/* LibTomMath, multiple-precision integer library -- Tom St Denis */ /* SPDX-License-Identifier: Unlicense */ #ifndef TOMMATH_H_ #define TOMMATH_H_ #include #include #include #ifndef MP_NO_FILE # include #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(_MSC_VER) || defined(__LLP64__) || defined(__e2k__) || defined(__LCC__)) && !defined(MP_64BIT) # 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_64BIT) || defined(MP_32BIT) || defined(MP_16BIT)) # if defined(__GNUC__) && defined(__SIZEOF_INT128__) && !defined(__hppa) /* 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 #ifdef MP_DIGIT_BIT # error Defining MP_DIGIT_BIT is disallowed, use MP_16/31/32/64BIT #endif /* some default configurations. * * A "mp_digit" must be able to hold MP_DIGIT_BIT + 1 bits * A "mp_word" must be able to hold 2*MP_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] */ #if defined(MP_16BIT) typedef uint16_t mp_digit; # define MP_DIGIT_BIT 15 #elif ((defined (MP_64BIT)) && !(defined(MP_31BIT)) ) typedef uint64_t mp_digit; # define MP_DIGIT_BIT 60 #else typedef uint32_t mp_digit; # ifdef MP_31BIT /* * This is an extension that uses 31-bit digits. * Please be aware that not all functions support this size, especially s_mp_mul_comba * will be reduced to work on small numbers only: * Up to 8 limbs, 248 bits instead of up to 512 limbs, 15872 bits with MP_28BIT. */ # define MP_DIGIT_BIT 31 # else /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */ # define MP_DIGIT_BIT 28 # define MP_28BIT # endif #endif #define MP_MASK ((((mp_digit)1)<<((mp_digit)MP_DIGIT_BIT))-((mp_digit)1)) #define MP_DIGIT_MAX MP_MASK /* Primality generation flags */ #define MP_PRIME_BBS 0x0001 /* BBS style prime */ #define MP_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */ #define MP_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */ typedef enum { MP_ZPOS = 0, /* positive */ MP_NEG = 1 /* negative */ } mp_sign; typedef enum { MP_LT = -1, /* less than */ MP_EQ = 0, /* equal */ MP_GT = 1 /* greater than */ } mp_ord; typedef enum { MP_OKAY = 0, /* no error */ MP_ERR = -1, /* unknown error */ MP_MEM = -2, /* out of mem */ MP_VAL = -3, /* invalid input */ MP_ITER = -4, /* maximum iterations reached */ MP_BUF = -5, /* buffer overflow, supplied buffer too small */ MP_OVF = -6 /* mp_int overflow, too many digits */ } mp_err; typedef enum { MP_LSB_FIRST = -1, MP_MSB_FIRST = 1 } mp_order; typedef enum { MP_LITTLE_ENDIAN = -1, MP_NATIVE_ENDIAN = 0, MP_BIG_ENDIAN = 1 } mp_endian; /* tunable cutoffs */ #ifndef MP_FIXED_CUTOFFS extern int MP_MUL_KARATSUBA_CUTOFF, MP_SQR_KARATSUBA_CUTOFF, MP_MUL_TOOM_CUTOFF, MP_SQR_TOOM_CUTOFF; #endif /* define this to use lower memory usage routines (exptmods mostly) */ /* #define MP_LOW_MEM */ #if defined(__GNUC__) && __GNUC__ >= 4 # define MP_NULL_TERMINATED __attribute__((sentinel)) #else # define MP_NULL_TERMINATED #endif /* * 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 defined(__GNUC__) && __GNUC__ >= 4 # define MP_WUR __attribute__((warn_unused_result)) #else # define MP_WUR #endif #if defined(__GNUC__) && (__GNUC__ * 100 + __GNUC_MINOR__ >= 405) # define MP_DEPRECATED(x) __attribute__((deprecated("replaced by " #x))) #elif defined(_MSC_VER) && _MSC_VER >= 1500 # define MP_DEPRECATED(x) __declspec(deprecated("replaced by " #x)) #else # define MP_DEPRECATED(x) #endif #ifndef MP_NO_DEPRECATED_PRAGMA #if defined(__GNUC__) && (__GNUC__ * 100 + __GNUC_MINOR__ >= 301) # 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_PRAGMA(s) __pragma(message(s)) #endif #endif #ifndef MP_DEPRECATED_PRAGMA # define MP_DEPRECATED_PRAGMA(s) #endif /* the infamous mp_int structure */ typedef struct { int used, alloc; mp_sign sign; mp_digit *dp; } mp_int; /* error code to char* string */ const char *mp_error_to_string(mp_err code) MP_WUR; /* ---> init and deinit bignum functions <--- */ /* init a bignum */ mp_err mp_init(mp_int *a) MP_WUR; /* free a bignum */ void mp_clear(mp_int *a); /* init a null terminated series of arguments */ mp_err mp_init_multi(mp_int *mp, ...) MP_NULL_TERMINATED MP_WUR; /* clear a null terminated series of arguments */ void mp_clear_multi(mp_int *mp, ...) MP_NULL_TERMINATED; /* 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) MP_WUR; /* grow an int to a given size */ mp_err mp_grow(mp_int *a, int size) MP_WUR; /* init to a given number of digits */ mp_err mp_init_size(mp_int *a, int size) MP_WUR; /* ---> Basic Manipulations <--- */ #define mp_iszero(a) ((a)->used == 0) #define mp_isone(a) ( ((a)->sign == MP_ZPOS) && ((a)->used == 1u) && ((a)->dp[0] == 1u) ) #define mp_isneg(a) ((a)->sign == MP_NEG) #define mp_iseven(a) (((a)->used == 0) || (((a)->dp[0] & 1u) == 0u)) #define mp_isodd(a) (!mp_iseven(a)) /* set to zero */ void mp_zero(mp_int *a); /* get and set doubles */ double mp_get_double(const mp_int *a) MP_WUR; mp_err mp_set_double(mp_int *a, double b) MP_WUR; /* get integer, set integer and init with integer (int32_t) */ int32_t mp_get_i32(const mp_int *a) MP_WUR; void mp_set_i32(mp_int *a, int32_t b); mp_err mp_init_i32(mp_int *a, int32_t b) MP_WUR; /* get integer, set integer and init with integer, behaves like two complement for negative numbers (uint32_t) */ #define mp_get_u32(a) ((uint32_t)mp_get_i32(a)) void mp_set_u32(mp_int *a, uint32_t b); mp_err mp_init_u32(mp_int *a, uint32_t b) MP_WUR; /* get integer, set integer and init with integer (int64_t) */ int64_t mp_get_i64(const mp_int *a) MP_WUR; void mp_set_i64(mp_int *a, int64_t b); mp_err mp_init_i64(mp_int *a, int64_t b) MP_WUR; /* get integer, set integer and init with integer, behaves like two complement for negative numbers (uint64_t) */ #define mp_get_u64(a) ((uint64_t)mp_get_i64(a)) void mp_set_u64(mp_int *a, uint64_t b); mp_err mp_init_u64(mp_int *a, uint64_t b) MP_WUR; /* get magnitude */ uint32_t mp_get_mag_u32(const mp_int *a) MP_WUR; uint64_t mp_get_mag_u64(const mp_int *a) MP_WUR; unsigned long mp_get_mag_ul(const mp_int *a) MP_WUR; /* get integer, set integer (long) */ long mp_get_l(const mp_int *a) MP_WUR; void mp_set_l(mp_int *a, long b); mp_err mp_init_l(mp_int *a, long b) MP_WUR; /* get integer, set integer (unsigned long) */ #define mp_get_ul(a) ((unsigned long)mp_get_l(a)) void mp_set_ul(mp_int *a, unsigned long b); mp_err mp_init_ul(mp_int *a, unsigned long b) MP_WUR; /* set to single unsigned digit, up to MP_DIGIT_MAX */ void mp_set(mp_int *a, mp_digit b); mp_err mp_init_set(mp_int *a, mp_digit b) MP_WUR; /* copy, b = a */ mp_err mp_copy(const mp_int *a, mp_int *b) MP_WUR; /* inits and copies, a = b */ mp_err mp_init_copy(mp_int *a, const mp_int *b) MP_WUR; /* trim unused digits */ void