/* LibTomMath, multiple-precision integer library -- Tom St Denis */ /* SPDX-License-Identifier: Unlicense */ #ifndef BN_H_ #define BN_H_ #include "tclTomMathDecls.h" #ifndef MODULE_SCOPE #define MODULE_SCOPE extern #endif #ifdef __cplusplus extern "C" { #endif /* MS Visual C++ doesn't have a 128bit type for words, so fall back to 32bit MPI's (where words are 64bit) */ #if defined(_WIN32) || defined(__LLP64__) || defined(__e2k__) || defined(__LCC__) # define MP_32BIT #endif /* detect 64-bit mode if possible */ #if defined(NEVER) # if !(defined(MP_32BIT) || defined(MP_16BIT) || defined(MP_8BIT)) # if defined(__GNUC__) /* we support 128bit integers only via: __attribute__((mode(TI))) */ # define MP_64BIT # else /* otherwise we fall back to MP_32BIT even on 64bit platforms */ # define MP_32BIT # endif # endif #endif /* some default configurations. * * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits * * At the very least a 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 #ifndef MP_DIGIT_DECLARED typedef unsigned char mp_digit; #define MP_DIGIT_DECLARED #endif #ifndef MP_WORD_DECLARED typedef unsigned short mp_word; #define MP_WORD_DECLARED #endif # define MP_SIZEOF_MP_DIGIT 1 # ifdef DIGIT_BIT # error You must not define DIGIT_BIT when using MP_8BIT # endif #elif defined(MP_16BIT) #ifndef MP_DIGIT_DECLARED typedef unsigned short mp_digit; #define MP_DIGIT_DECLARED #endif #ifndef MP_WORD_DECLARED typedef unsigned int mp_word; #define MP_WORD_DECLARED #endif # define MP_SIZEOF_MP_DIGIT 2 # ifdef DIGIT_BIT # error You must not define DIGIT_BIT when using MP_16BIT # endif #elif defined(MP_64BIT) /* for GCC only on supported platforms */ #ifndef MP_DIGIT_DECLARED typedef unsigned long long mp_digit; #define MP_DIGIT_DECLARED #endif typedef unsigned long 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 MP_DIGIT_DECLARED typedef unsigned int mp_digit; #define MP_DIGIT_DECLARED #endif #ifndef MP_WORD_DECLARED #ifdef _WIN32 typedef unsigned __int64 mp_word; #else typedef unsigned long long mp_word; #endif #define MP_WORD_DECLARED #endif # 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 /* otherwise the bits per digit is calculated automatically from the size of a mp_digit */ #ifndef DIGIT_BIT # define DIGIT_BIT (((CHAR_BIT * MP_SIZEOF_MP_DIGIT) - 1)) /* bits per digit */ #endif #define MP_DIGIT_BIT DIGIT_BIT #define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1)) #define MP_DIGIT_MAX MP_MASK typedef int mp_sign; #define MP_ZPOS 0 /* positive integer */ #define MP_NEG 1 /* negative */ typedef int mp_ord; #define MP_LT -1 /* less than */ #define MP_EQ 0 /* equal to */ #define MP_GT 1 /* greater than */ typedef int mp_bool; #define MP_YES 1 /* yes response */ #define MP_NO 0 /* no response */ typedef int mp_err; #define MP_OKAY 0 /* ok result */ #define MP_ERR -1 /* unknown error */ #define MP_MEM -2 /* out of mem */ #define MP_VAL -3 /* invalid input */ #define MP_RANGE MP_VAL #define MP_ITER -4 /* Max. iterations reached */ /* 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 */ /* tunable cutoffs */ /* 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 */ # elif defined(MP_8BIT) # define MP_PREC 16 /* 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 (1u << (((sizeof(mp_word) * CHAR_BIT) - (2 * DIGIT_BIT)) + 1)) /* * MP_WUR - warn unused result * --------------------------- * * The result of functions annotated with MP_WUR must be * checked and cannot be ignored. * * Most functions in libtommath return an error code. * This error code must be checked in order to prevent crashes or invalid * results. * * If you still want to avoid the error checks for quick and dirty programs * without robustness guarantees, you can `#define MP_WUR` before including * tommath.h, disabling the warnings. */ #ifndef MP_WUR # if defined(__GNUC__) && __GNUC__ >= 4 # define MP_WUR __attribute__((warn_unused_result)) # else # define MP_WUR # endif #endif #if defined(__GNUC__) && (__GNUC__ * 100 + __GNUC_MINOR__ >= 301) # define MP_DEPRECATED(x) __attribute__((deprecated("replaced by " #x))) # define PRIVATE_MP_DEPRECATED_PRAGMA(s) _Pragma(#s) # define MP_DEPRECATED_PRAGMA(s) PRIVATE_MP_DEPRECATED_PRAGMA(GCC warning s) #elif defined(_MSC_VER) && _MSC_VER >= 1500 # define MP_DEPRECATED(x) __declspec(deprecated("replaced