/* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ #ifndef TMA_H #define TMA_H #include #include #include #include #include #include "tma_class.h" /* Assure these -Pekka */ #undef MP_8BIT #undef MP_16BIT #undef CRYPT #ifndef MIN #define MIN(x,y) ((x)<(y)?(x):(y)) #endif #ifndef MAX #define MAX(x,y) ((x)>(y)?(x):(y)) #endif #ifdef __cplusplus extern "C" { /* C++ compilers don't like assigning void * to tma_mp_digit * */ #define OPT_CAST(x) (x *) #else /* C on the other hand doesn't care */ #define OPT_CAST(x) #endif /* detect 64-bit mode if possible */ #if defined(__x86_64__) #if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT)) #define MP_64BIT #endif #endif /* some default configurations. * * A "tma_mp_digit" must be able to hold DIGIT_BIT + 1 bits * A "tma_mp_word" must be able to hold 2*DIGIT_BIT + 1 bits * * At the very least a tma_mp_digit must be able to hold 7 bits * [any size beyond that is ok provided it doesn't overflow the data type] */ #ifdef MP_8BIT typedef unsigned char tma_mp_digit; typedef unsigned short tma_mp_word; #elif defined(MP_16BIT) typedef unsigned short tma_mp_digit; typedef unsigned long tma_mp_word; #elif defined(MP_64BIT) /* for GCC only on supported platforms */ #ifndef CRYPT typedef unsigned long long ulong64; typedef signed long long long64; #endif typedef unsigned long tma_mp_digit; typedef unsigned long tma_mp_word __attribute__ ((mode(TI))); #define DIGIT_BIT 60 #else /* this is the default case, 28-bit digits */ /* this is to make porting into LibTomCrypt easier :-) */ #ifndef CRYPT #if defined(_MSC_VER) || defined(__BORLANDC__) typedef unsigned __int64 ulong64; typedef signed __int64 long64; #else typedef unsigned long long ulong64; typedef signed long long long64; #endif #endif typedef unsigned long tma_mp_digit; typedef ulong64 tma_mp_word; #ifdef MP_31BIT /* this is an extension that uses 31-bit digits */ #define DIGIT_BIT 31 #else /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */ #define DIGIT_BIT 28 #define MP_28BIT #endif #endif /* define heap macros */ #ifndef CRYPT /* default to libc stuff */ #ifndef XMALLOC #define XMALLOC malloc #define XFREE free #define XREALLOC realloc #define XCALLOC calloc #else /* prototypes for our heap functions */ extern void *XMALLOC(size_t n); extern void *XREALLOC(void *p, size_t n); extern void *XCALLOC(size_t n, size_t s); extern void XFREE(void *p); #endif #endif /* otherwise the bits per digit is calculated automatically from the size of a tma_mp_digit */ #ifndef DIGIT_BIT #define DIGIT_BIT ((int)((CHAR_BIT * sizeof(tma_mp_digit) - 1))) /* bits per digit */ #endif #define MP_DIGIT_BIT DIGIT_BIT #define MP_MASK ((((tma_mp_digit)1)<<((tma_mp_digit)DIGIT_BIT))-((tma_mp_digit)1)) #define MP_DIGIT_MAX MP_MASK /* equalities */ #define MP_LT -1 /* less than */ #define MP_EQ 0 /* equal to */ #define MP_GT 1 /* greater than */ #define MP_ZPOS 0 /* positive integer */ #define MP_NEG 1 /* negative */ #define MP_OKAY 0 /* ok result */ #define MP_MEM -2 /* out of mem */ #define MP_VAL -3 /* invalid input */ #define MP_RANGE MP_VAL #define MP_YES 1 /* yes response */ #define MP_NO 0 /* no response */ /* Primality generation flags */ #define LTM_PRIME_BBS 0x0001 /* BBS style prime */ #define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */ #define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */ typedef int tma_mp_err; /* you'll have to tune these... */ extern int KARATSUBA_MUL_CUTOFF, KARATSUBA_SQR_CUTOFF, TOOM_MUL_CUTOFF, TOOM_SQR_CUTOFF; /* define