/* 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. * * SPDX-License-Identifier: Unlicense */ #ifndef BN_H_ #define BN_H_ #include #include #include #include #include "tommath_class.h" #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(_MSC_VER) || defined(__LLP64__) || defined(__e2k__) || defined(__LCC__) # define MP_32BIT #endif /* detect 64-bit mode if possible */ #if defined(__x86_64__) || defined(_M_X64) || defined(_M_AMD64) || \ defined(__powerpc64__) || defined(__ppc64__) || defined(__PPC64__) || \ defined(__s390x__) || defined(__arch64__) || defined(__aarch64__) || \ defined(__sparcv9) || defined(__sparc_v9__) || defined(__sparc64__) || \ defined(__ia64) || defined(__ia64__) || defined(__itanium__) || defined(_M_IA64) || \ defined(__LP64__) || defined(_LP64) || defined(__64BIT__) # 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 typedef uint8_t mp_digit; typedef uint16_t mp_word; # 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) typedef uint16_t mp_digit; typedef uint32_t mp_word; # 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 */ typedef uint64_t mp_digit; 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 :-) */ typedef uint32_t mp_digit; typedef uint64_t 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 /* 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 */ typedef uint_least32_t mp_min_u32; #else typedef mp_digit mp_min_u32; #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 /* 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_ITER -4 /* Max. iterations reached */ #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 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 (1u << (((sizeof(mp_word) * CHAR_BIT) - (2 * DIGIT_BIT)) + 1)) /* the infamous mp_int structure */ typedef struct { int used, alloc, sign; mp_digit *dp; } mp_int; /* 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); #define USED(m) ((m)->used) #define DIGIT(m, k) ((m)->dp[(k)]) #define SIGN(m) ((m)->sign) /* error code to char* string */ const char *mp_error_to_string(int code); /* ---> init and deinit bignum functions <--- */ /* init a bignum */ int mp_init(mp_int *a); /* free a bignum */ void mp_clear(mp_int *a); /* init a null terminated series of arguments */ int 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 */ int mp_shrink(mp_int *a); /* grow an int to a given size */ int mp_grow(mp_int *a, int size); /* init to a given number of digits */ int 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] & 1u) == 0u)) ? MP_YES : MP_NO) #define mp_isodd(a) ((((a)->used > 0) && (((a)->dp[0] & 1u) == 1u)) ? 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 double */ int mp_set_double(mp_int *a, double 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 double */ double mp_get_double(const mp_int *a); /* 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); /* Checks the bit at position b and returns MP_YES if the bit is 1, MP_NO if it is 0 and MP_VAL in case of error */ int mp_get_bit(const mp_int *a, int b); /* c = a XOR b (two complement) */ int mp_tc_xor(const mp_int *a, const mp_int *b, mp_int *c); /* c = a OR b (two complement) */ int mp_tc_or(const mp_int *a, const mp_int *b, mp_int *c); /* c = a AND b (two complement) */ int mp_tc_and(const mp_int *a, const mp_int *b, mp_int *c); /* right shift (two complement) */ int mp_tc_div_2d(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); /* computes the Kronecker symbol c = (a | p) (like jacobi() but with {a,p} in Z */ int mp_kronecker(const mp_int *a, const mp_int *p, 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 */ extern const mp_digit ltm_prime_tab[PRIME_SIZE]; /* 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 one strong Lucas-Selfridge test of "a". * Sets result to 0 if composite or 1 if probable prime */ int mp_prime_strong_lucas_selfridge(const mp_int *a, int *result); /* performs one Frobenius test of "a" as described by Paul Underwood. * Sets result to 0 if composite or 1 if probable prime */ int mp_prime_frobenius_underwood(const mp_int *N, int *result); /* 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: $Format:%ai$ */