize || (bsize == asize && lbnCmp_32((BNWORD32 *)b->ptr, (BNWORD32 *)a->ptr, asize) > 0)) { i = lbnGcd_32((BNWORD32 *)dest->ptr, bsize, tmp, asize, &dest->size); if (i > 0) /* Result in tmp, not dest */ lbnCopy_32((BNWORD32 *)dest->ptr, tmp, dest->size); } else { i = lbnGcd_32(tmp, asize, (BNWORD32 *)dest->ptr, bsize, &dest->size); if (i == 0) /* Result in tmp, not dest */ lbnCopy_32((BNWORD32 *)dest->ptr, tmp, dest->size); } LBNFREE(tmp, asize+1); MALLOCDB; return (i < 0) ? i : 0; } /* * dest = 1/src (mod mod). Returns >0 if gcd(src, mod) != 1 (in which case * the inverse does not exist). */ int bnInv_32(struct BigNum *dest, struct BigNum const *src, struct BigNum const *mod) { unsigned s, m; int i; s = lbnNorm_32((BNWORD32 *)src->ptr, src->size); m = lbnNorm_32((BNWORD32 *)mod->ptr, mod->size); /* lbnInv_32 requires that the input be less than the modulus */ if (m < s || (m==s && lbnCmp_32((BNWORD32 *)src->ptr, (BNWORD32 *)mod->ptr, s))) { bnSizeCheck(dest, s + (m==s)); if (dest != src) lbnCopy_32((BNWORD32 *)dest->ptr, (BNWORD32 *)src->ptr, s); /* Pre-reduce modulo the modulus */ (void)lbnDiv_32((BNWORD32 *)dest->ptr BIGLITTLE(-m,+m), (BNWORD32 *)dest->ptr, s, (BNWORD32 *)mod->ptr, m); s = lbnNorm_32((BNWORD32 *)dest->ptr, m); MALLOCDB; } else { bnSizeCheck(dest, m+1); if (dest != src) lbnCopy_32((BNWORD32 *)dest->ptr, (BNWORD32 *)src->ptr, s); } i = lbnInv_32((BNWORD32 *)dest->ptr, s, (BNWORD32 *)mod->ptr, m); if (i == 0) dest->size = lbnNorm_32((BNWORD32 *)dest->ptr, m); MALLOCDB; return i; } /* * Shift a bignum left the appropriate number of bits, * multiplying by 2^amt. */ int bnLShift_32(struct BigNum *dest, unsigned amt) { unsigned s = dest->size; BNWORD32 carry; if (amt % 32) { carry = lbnLshift_32((BNWORD32 *)dest->ptr, s, amt % 32); if (carry) { s++; bnSizeCheck(dest, s); ((BNWORD32 *)dest->ptr)[BIGLITTLE(-s,s-1)] = carry; } } amt /= 32; if (amt) { bnSizeCheck(dest, s+amt); memmove((BNWORD32 *)dest->ptr BIGLITTLE(-s-amt, +amt), (BNWORD32 *)dest->ptr BIG(-s), s * sizeof(BNWORD32)); lbnZero_32((BNWORD32 *)dest->ptr, amt); s += amt; } dest->size = s; MALLOCDB; return 0; } /* * Shift a bignum right the appropriate number of bits, * dividing by 2^amt. */ void bnRShift_32(struct BigNum *dest, unsigned amt) { unsigned s = dest->size; if (amt >= 32) { memmove( (BNWORD32 *)dest->ptr BIG(-s+amt/32), (BNWORD32 *)dest->ptr BIGLITTLE(-s, +amt/32), (s-amt/32) * sizeof(BNWORD32)); s -= amt/32; amt %= 32; } if (amt) (void)lbnRshift_32((BNWORD32 *)dest->ptr, s, amt); dest->size = lbnNorm_32((BNWORD32 *)dest->ptr, s); MALLOCDB; } /* * Shift a bignum right until it is odd, and return the number of * bits shifted. n = d * 2^s. Replaces n with d and returns s. * Returns 0 when given 0. (Another valid answer is infinity.) */ unsigned bnMakeOdd_32(struct BigNum *n) { unsigned size; unsigned s; /* shift amount */ BNWORD32 *p; BNWORD32 t; p = (BNWORD32 *)n->ptr; size = lbnNorm_32(p, n->size); if (!size) return 0; t = BIGLITTLE(p[-1],p[0]); s = 0; /* See how many words we have to shift */ if (!t) { /* Shift by words */ do { s++; BIGLITTLE(--p,p++); } while ((t = BIGLITTLE(p[-1],p[0])) == 0); size -= s; s *= 32; memmove((BNWORD32 *)n->ptr BIG(-size), p BIG(-size), size * sizeof(BNWORD32)); p = (BNWORD32 *)n->ptr; MALLOCDB; } assert(t); if (!