by " #x)) # define MP_DEPRECATED_PRAGMA(s) __pragma(message(s)) #else # define MP_DEPRECATED # define MP_DEPRECATED_PRAGMA(s) #endif #define USED(m) ((m)->used) #define DIGIT(m,k) ((m)->dp[(k)]) #define SIGN(m) ((m)->sign) /* the infamous mp_int structure */ #ifndef MP_INT_DECLARED #define MP_INT_DECLARED typedef struct mp_int mp_int; #endif struct mp_int { int used, alloc, sign; mp_digit *dp; }; /* callback for 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); /* error code to char* string */ /* const char *mp_error_to_string(mp_err code); */ /* ---> init and deinit bignum functions <--- */ /* init a bignum */ /* mp_err mp_init(mp_int *a); */ /* free a bignum */ /* void mp_clear(mp_int *a); */ /* init a null terminated series of arguments */ /* mp_err mp_init_multi(mp_int *mp, ...); */ /* clear a null terminated series of arguments */ /* void mp_clear_multi(mp_int *mp, ...); */ /* exchange two ints */ /* void mp_exch(mp_int *a, mp_int *b); */ /* shrink ram required for a bignum */ /* mp_err mp_shrink(mp_int *a); */ /* grow an int to a given size */ /* mp_err mp_grow(mp_int *a, int size); */ /* init to a given number of digits */ /* mp_err mp_init_size(mp_int *a, int size); */ /* ---> Basic Manipulations <--- */ #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO) #define mp_iseven(a) (((a)->used == 0 || (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO) #define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO) #define mp_isneg(a) (((a)->sign != MP_ZPOS) ? MP_YES : MP_NO) /* set to zero */ /* void mp_zero(mp_int *a); */ /* set to a digit */ /* void mp_set(mp_int *a, mp_digit b); */ /* set a 32-bit const */ /* int mp_set_int(mp_int *a, unsigned long b); */ /* set a platform dependent unsigned long value */ /* int mp_set_long(mp_int *a, unsigned long b); */ /* set a platform dependent unsigned long long value */ /* int mp_set_long_long(mp_int *a, unsigned long long b); */ /* get a 32-bit value */ /* unsigned long mp_get_int(const mp_int *a); */ /* get a platform dependent unsigned long value */ /* unsigned long mp_get_long(const mp_int *a); */ /* get a platform dependent unsigned long long value */ /* unsigned long long mp_get_long_long(const mp_int *a); */ /* initialize and set a digit */ /* int mp_init_set(mp_int *a, mp_digit b); */ /* initialize and set 32-bit value */ /* int mp_init_set_int(mp_int *a, unsigned long b); */ /* copy, b = a */ /* int mp_copy(const mp_int *a, mp_int *b); */ /* inits and copies, a = b */ /* int mp_init_copy(mp_int *a, const mp_int *b); */ /* trim unused digits */ /* void mp_clamp(mp_int *a); */ /* import binary data */ /* int mp_import(mp_int *rop, size_t count, int order, size_t size, int endian, size_t nails, const void *op); */ /* export binary data */ /* int mp_export(void *rop, size_t *countp, int order, size_t size, int endian, size_t nails, const mp_int *op); */ /* ---> digit manipulation <--- */ /* right shift by "b" digits */ /* void mp_rshd(mp_int *a, int b); */ /* left shift by "b" digits */ /* int mp_lshd(mp_int *a, int b); */ /* c = a / 2**b, implemented as c = a >> b */ /* int mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d); */ /* b = a/2 */ /* int mp_div_2(const mp_int *a, mp_int *b); */ /* c = a * 2**b, implemented as c = a << b */ /* int mp_mul_2d(const mp_int *a, int b, mp_int *c); */ /* b = a*2 */ /* int mp_mul_2(const mp_int *a, mp_int *b); */ /* c = a mod 2**b */ /* int mp_mod_2d(const mp_int *a, int b, mp_int *c); */ /* computes a = 2**b */ /* int mp_2expt(mp_int *a, int b); */ /* Counts the number of lsbs which are zero before the first zero bit */ /* int mp_cnt_lsb(const mp_int *a); */ /* I Love Earth! */ /* makes a pseudo-random mp_int of a given size */ /* int mp_rand(mp_int *a, int digits); */ /* makes a pseudo-random small int of a given size */ /* int mp_rand_digit(mp_digit *r); */ #ifdef MP_PRNG_ENABLE_LTM_RNG /* A last resort to provide random data on systems without any of the other * implemented ways to gather entropy. * It is compatible with `rng_get_bytes()` from libtomcrypt so you could * provide that one and then set `ltm_rng = rng_get_bytes;` */ extern unsigned long (*ltm_rng)(unsigned char *out, unsigned long outlen, void (*callback)(void)); extern void (*ltm_rng_callback)(void); #endif /* ---> binary