this to use lower memory usage routines (exptmods mostly) */ /* #define MP_LOW_MEM */ /* default precision */ #ifndef MP_PREC #ifndef MP_LOW_MEM #define MP_PREC 32 /* default digits of precision */ #else #define MP_PREC 8 /* default digits of precision */ #endif #endif /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */ #define MP_WARRAY (1 << (sizeof(tma_mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1)) /* the infamous tma_mp_int structure */ typedef struct { int used, alloc, sign; tma_mp_digit *dp; } tma_mp_int; /* callback for tma_mp_prime_random, should fill dst with random bytes and return how many read [upto len] */ typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat); #define USED(m) ((m)->used) #define DIGIT(m,k) ((m)->dp[(k)]) #define SIGN(m) ((m)->sign) /* error code to char* string */ char *tma_mp_error_to_string(int code); /* ---> init and deinit bignum functions <--- */ /* init a bignum */ int tma_mp_init(tma_mp_int *a); /* free a bignum */ void tma_mp_clear(tma_mp_int *a); /* init a null terminated series of arguments */ int tma_mp_init_multi(tma_mp_int *mp, ...); /* clear a null terminated series of arguments */ void tma_mp_clear_multi(tma_mp_int *mp, ...); /* exchange two ints */ void tma_mp_exch(tma_mp_int *a, tma_mp_int *b); /* shrink ram required for a bignum */ int tma_mp_shrink(tma_mp_int *a); /* grow an int to a given size */ int tma_mp_grow(tma_mp_int *a, int size); /* init to a given number of digits */ int tma_mp_init_size(tma_mp_int *a, int size); /* ---> Basic Manipulations <--- */ #define tma_mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO) #define tma_mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO) #define tma_mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO) /* set to zero */ void tma_mp_zero(tma_mp_int *a); /* set to a digit */ void tma_mp_set(tma_mp_int *a, tma_mp_digit b); /* set a 32-bit const */ int tma_mp_set_int(tma_mp_int *a, unsigned long b); /* get a 32-bit value */ unsigned long tma_mp_get_int(tma_mp_int * a); /* initialize and set a digit */ int tma_mp_init_set (tma_mp_int * a, tma_mp_digit b); /* initialize and set 32-bit value */ int tma_mp_init_set_int (tma_mp_int * a, unsigned long b); /* copy, b = a */ int tma_mp_copy(tma_mp_int *a, tma_mp_int *b); /* inits and copies, a = b */ int tma_mp_init_copy(tma_mp_int *a, tma_mp_int *b); /* trim unused digits */ void tma_mp_clamp(tma_mp_int *a); /* ---> digit manipulation <--- */ /* right shift by "b" digits */ void tma_mp_rshd(tma_mp_int *a, int b); /* left shift by "b" digits */ int tma_mp_lshd(tma_mp_int *a, int b); /* c = a / 2**b */ int tma_mp_div_2d(tma_mp_int *a, int b, tma_mp_int *c, tma_mp_int *d); /* b = a/2 */ int tma_mp_div_2(tma_mp_int *a, tma_mp_int *b); /* c = a * 2**b */ int tma_mp_mul_2d(tma_mp_int *a, int b, tma_mp_int *c); /* b = a*2 */ int tma_mp_mul_2(tma_mp_int *a, tma_mp_int *b); /* c = a mod 2**d */ int tma_mp_mod_2d(tma_mp_int *a, int b, tma_mp_int *c); /* computes a = 2**b */ int tma_mp_2expt(tma_mp_int *a, int b); /* Counts the number of lsbs which are zero before the first zero bit */ int tma_mp_cnt_lsb(tma_mp_int *a); /* I Love Earth! */ /* makes a pseudo-random int of a given size */ int tma_mp_rand(tma_mp_int *a, int digits); /* ---> binary operations <--- */ /* c = a XOR b */ int tma_mp_xor(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c); /* c = a OR b */ int tma_mp_or(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c); /* c = a AND b */ int tma_mp_and(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c); /* ---> Basic arithmetic <--- */ /* b = -a */ int tma_mp_neg(tma_mp_int *a, tma_mp_int *b); /* b = |a| */ int tma_mp_abs(tma_mp_int *a, tma_mp_int *b); /* compare a to b */ int tma_mp_cmp(tma_mp_int *a, tma_mp_int *b); /* compare |a| to |b| */ int tma_mp_cmp_mag(tma_mp_int *a, tma_mp_int *b); /* c = a + b */ int tma_mp_add(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c); /* c = a - b */ int tma_mp_sub(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c); /* c = a * b */ int tma_mp_mul(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c); /* b = a*a */ int tma_mp_sqr(tma_mp_int *a, tma_mp_int *b); /* a/b => cb + d == a */ int tma_mp_div(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c, tma_mp_int *d); /* c = a mod b, 0 <= c < b */ int tma_mp_mod(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c); /* ---> single digit functions <--- */ /* compare against a single digit */ int tma_mp_cmp_d(tma_mp_int *a, tma_mp_digit b); /* c = a + b */ int tma_mp_add_d(tma_mp_int *a, tma_mp_digit b, tma_mp_int *c); /* c = a - b */ int tma_mp_sub_d(tma_mp_int *a, tma_mp_digit b, tma_mp_int *c); /* c = a * b */ int tma_mp_mul_d(tma_mp_int *a, tma_mp_digit b, tma_mp_int *c); /* a/b => cb + d == a */ int tma_mp_div_d(tma_mp_int *a, tma_mp_digit b, tma_mp_int *c, tma_mp_digit *d); /* a/3 => 3c + d == a */ int tma_mp_div_3(tma_mp_int *a, tma_mp_int *c, tma_mp_digit *d); /* c = a**b */ int tma_mp_expt_d(tma_mp_int *a, tma_mp_digit b, tma_mp_int *c); /* c = a mod b, 0 <= c < b */ int tma_mp_mod_d(tma_mp_int *a, tma_mp_digit b, tma_mp_digit *c); /* ---> number theory <--- */ /* d = a + b (mod c) */ int tma_mp_addmod(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c, tma_mp_int *d); /* d = a - b (mod c) */ int tma_mp_submod(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c, tma_mp_int *d); /* d = a * b (mod c) */ int tma_mp_mulmod(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c, tma_mp_int *d); /* c = a * a (mod b) */ int tma_mp_sqrmod(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c); /* c = 1/a (mod b) */ int tma_mp_invmod(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c); /* c = (a, b) */ int tma_mp_gcd(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c); /* produces value such that U1*a + U2*b = U3 */ int tma_mp_exteuclid(tma_mp_int *a, tma_mp_int *b, tma_mp_int *U1, tma_mp_int *U2, tma_mp_int *U3); /* c = [a, b] or (a*b)/(a, b) */ int tma_mp_lcm(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c); /* finds one of the b'th root of a, such that |c|**b <= |a| * * returns error if a < 0 and b is even */ int tma_mp_n_root(tma_mp_int *a, tma_mp_digit b, tma_mp_int *c); /* special sqrt algo */ int tma_mp_sqrt(tma_mp_int *arg, tma_mp_int *ret); /* is number a square? */ int tma_mp_is_square(tma_mp_int *arg, int *ret); /* computes the jacobi c = (a | n) (or Legendre if b is prime) */ int tma_mp_jacobi(tma_mp_int *a, tma_mp_int *n, int *c); /* used to setup the Barrett reduction for a given modulus b */ int tma_mp_reduce_setup(tma_mp_int *a, tma_mp_int *b); /* Barrett Reduction, computes a (mod b) with a precomputed value c * * Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely * compute the reduction as -1 * tma_mp_reduce(tma_mp_abs(a)) [pseudo code]. */ int tma_mp_reduce(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c); /* setups the montgomery reduction */ int