(t & 1)) { /* Now count the bits */ do { t >>= 1; s++; } while ((t & 1) == 0); /* Shift the bits */ lbnRshift_32(p, size, s & (32-1)); /* Renormalize */ if (BIGLITTLE(*(p-size),*(p+(size-1))) == 0) --size; } n->size = size; MALLOCDB; return s; } /* * Do base- and modulus-dependent precomputation for rapid computation of * base^exp (mod mod) with various exponents. * * See lbn32.c for the details on how the algorithm works. Basically, * it involves precomputing a table of powers of base, base^(order^k), * for a suitable range 0 <= k < n detemined by the maximum exponent size * desired. To do eht exponentiation, the exponent is expressed in base * "order" (sorry for the confusing terminology) and the precomputed powers * are combined. * * This implementation allows only power-of-2 values for "order". Using * other numbers can be more efficient, but it's more work and for the * popular exponent size of 320 bits, an order of 8 is optimal, so it * hasn't seemed worth it to implement. * * Here's a table of the optimal power-of-2 order for various exponent * sizes and the associated (average) cost for an exponentiation. * Note that *higher* orders are more memory-efficient; the number * of precomputed values required is ceil(ebits/order). (Ignore the * underscores in the middle of numbers; they're harmless.) * * At 2 bits, order 2 uses 0.000000 multiplies * At 4 bits, order 2 uses 1.000000 multiplies * At 8 bits, order 2 uses 3.000000 multiplies * At 1_6 bits, order 2 uses 7.000000 multiplies * At 3_2 bits, order 2 uses 15.000000 multiplies * At 34 bits, 15.750000 (order 4) < 1_6.000000 (order 2) * At 6_4 bits, order 4 uses 27.000000 multiplies * At 99 bits, 39.875000 (order 8) < 40.250000 (order 4) * At 128 bits, order 8 uses 48.500000 multiplies * At 256 bits, order 8 uses 85.875000 multiplies * At 280 bits, 92.625000 (order 1_6) < 92.875000 (order 8) * At 512 bits, order 1_6 uses 147.000000 multiplies * At 785 bits, 211.093750 (order 3_2) < 211.250000 (order 1_6) * At 1024 bits, order 3_2 uses 257.562500 multiplies * At 2048 bits, order 3_2 uses 456.093750 multiplies * At 2148 bits, 475.406250 (order 6_4) < 475.468750 (order 3_2) * At 4096 bits, order 6_4 uses 795.281250 multiplies * At 5726 bits, 1062.609375 (order 128) < 1062.843750 (order 6_4) * At 8192 bits, order 128 uses 1412.609375 multiplies * At 14848 bits, 2355.750000 (order 256) < 2355.929688 (order 128) * At 37593 bits, 5187.841797 (order 512) < 5188.144531 (order 256) */ int bnBasePrecompBegin_32(struct BnBasePrecomp *pre, struct BigNum const *base, struct BigNum const *mod, unsigned maxebits) { int i; BNWORD32 **array; /* Array of precomputed powers of base */ unsigned n; /* Number of entries in array (needed) */ unsigned m; /* Number of entries in array (non-NULL) */ unsigned arraysize; /* Number of entries in array (allocated) */ unsigned bits; /* log2(order) */ unsigned msize = lbnNorm_32((BNWORD32 *)mod->ptr, mod->size); static unsigned const bnBasePrecompThreshTable[] = { 33, 98, 279, 784, 2147, 5725, 14847, 37592, (unsigned)-1 }; /* Clear pre in case of failure */ pre->array = 0; pre->msize = 0; pre->bits = 0; pre->maxebits = 0; pre->arraysize = 0; pre->entries = 0; /* Find the correct bit-window size */ bits = 0; do bits++; while (maxebits > bnBasePrecompThreshTable[bits]); /* Now the number of precomputed values we need */ n = (maxebits+bits-1)/bits; assert(n*bits >= maxebits); arraysize = n+1; /* Add one trailing NULL for safety */ array = lbnMemAlloc(arraysize * sizeof(*array)); if (!array) return -1; /* Out of memory */ /* Now allocate the entries (precomputed powers of base) */ for (m = 0; m < n; m++) { BNWORD32 *entry; LBNALLOC(entry, BNWORD32, msize); if (!entry) break; array[m] = entry; } /* "m" is the number of successfully allocated entries */ if (m < n) { /* Ran out of memory; see if we can use a smaller array */ BNWORD32 **newarray; if (m < 2) { n = 0; /* Forget it */ } else { /* How few bits can we use with what's allocated? */ bits = (maxebits + m - 1) / m; retry: n = (maxebits + bits - 1) / bits; if (! (n >> bits) ) n = 0; /* Not enough to amount to anything */ } /* Free excess allocated array entries */ while (m > n) { BNWORD32 *entry = array[--m]; LBNFREE(entry, msize); } if (!n) { /* Give it up */ lbnMemFree(array, arraysize * sizeof(*array)); return -1; } /* * Try to shrink the pointer array. This might fail, but * it's not critical. lbnMemRealloc isn't guarnateed to * exist, so we may have to allocate, copy, and free. */ #ifdef lbnMemRealloc newarray = lbnMemRealloc(array, arraysize * sizeof(*array), (n+1) * sizeof(*array)); if (newarray) { array = newarray; arraysize = n+1; } #else newarray = lbnMemAlloc((n+1) * sizeof(*array)); if (newarray) { memcpy(newarray, array, n * sizeof(*array)); lbnMemFree(array, arraysize * sizeof(*array)); array = newarray; arraysize = n+1; } #endif } /* Pad with null pointers */ while (m < arraysize) array[m++] = 0; /* Okay, we have our array, now initialize it */ i = lbnBasePrecompBegin_32(array, n, bits, (BNWORD32 *)base->ptr, base->size, (BNWORD32 *)mod->ptr, msize); if (i < 0) { /* Ack, still out of memory */ bits++; m = n; goto retry; } /* Finally, totoal success */ pre->array = array; pre->bits = bits; pre->msize = msize; pre->maxebits = n * bits; pre->arraysize = arraysize; pre->entries = n; return 0; } /* Free everything preallocated */ void bnBasePrecompEnd_32(struct BnBasePrecomp *pre) { BNWORD32 **array = pre->array; if (array) { unsigned entries = pre->entries; unsigned msize = pre->msize; unsigned m; for (m = 0; m < entries; m++) { BNWORD32 *entry = array[m]; if (entry) LBNFREE(entry, msize); } lbnMemFree(array, pre->arraysize * sizeof(array)); } pre->array = 0; pre->bits = 0; pre->msize = 0; pre->maxebits = 0; pre->arraysize = 0; pre->entries = 0; } int bnBasePrecompExpMod_32(struct BigNum *dest, struct BnBasePrecomp const *pre, struct BigNum const *exp, struct BigNum const *mod) { unsigned msize = lbnNorm_32((BNWORD32 *)mod->ptr, mod->size); unsigned esize = lbnNorm_32((BNWORD32 *)exp->ptr, exp->size); BNWORD32 const * const *array = pre->array; int i; assert(msize == pre->msize); assert(((BNWORD32 *)mod->ptr)[BIGLITTLE(-1,0)] & 1); assert(lbnBits_32((BNWORD32 *)exp->ptr, esize) <= pre->maxebits); bnSizeCheck(dest, msize); i = lbnBasePrecompExp_32(dest->ptr, array, pre->bits, exp->ptr, esize, mod->ptr, msize); if (i == 0) dest->size = lbnNorm_32((BNWORD32 *)dest->ptr, msize); return i; } int bnDoubleBasePrecompExpMod_32(struct BigNum *dest, struct BnBasePrecomp const *pre1, struct BigNum const *exp1, struct BnBasePrecomp const *pre2, struct BigNum const *exp2, struct BigNum const *mod) { unsigned msize = lbnNorm_32((BNWORD32 *)mod->ptr, mod->size); unsigned e1size = lbnNorm_32((BNWORD32 *)exp1->ptr, exp1->size); unsigned e2size = lbnNorm_32((BNWORD32 *)exp1->ptr, exp2->size); BNWORD32 const * const *array1 = pre1->array; BNWORD32 const * const *array2 = pre2->array; int i; assert(msize == pre1->msize); assert(msize == pre2->msize); assert(((BNWORD32 *)mod->ptr)[BIGLITTLE(-1,0)] & 1); assert(lbnBits_32((BNWORD32 *)exp1->ptr, e1size) <= pre1->maxebits); assert(lbnBits_32((BNWORD32 *)exp2->ptr, e2size) <= pre2->maxebits); assert(pre1->bits == pre2->bits); bnSizeCheck(dest, msize); i = lbnDoubleBasePrecompExp_32(dest->ptr, pre1->bits, array1, exp1->ptr, e1size, array2, exp2->ptr, e2size, mod->ptr, msize); if (i == 0) dest->size = lbnNorm_32((BNWORD32 *)dest->ptr, msize); return i; }