/* * Copyright (c) 1995 Colin Plumb. All rights reserved. * For licensing and other legal details, see the file legal.c. * * bn.h - the interface to the bignum routines. * All functions which return ints can potentially allocate memory * and return -1 if they are unable to. All "const" arguments * are unmodified. * * This is not particularly asymmetric, as some operations are of the * form a = b @ c, while others do a @= b. In general, outputs may not * point to the same struct BigNums as inputs, except as specified * below. This relationship is referred to as "being the same as". * This is not numerical equivalence. * * The "Q" operations take "unsigned" inputs. Higher values of the * extra input may work on some implementations, but 65535 is the * highest portable value. Just because UNSIGNED_MAX is larger than * that, or you know that the word size of the library is larger than that, * that, does *not* mean it's allowed. */ #ifndef BN_H #define BN_H struct BigNum { void *ptr; unsigned size; /* Note: in (variable-sized) words */ unsigned allocated; }; /* * User-supplied function: if non-NULL, this is called during long-running * computations. You may put Yield() calls in here to give CPU time to * other processes. You may also force the computation to be aborted, * by returning a value < 0, which will be the return value of the * bnXXX call. (You probably want the value to be someting other than * -1, to distinguish it from a n out-of-memory error.) * * The functions that this is called from, and the intervals at which it * is called, are not well defined, just "reasonably often". (Currently, * once per exponent bit in nodular exponentiation, and once per two * divisions in GCD and inverse computation.) */ extern int (*bnYield)(void); /* Functions */ /* * You usually never have to call this function explicitly, as * bnBegin() takes care of it. If the program jumps to address 0, * this function has bot been called. */ void bnInit(void); /* * This initializes an empty struct BigNum to a zero value. * Do not use this on a BigNum which has had a value stored in it! */ void bnBegin(struct BigNum *bn); /* Swap two BigNums. Cheap. */ void bnSwap(struct BigNum *a, struct BigNum *b); /* Reset an initialized bigNum to empty, pending deallocation. */ extern void (*bnEnd)(struct BigNum *bn); /* * If you know you'll need space in the number soon, you can use this function * to ensure that there is room for at least "bits" bits. Optional. * Returns <0 on out of memory, but the value is unaffected. */ extern int (*bnPrealloc)(struct BigNum *bn, unsigned bits); /* Hopefully obvious. dest = src. dest may be the same as src. */ extern int (*bnCopy)(struct BigNum *dest, struct BigNum const *src); /* * Mostly done automatically, but this removes leading zero words from * the internal representation of the BigNum. Use is unclear. */ extern void (*bnNorm)(struct BigNum *bn); /* * Move bytes between the given buffer and the given BigNum encoded in * base 256. I.e. after either of these, the buffer will be equal to * (bn / 256^lsbyte) % 256^len. The difference is which is altered to * match the other! */ extern void (*bnExtractBigBytes)(struct BigNum const *bn, unsigned char *dest, unsigned lsbyte, unsigned len); extern int (*bnInsertBigBytes)(struct BigNum *bn, unsigned char const *src, unsigned lsbyte, unsigned len); /* The same, but the buffer is little-endian. */ extern void (*bnExtractLittleBytes)(struct BigNum const *bn, unsigned char *dest, unsigned lsbyte, unsigned len); extern int (*bnInsertLittleBytes)(struct BigNum *bn, unsigned char const *src, unsigned lsbyte, unsigned len); /* Return the least-significant bits (at least 16) of the BigNum */ extern unsigned (*bnLSWord)(struct BigNum const *src); /* Return the selected bit of the BigNum (bit 0 is bn mod 2) */ extern int (*bnReadBit)(struct BigNum const *bn, unsigned bit); /* * Return the number of significant bits in the BigNum. * 0 or 1+floor(log2(src)) */ extern unsigned (*bnBits)(struct BigNum const *src); #define bnBytes(bn) ((bnBits(bn)+7)/8) /* * dest += src. dest and src may be the same. Guaranteed not to * allocate memory unnecessarily, so if you're sure