mp_clamp(mp_int *a); /* unpack binary data */ mp_err mp_unpack(mp_int *rop, size_t count, mp_order order, size_t size, mp_endian endian, size_t nails, const void *op) MP_WUR; /* pack binary data */ size_t mp_pack_count(const mp_int *a, size_t nails, size_t size) MP_WUR; mp_err mp_pack(void *rop, size_t maxcount, size_t *written, mp_order order, size_t size, mp_endian endian, size_t nails, const mp_int *op) MP_WUR; /* ---> digit manipulation <--- */ /* right shift by "b" digits */ void mp_rshd(mp_int *a, int b); /* left shift by "b" digits */ mp_err mp_lshd(mp_int *a, int b) MP_WUR; /* c = a / 2**b, implemented as c = a >> b */ mp_err mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d) MP_WUR; /* b = a/2 */ mp_err mp_div_2(const mp_int *a, mp_int *b) MP_WUR; /* c = a * 2**b, implemented as c = a << b */ mp_err mp_mul_2d(const mp_int *a, int b, mp_int *c) MP_WUR; /* b = a*2 */ mp_err mp_mul_2(const mp_int *a, mp_int *b) MP_WUR; /* c = a mod 2**b */ mp_err mp_mod_2d(const mp_int *a, int b, mp_int *c) MP_WUR; /* computes a = 2**b */ mp_err mp_2expt(mp_int *a, int b) MP_WUR; /* Counts the number of lsbs which are zero before the first zero bit */ int mp_cnt_lsb(const mp_int *a) MP_WUR; /* I Love Earth! */ /* makes a pseudo-random mp_int of a given size */ mp_err mp_rand(mp_int *a, int digits) MP_WUR; /* use custom random data source instead of source provided the platform */ void mp_rand_source(mp_err(*source)(void *out, size_t size)); /* ---> binary operations <--- */ /* c = a XOR b (two complement) */ mp_err mp_xor(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* c = a OR b (two complement) */ mp_err mp_or(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* c = a AND b (two complement) */ mp_err mp_and(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* b = ~a (bitwise not, two complement) */ mp_err mp_complement(const mp_int *a, mp_int *b) MP_WUR; /* right shift with sign extension */ mp_err mp_signed_rsh(const mp_int *a, int b, mp_int *c) MP_WUR; /* ---> Basic arithmetic <--- */ /* b = -a */ mp_err mp_neg(const mp_int *a, mp_int *b) MP_WUR; /* b = |a| */ mp_err mp_abs(const mp_int *a, mp_int *b) MP_WUR; /* compare a to b */ mp_ord mp_cmp(const mp_int *a, const mp_int *b) MP_WUR; /* compare |a| to |b| */ mp_ord mp_cmp_mag(const mp_int *a, const mp_int *b) MP_WUR; /* c = a + b */ mp_err mp_add(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* c = a - b */ mp_err mp_sub(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* c = a * b */ mp_err mp_mul(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* b = a*a */ #define mp_sqr(a, b) mp_mul((a), (a), (b)) /* a/b => cb + d == a */ mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d) MP_WUR; /* c = a mod b, 0 <= c < b */ mp_err mp_mod(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* Increment "a" by one like "a++". Changes input! */ #define mp_incr(a) mp_add_d((a), 1u, (a)) /* Decrement "a" by one like "a--". Changes input! */ #define mp_decr(a) mp_sub_d((a), 1u, (a)) /* ---> single digit functions <--- */ /* compare against a single digit */ mp_ord mp_cmp_d(const mp_int *a, mp_digit b) MP_WUR; /* c = a + b */ mp_err mp_add_d(const mp_int *a, mp_digit b, mp_int *c) MP_WUR; /* c = a - b */ mp_err mp_sub_d(const mp_int *a, mp_digit b, mp_int *c) MP_WUR; /* c = a * b */ mp_err mp_mul_d(const mp_int *a, mp_digit b, mp_int *c) MP_WUR; /* a/b => cb + d == a */ mp_err mp_div_d(const mp_int *a, mp_digit b, mp_int *c, mp_digit *d) MP_WUR; /* c = a mod b, 0 <= c < b */ #define mp_mod_d(a, b, c) mp_div_d((a), (b), NULL, (c)) /* ---> number theory <--- */ /* d = a + b (mod c) */ mp_err mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) MP_WUR; /* d = a - b (mod c) */ mp_err mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) MP_WUR; /* d = a * b (mod c) */ mp_err mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) MP_WUR; /* c = a * a (mod b) */ mp_err mp_sqrmod(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* c = 1/a (mod b) */ mp_err mp_invmod(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* c = (a, b) */ mp_err mp_gcd(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* produces value such that U1*a + U2*b = U3 */ mp_err mp_exteuclid(const mp_int *a, const mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3) MP_WUR; /* c = [a, b] or (a*b)/(a, b) */ mp_err mp_lcm(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* Integer logarithm to integer base */ mp_err mp_log_n(const mp_int *a, int base, int *c) MP_WUR; /* Integer logarithm to bigint base */ mp_err mp_log(const mp_int *a, const mp_int *base, int *c) MP_WUR; /* c = a**b */ mp_err mp_expt_n(const mp_int *a, int b, mp_int *c) MP_WUR; /* finds one of the b'th root of a, such that |c|**b <= |a| * * returns error if a < 0 and b is even */ mp_err mp_root_n(const mp_int *a, int b, mp_int *c) MP_WUR; /* special sqrt algo */ mp_err mp_sqrt(const mp_int *arg, mp_int *ret) MP_WUR; /* special sqrt (mod prime) */ mp_err mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret) MP_WUR; /* is number a square? */ mp_err mp_is_square(const mp_int *arg, bool *ret) MP_WUR; /* computes the Kronecker symbol c = (a | p) (like jacobi() but with {a,p} in Z */ mp_err mp_kronecker(const mp_int *a, const mp_int *p, int *c) MP_WUR; /* used to setup the Barrett reduction for a given modulus b */ mp_err mp_reduce_setup(mp_int *a, const mp_int *b) MP_WUR; /* 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]. */ mp_err mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu) MP_WUR; /* setups the montgomery reduction */ mp_err mp_montgomery_setup(const mp_int *n, mp_digit *rho) MP_WUR; /* computes a = B**n mod b without division or multiplication useful for * normalizing numbers in a Montgomery system. */ mp_err mp_montgomery_calc_normalization(mp_int *a, const mp_int *b) MP_WUR; /* computes x/R == x (mod N) via Montgomery Reduction */ mp_err mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho) MP_WUR; /* returns 1 if a is a valid DR modulus */ bool mp_dr_is_modulus(const mp_int *a) MP_WUR; /* 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 */ mp_err mp_dr_reduce(mp_int *x, const mp_int *n, mp_digit k) MP_WUR; /* returns true if a can be reduced with mp_reduce_2k */ bool mp_reduce_is_2k(const mp_int *a) MP_WUR; /* determines k value for 2k reduction */ mp_err mp_reduce_2k_setup(const mp_int *a, mp_digit *d) MP_WUR; /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ mp_err mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d) MP_WUR; /* returns true if a can be reduced with mp_reduce_2k_l */ bool mp_reduce_is_2k_l(const mp_int *a) MP_WUR; /* determines