operations <--- */ /* c = a XOR b */ /* int mp_xor(const mp_int *a, const mp_int *b, mp_int *c); */ /* c = a OR b */ /* int mp_or(const mp_int *a, const mp_int *b, mp_int *c); */ /* c = a AND b */ /* int mp_and(const mp_int *a, const mp_int *b, mp_int *c); */ /* right shift (two complement) */ /* int mp_signed_rsh(const mp_int *a, int b, mp_int *c); */ /* ---> Basic arithmetic <--- */ /* b = ~a */ /* int mp_complement(const mp_int *a, mp_int *b); */ /* b = -a */ /* int mp_neg(const mp_int *a, mp_int *b); */ /* b = |a| */ /* int mp_abs(const mp_int *a, mp_int *b); */ /* compare a to b */ /* int mp_cmp(const mp_int *a, const mp_int *b); */ /* compare |a| to |b| */ /* int mp_cmp_mag(const mp_int *a, const mp_int *b); */ /* c = a + b */ /* int mp_add(const mp_int *a, const mp_int *b, mp_int *c); */ /* c = a - b */ /* int mp_sub(const mp_int *a, const mp_int *b, mp_int *c); */ /* c = a * b */ /* int mp_mul(const mp_int *a, const mp_int *b, mp_int *c); */ /* b = a*a */ /* int mp_sqr(const mp_int *a, mp_int *b); */ /* a/b => cb + d == a */ /* int mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d); */ /* c = a mod b, 0 <= c < b */ /* int mp_mod(const mp_int *a, const mp_int *b, mp_int *c); */ /* ---> single digit functions <--- */ /* compare against a single digit */ /* int mp_cmp_d(const mp_int *a, mp_digit b); */ /* c = a + b */ /* int mp_add_d(const mp_int *a, mp_digit b, mp_int *c); */ /* c = a - b */ /* int mp_sub_d(const mp_int *a, mp_digit b, mp_int *c); */ /* c = a * b */ /* int mp_mul_d(const mp_int *a, mp_digit b, mp_int *c); */ /* a/b => cb + d == a */ /* int mp_div_d(const mp_int *a, mp_digit b, mp_int *c, mp_digit *d); */ /* a/3 => 3c + d == a */ /* int mp_div_3(const mp_int *a, mp_int *c, mp_digit *d); */ /* c = a**b */ /* int mp_expt_d(const mp_int *a, mp_digit b, mp_int *c); */ /* int mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast); */ /* c = a mod b, 0 <= c < b */ /* int mp_mod_d(const mp_int *a, mp_digit b, mp_digit *c); */ /* ---> number theory <--- */ /* d = a + b (mod c) */ /* int mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); */ /* d = a - b (mod c) */ /* int mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); */ /* d = a * b (mod c) */ /* int mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); */ /* c = a * a (mod b) */ /* int mp_sqrmod(const mp_int *a, const mp_int *b, mp_int *c); */ /* c = 1/a (mod b) */ /* int mp_invmod(const mp_int *a, const mp_int *b, mp_int *c); */ /* c = (a, b) */ /* int mp_gcd(const mp_int *a, const mp_int *b, mp_int *c); */ /* produces value such that U1*a + U2*b = U3 */ /* int mp_exteuclid(const mp_int *a, const mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3); */ /* c = [a, b] or (a*b)/(a, b) */ /* int mp_lcm(const mp_int *a, const mp_int *b, 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 mp_n_root(const mp_int *a, mp_digit b, mp_int *c); */ /* int mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast); */ /* special sqrt algo */ /* int mp_sqrt(const mp_int *arg, mp_int *ret); */ /* special sqrt (mod prime) */ /* int mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret); */ /* is number a square? */ /* int mp_is_square(const mp_int *arg, int *ret); */ /* computes the jacobi c = (a | n) (or Legendre if b is prime) */ /* int mp_jacobi(const mp_int *a, const mp_int *n, int *c); */ /* used to setup the Barrett reduction for a given modulus b */ /* int mp_reduce_setup(mp_int *a, const mp_int *b); */ /* Barrett Reduction, computes a (mod b) with a precomputed value c * * Assumes that 0 < x <= m*m, note if 0 > x > -(m*m) then you can merely * compute the reduction as -1 * mp_reduce(mp_abs(x)) [pseudo code]. */ /* int mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu); */ /* setups the montgomery reduction */ /* int mp_montgomery_setup(const mp_int *n, mp_digit *rho); */ /* computes a = B**n mod b without division or multiplication useful for * normalizing numbers in a Montgomery system. */ /* int mp_montgomery_calc_normalization(mp_int *a, const mp_int *b); */ /* computes x/R == x (mod N) via Montgomery Reduction */ /* int mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho); */ /* returns 1 if a is a valid DR modulus */ /* int mp_dr_is_modulus(const mp_int *a); */ /* sets the value of "d" required for mp_dr_reduce */ /* void mp_dr_setup(const mp_int *a, mp_digit *d); */ /* reduces a modulo n using the Diminished Radix method */ /* int mp_dr_reduce(mp_int *x, const mp_int *n, mp_digit k); */ /* returns true if a can be reduced with mp_reduce_2k */ /* int mp_reduce_is_2k(const mp_int *a); */ /* determines k value for 2k reduction */ /* int mp_reduce_2k_setup(const mp_int *a, mp_digit *d); */ /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ /* int mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d); */ /* returns true if a can be reduced with mp_reduce_2k_l */ /* int mp_reduce_is_2k_l(const mp_int *a); */ /* determines k value for 2k reduction */ /* int mp_reduce_2k_setup_l(const mp_int *a, mp_int *d); */ /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ /* int mp_reduce_2k_l(mp_int *a, const mp_int *n, const mp_int *d); */ /* Y = G**X (mod P) */ /* int mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y); */ /* ---> Primes <--- */ /* number of primes */ #ifdef MP_8BIT # define PRIME_SIZE 31 #else # define PRIME_SIZE 256 #endif /* table of first PRIME_SIZE primes */ #if defined(BUILD_tcl) || !defined(_WIN32) MODULE_SCOPE const mp_digit ltm_prime_tab[PRIME_SIZE]; #endif /* result=1 if a is divisible by one of the first PRIME_SIZE primes */ /* int mp_prime_is_divisible(const 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 mp_prime_fermat(const mp_int *a, const 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 mp_prime_miller_rabin(const mp_int *a, const 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 mp_prime_rabin_miller_trials(int size); */ /* performs t random rounds of Miller-Rabin on "a" additional to * bases 2 and 3. Also performs an initial sieve of trial * division. Determines if "a" is prime with probability * of error no more than (1/4)**t. * Both a strong Lucas-Selfridge to complete the BPSW test * and a separate Frobenius test are available at compile time. * With t<0 a deterministic test is run for primes up to * 318665857834031151167461. With t<13 (abs(t)-13) additional * tests with sequential small primes are run starting at 43. * Is Fips 186.4 compliant if called with t as computed by * mp_prime_rabin_miller_trials(); * * Sets result to 1 if probably prime, 0 otherwise */ /* int mp_prime_is_prime(const 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 mp_prime_next_prime(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 mp_prime_random(a, t, size, bbs, cb, dat) 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_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 mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat); */ /* ---> radix conversion <--- */ /* int mp_count_bits(const mp_int *a); */ /* int mp_unsigned_bin_size(const mp_int *a); */ /* int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c); */ /* int mp_to_unsigned_bin(const mp_int *a, unsigned char *b); */ /* int mp_to_unsigned_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen); */ /* int mp_signed_bin_size(const mp_int *a); */ /* int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c); */ /* int mp_to_signed_bin(const mp_int *a, unsigned char *b); */ /* int mp_to_signed_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen); */ /* int mp_read_radix(mp_int *a, const char *str, int radix); */ /* int mp_toradix(const mp_int *a, char *str, int radix); */ /* int mp_toradix_n(const mp_int *a, char *str, int radix, int maxlen); */ /* int mp_radix_size(const mp_int *a, int radix, int *size); */ #ifndef LTM_NO_FILE /* int mp_fread(mp_int *a, int radix, FILE *stream); */ /* int mp_fwrite(const mp_int *a, int radix, FILE *stream); */ #endif #define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len)) #define mp_raw_size(mp) mp_signed_bin_size(mp) #define mp_toraw(mp, str) mp_to_signed_bin((mp), (str)) #define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len)) #define mp_mag_size(mp) mp_unsigned_bin_size(mp) #define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str)) #define mp_tobinary(M, S) mp_toradix((M), (S), 2) #define mp_tooctal(M, S) mp_toradix((M), (S), 8) #define mp_todecimal(M, S) mp_toradix((M), (S), 10) #define mp_tohex(M, S) mp_toradix((M), (S), 16) #ifdef __cplusplus } #endif #endif /* ref: $Format:%D$ */ /* git commit: $Format:%H$ */ /* commit time: $Format:%ai$ */