tma_mp_montgomery_setup(tma_mp_int *a, tma_mp_digit *mp); /* computes a = B**n mod b without division or multiplication useful for * normalizing numbers in a Montgomery system. */ int tma_mp_montgomery_calc_normalization(tma_mp_int *a, tma_mp_int *b); /* computes x/R == x (mod N) via Montgomery Reduction */ int tma_mp_montgomery_reduce(tma_mp_int *a, tma_mp_int *m, tma_mp_digit mp); /* returns 1 if a is a valid DR modulus */ int tma_mp_dr_is_modulus(tma_mp_int *a); /* sets the value of "d" required for tma_mp_dr_reduce */ void tma_mp_dr_setup(tma_mp_int *a, tma_mp_digit *d); /* reduces a modulo b using the Diminished Radix method */ int tma_mp_dr_reduce(tma_mp_int *a, tma_mp_int *b, tma_mp_digit mp); /* returns true if a can be reduced with tma_mp_reduce_2k */ int tma_mp_reduce_is_2k(tma_mp_int *a); /* determines k value for 2k reduction */ int tma_mp_reduce_2k_setup(tma_mp_int *a, tma_mp_digit *d); /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ int tma_mp_reduce_2k(tma_mp_int *a, tma_mp_int *n, tma_mp_digit d); /* returns true if a can be reduced with tma_mp_reduce_2k_l */ int tma_mp_reduce_is_2k_l(tma_mp_int *a); /* determines k value for 2k reduction */ int tma_mp_reduce_2k_setup_l(tma_mp_int *a, tma_mp_int *d); /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ int tma_mp_reduce_2k_l(tma_mp_int *a, tma_mp_int *n, tma_mp_int *d); /* d = a**b (mod c) */ int tma_mp_exptmod(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c, tma_mp_int *d); /* ---> Primes <--- */ /* number of primes */ #ifdef MP_8BIT #define PRIME_SIZE 31 #else #define PRIME_SIZE 256 #endif /* table of first PRIME_SIZE primes */ extern const tma_mp_digit ltm_prime_tab[]; /* result=1 if a is divisible by one of the first PRIME_SIZE primes */ int tma_mp_prime_is_divisible(tma_mp_int *a, int *result); /* performs one Fermat test of "a" using base "b". * Sets result to 0 if composite or 1 if probable prime */ int tma_mp_prime_fermat(tma_mp_int *a, tma_mp_int *b, int *result); /* performs one Miller-Rabin test of "a" using base "b". * Sets result to 0 if composite or 1 if probable prime */ int tma_mp_prime_miller_rabin(tma_mp_int *a, tma_mp_int *b, int *result); /* This gives [for a given bit size] the number of trials required * such that Miller-Rabin gives a prob of failure lower than 2^-96 */ int tma_mp_prime_rabin_miller_trials(int size); /* performs t rounds of Miller-Rabin on "a" using the first * t prime bases. Also performs an initial sieve of trial * division. Determines if "a" is prime with probability * of error no more than (1/4)**t. * * Sets result to 1 if probably prime, 0 otherwise */ int tma_mp_prime_is_prime(tma_mp_int *a, int t, int *result); /* finds the next prime after the number "a" using "t" trials * of Miller-Rabin. * * bbs_style = 1 means the prime must be congruent to 3 mod 4 */ int tma_mp_prime_next_prime(tma_mp_int *a, int t, int bbs_style); /* makes a truly random prime of a given size (bytes), * call with bbs = 1 if you want it to be congruent to 3 mod 4 * * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself * so it can be NULL * * The prime generated will be larger than 2^(8*size). */ #define tma_mp_prime_random(a, t, size, bbs, cb, dat) tma_mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat) /* makes a truly random prime of a given size (bits), * * Flags are as follows: * * LTM_PRIME_BBS - make prime congruent to 3 mod 4 * LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS) * LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero * LTM_PRIME_2MSB_ON - make the 2nd highest bit one * * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself * so it can be NULL * */ int tma_mp_prime_random_ex(tma_mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat); /* ---> radix conversion <--- */ int tma_mp_count_bits(tma_mp_int *a); int tma_mp_unsigned_bin_size(tma_mp_int *a); int tma_mp_read_unsigned_bin(tma_mp_int *a, const unsigned char *b, int c); int tma_mp_to_unsigned_bin(tma_mp_int *a, unsigned char *b); int tma_mp_to_unsigned_bin_n (tma_mp_int * a, unsigned char *b, unsigned long *outlen); int tma_mp_signed_bin_size(tma_mp_int *a); int tma_mp_read_signed_bin(tma_mp_int *a, const unsigned char *b, int c); int tma_mp_to_signed_bin(tma_mp_int *a, unsigned char *b); int tma_mp_to_signed_bin_n (tma_mp_int * a, unsigned char *b, unsigned long *outlen); int tma_mp_read_radix(tma_mp_int *a, const char *str, int radix); int tma_mp_toradix(tma_mp_int *a, char *str, int radix); int tma_mp_toradix_n(tma_mp_int * a, char *str, int radix, int maxlen); int tma_mp_radix_size(tma_mp_int *a, int radix, int *size); int tma_mp_fread(tma_mp_int *a, int radix, FILE *stream); int tma_mp_fwrite(tma_mp_int *a, int radix, FILE *stream); #define tma_mp_read_raw(mp, str, len) tma_mp_read_signed_bin((mp), (str), (len)) #define tma_mp_raw_size(mp) tma_mp_signed_bin_size(mp) #define tma_mp_toraw(mp, str) tma_mp_to_signed_bin((mp), (str)) #define tma_mp_read_mag(mp, str, len) tma_mp_read_unsigned_bin((mp), (str), (len)) #define tma_mp_mag_size(mp) tma_mp_unsigned_bin_size(mp) #define tma_mp_tomag(mp, str) tma_mp_to_unsigned_bin((mp), (str)) #define tma_mp_tobinary(M, S) tma_mp_toradix((M), (S), 2) #define tma_mp_tooctal(M, S) tma_mp_toradix((M), (S), 8) #define tma_mp_todecimal(M, S) tma_mp_toradix((M), (S), 10) #define tma_mp_tohex(M, S) tma_mp_toradix((M), (S), 16) /* lowlevel functions, do not call! */ int s_tma_mp_add(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c); int s_tma_mp_sub(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c); #define s_tma_mp_mul(a, b, c) s_tma_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1) int fast_s_tma_mp_mul_digs(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c, int digs); int s_tma_mp_mul_digs(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c, int digs); int fast_s_tma_mp_mul_high_digs(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c, int digs); int s_tma_mp_mul_high_digs(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c, int digs); int fast_s_tma_mp_sqr(tma_mp_int *a, tma_mp_int *b); int s_tma_mp_sqr(tma_mp_int *a, tma_mp_int *b); int tma_mp_karatsuba_mul(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c); int tma_mp_toom_mul(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c); int tma_mp_karatsuba_sqr(tma_mp_int *a, tma_mp_int *b); int tma_mp_toom_sqr(tma_mp_int *a, tma_mp_int *b); int fast_tma_mp_invmod(tma_mp_int *a, tma_mp_int *b, tma_mp_int *c); int tma_mp_invmod_slow (tma_mp_int * a, tma_mp_int * b, tma_mp_int * c); int fast_tma_mp_montgomery_reduce(tma_mp_int *a, tma_mp_int *m, tma_mp_digit mp); int tma_mp_exptmod_fast(tma_mp_int *G, tma_mp_int *X, tma_mp_int *P, tma_mp_int *Y, int mode); int s_tma_mp_exptmod (tma_mp_int * G, tma_mp_int * X, tma_mp_int * P, tma_mp_int * Y, int mode); void bn_reverse(unsigned char *s, int len); extern const char *tma_mp_s_rmap; #ifdef __cplusplus } #endif /* $Source$ */ /* $Revision$ */ /* $Date$ */ #endif /* TMA_H */