k value for 2k reduction */ mp_err mp_reduce_2k_setup_l(const mp_int *a, mp_int *d) MP_WUR; /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ mp_err mp_reduce_2k_l(mp_int *a, const mp_int *n, const mp_int *d) MP_WUR; /* Y = G**X (mod P) */ mp_err mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y) MP_WUR; #if defined(MP_16BIT) typedef uint32_t mp_hval; #else typedef uint64_t mp_hval; #endif /* computes hash */ mp_err mp_hash(const mp_int *a, mp_hval *hash) MP_WUR; /* ---> Primes <--- */ /* performs one Fermat test of "a" using base "b". * Sets result to 0 if composite or 1 if probable prime */ mp_err mp_prime_fermat(const mp_int *a, const mp_int *b, bool *result) MP_WUR; /* performs one Miller-Rabin test of "a" using base "b". * Sets result to 0 if composite or 1 if probable prime */ mp_err mp_prime_miller_rabin(const mp_int *a, const mp_int *b, bool *result) MP_WUR; /* 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) MP_WUR; /* performs one strong Lucas-Selfridge test of "a". * Sets result to 0 if composite or 1 if probable prime */ mp_err mp_prime_strong_lucas_selfridge(const mp_int *a, bool *result) MP_WUR; /* performs one Frobenius test of "a" as described by Paul Underwood. * Sets result to 0 if composite or 1 if probable prime */ mp_err mp_prime_frobenius_underwood(const mp_int *N, bool *result) MP_WUR; /* 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 */ mp_err mp_prime_is_prime(const mp_int *a, int t, bool *result) MP_WUR; /* finds the next prime after the number "a" using "t" trials * of Miller-Rabin. * * bbs_style = true means the prime must be congruent to 3 mod 4 */ mp_err mp_prime_next_prime(mp_int *a, int t, bool bbs_style) MP_WUR; /* makes a truly random prime of a given size (bits), * * Flags are as follows: * * MP_PRIME_BBS - make prime congruent to 3 mod 4 * MP_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies MP_PRIME_BBS) * MP_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 * */ mp_err mp_prime_rand(mp_int *a, int t, int size, int flags) MP_WUR; /* ---> radix conversion <--- */ int mp_count_bits(const mp_int *a) MP_WUR; size_t mp_ubin_size(const mp_int *a) MP_WUR; mp_err mp_from_ubin(mp_int *a, const uint8_t *buf, size_t size) MP_WUR; mp_err mp_to_ubin(const mp_int *a, uint8_t *buf, size_t maxlen, size_t *written) MP_WUR; size_t mp_sbin_size(const mp_int *a) MP_WUR; mp_err mp_from_sbin(mp_int *a, const uint8_t *buf, size_t size) MP_WUR; mp_err mp_to_sbin(const mp_int *a, uint8_t *buf, size_t maxlen, size_t *written) MP_WUR; mp_err mp_read_radix(mp_int *a, const char *str, int radix) MP_WUR; mp_err mp_to_radix(const mp_int *a, char *str, size_t maxlen, size_t *written, int radix) MP_WUR; mp_err mp_radix_size(const mp_int *a, int radix, size_t *size) MP_WUR; mp_err mp_radix_size_overestimate(const mp_int *a, const int radix, size_t *size) MP_WUR; #ifndef MP_NO_FILE mp_err mp_fread(mp_int *a, int radix, FILE *stream) MP_WUR; mp_err mp_fwrite(const mp_int *a, int radix, FILE *stream) MP_WUR; #endif #define mp_to_binary(M, S, N) mp_to_radix((M), (S), (N), NULL, 2) #define mp_to_octal(M, S, N) mp_to_radix((M), (S), (N), NULL, 8) #define mp_to_decimal(M, S, N) mp_to_radix((M), (S), (N), NULL, 10) #define mp_to_hex(M, S, N) mp_to_radix((M), (S), (N), NULL, 16) #ifdef __cplusplus } #endif #endif