bnBits(dest) * won't change, you don't need to check the return value. */ extern int (*bnAdd)(struct BigNum *dest, struct BigNum const *src); /* * dest -= src. dest and src may be the same, but bnSetQ(dest, 0) is faster. * if dest < src, returns +1 and sets dest = src-dest. */ extern int (*bnSub)(struct BigNum *dest, struct BigNum const *src); /* Return sign (-1, 0, +1) of a-b. a <=> b --> bnCmpQ(a, b) <=> 0 */ extern int (*bnCmpQ)(struct BigNum const *a, unsigned b); /* dest = src, where 0 <= src < 2^16. */ extern int (*bnSetQ)(struct BigNum *dest, unsigned src); /* dest += src, where 0 <= src < 2^16 */ extern int (*bnAddQ)(struct BigNum *dest, unsigned src); /* dest -= src, where 0 <= src < 2^16 */ extern int (*bnSubQ)(struct BigNum *dest, unsigned src); /* Return sign (-1, 0, +1) of a-b. a <=> b --> bnCmp(a, b) <=> 0 */ extern int (*bnCmp)(struct BigNum const *a, struct BigNum const *b); /* dest = src^2. dest may be the same as src, but it costs time. */ extern int (*bnSquare)(struct BigNum *dest, struct BigNum const *src); /* dest = a * b. dest may be the same as a or b, but it costs time. */ extern int (*bnMul)(struct BigNum *dest, struct BigNum const *a, struct BigNum const *b); /* dest = a * b, where 0 <= b < 2^16. dest and a may be the same. */ extern int (*bnMulQ)(struct BigNum *dest, struct BigNum const *a, unsigned b); /* * q = n/d, r = n%d. r may be the same as n, but not d, * and q may not be the same as n or d. * re-entrancy issue: this temporarily modifies d, but restores * it for return. */ extern int (*bnDivMod)(struct BigNum *q, struct BigNum *r, struct BigNum const *n, struct BigNum const *d); /* * dest = src % d. dest and src may be the same, but not dest and d. * re-entrancy issue: this temporarily modifies d, but restores * it for return. */ extern int (*bnMod)(struct BigNum *dest, struct BigNum const *src, struct BigNum const *d); /* return src % d, where 0 <= d < 2^16. */ extern unsigned int (*bnModQ)(struct BigNum const *src, unsigned d); /* n = n^exp, modulo "mod" "mod" *must* be odd */ extern int (*bnExpMod)(struct BigNum *result, struct BigNum const *n, struct BigNum const *exp, struct BigNum const *mod); /* * dest = n1^e1 * n2^e2, modulo "mod". "mod" *must* be odd. * dest may be the same as n1 or n2. */ extern int (*bnDoubleExpMod)(struct BigNum *dest, struct BigNum const *n1, struct BigNum const *e1, struct BigNum const *n2, struct BigNum const *e2, struct BigNum const *mod); /* n = 2^exp, modulo "mod" "mod" *must* be odd */ extern int (*bnTwoExpMod)(struct BigNum *n, struct BigNum const *exp, struct BigNum const *mod); /* dest = gcd(a, b). The inputs may overlap arbitrarily. */ extern int (*bnGcd)(struct BigNum *dest, struct BigNum const *a, struct BigNum const *b); /* dest = src^-1, modulo "mod". dest may be the same as src. */ extern int (*bnInv)(struct BigNum *dest, struct BigNum const *src, struct BigNum const *mod); /* Shift dest left "amt" places */ extern int (*bnLShift)(struct BigNum *dest, unsigned amt); /* Shift dest right "amt" places, discarding low-order bits */ extern void (*bnRShift)(struct BigNum *dest, unsigned amt); /* For the largest 2^k that divides n, divide n by it and return k. */ extern unsigned (*bnMakeOdd)(struct BigNum *n); /* * Precomputed data for rapid base^exp (mod mod) computation with fixed * base and mod. */ struct BnBasePrecomp { void *array; /* Ponter to array of pointers to words */ unsigned msize; /* Words in modulis (normalized) */ unsigned bits; /* Bits per array element */ unsigned maxebits; /* Maximum exponent bits */ unsigned entries; /* Number of entries */ unsigned arraysize; }; extern int (*bnBasePrecompBegin)(struct BnBasePrecomp *pre, struct BigNum const *base, struct BigNum const *mod, unsigned maxebits); extern void (*bnBasePrecompEnd)(struct BnBasePrecomp *pre); extern int (*bnBasePrecompExpMod)(struct BigNum *dest, struct BnBasePrecomp const *pre, struct BigNum const *exp, struct BigNum const *mod); extern int (*bnDoubleBasePrecompExpMod)(struct BigNum *dest, struct BnBasePrecomp const *pre1, struct BigNum const *exp1, struct BnBasePrecomp const *pre2, struct BigNum const *exp2, struct BigNum const *mod); #endif/* !BN_H */