/* LibTomMath, multiple-precision integer library -- Tom St Denis */ /* SPDX-License-Identifier: Unlicense */ #ifndef BN_H_ #define BN_H_ #include #include #ifdef LTM_NO_FILE # warning LTM_NO_FILE has been deprecated, use MP_NO_FILE. # define MP_NO_FILE #endif #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) || defined(MP_8BIT)) # if defined(__GNUC__) && !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_8/16/31/32/64BIT #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] */ #ifdef MP_8BIT typedef uint8_t mp_digit; typedef uint16_t private_mp_word; # define MP_DIGIT_BIT 7 #elif defined(MP_16BIT) typedef uint16_t mp_digit; typedef uint32_t private_mp_word; # define MP_DIGIT_BIT 15 #elif defined(MP_64BIT) /* for GCC only on supported platforms */ typedef uint64_t mp_digit; #if defined(__GNUC__) typedef unsigned long private_mp_word __attribute__((mode(TI))); #endif # define MP_DIGIT_BIT 60 #else typedef uint32_t mp_digit; typedef uint64_t private_mp_word; # 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_digs_fast * 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 /* mp_word is a private type */ #define mp_word MP_DEPRECATED_PRAGMA("mp_word has been made private") private_mp_word #define MP_SIZEOF_MP_DIGIT (MP_DEPRECATED_PRAGMA("MP_SIZEOF_MP_DIGIT has been deprecated, use sizeof (mp_digit)") sizeof (mp_digit)) #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 */ #define LTM_PRIME_BBS (MP_DEPRECATED_PRAGMA("LTM_PRIME_BBS has been deprecated, use MP_PRIME_BBS") MP_PRIME_BBS) #define LTM_PRIME_SAFE (MP_DEPRECATED_PRAGMA("LTM_PRIME_SAFE has been deprecated, use MP_PRIME_SAFE") MP_PRIME_SAFE) #define LTM_PRIME_2MSB_ON (MP_DEPRECATED_PRAGMA("LTM_PRIME_2MSB_ON has been deprecated, use MP_PRIME_2MSB_ON") MP_PRIME_2MSB_ON) #ifdef MP_USE_ENUMS typedef enum { MP_ZPOS = 0, MP_NEG = 1 } mp_sign; typedef enum { MP_LT = -1, MP_EQ = 0, MP_GT = 1 } mp_ord; typedef enum { MP_NO = 0, MP_YES = 1 } mp_bool; typedef enum { MP_OKAY = 0, MP_ERR = -1, MP_MEM = -2, MP_VAL = -3, MP_ITER = -4 } mp_err; #else 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_DEPRECATED_PRAGMA("MP_RANGE has been deprecated in favor of MP_VAL") MP_VAL) #define MP_ITER -4 /* Max. iterations reached */ #endif /* tunable cutoffs */ #ifndef MP_FIXED_CUTOFFS extern int KARATSUBA_MUL_CUTOFF, KARATSUBA_SQR_CUTOFF, TOOM_MUL_CUTOFF, TOOM_SQR_CUTOFF; #endif /* define this to use lower memory usage routines (exptmods mostly) */ /* #define MP_LOW_MEM */ /* default precision */ #ifndef MP_PREC # ifndef MP_LOW_MEM # define PRIVATE_MP_PREC 32 /* default digits of precision */ # elif defined(MP_8BIT) # define PRIVATE_MP_PREC 16 /* default digits of precision */ # else # define PRIVATE_MP_PREC 8 /* default digits of precision */ # endif # define MP_PREC (MP_DEPRECATED_PRAGMA("MP_PREC is an internal macro") PRIVATE_MP_PREC) #endif /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */ #define PRIVATE_MP_WARRAY (int)(1uLL << (((CHAR_BIT * sizeof(private_mp_word)) - (2 * MP_DIGIT_BIT)) + 1)) #define MP_WARRAY (MP_DEPRECATED_PRAGMA("MP_WARRAY is an internal macro") PRIVATE_MP_WARRAY) #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 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(s) # define MP_DEPRECATED_PRAGMA(s) #endif #define DIGIT_BIT (MP_DEPRECATED_PRAGMA("DIGIT_BIT macro is deprecated, MP_DIGIT_BIT instead") MP_DIGIT_BIT) #define USED(m) (MP_DEPRECATED_PRAGMA("USED macro is deprecated, use z->used instead") (m)->used) #define DIGIT(m, k) (MP_DEPRECATED_PRAGMA("DIGIT macro is deprecated, use z->dp instead") (m)->dp[(k)]) #define SIGN(m) (MP_DEPRECATED_PRAGMA("SIGN macro is deprecated, use z->sign instead") (m)->sign) /* the infamous mp_int structure */ typedef struct { int used, alloc; mp_sign 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 private_mp_prime_callback(unsigned char *dst, int len, void *dat); typedef private_mp_prime_callback MP_DEPRECATED(mp_rand_source) ltm_prime_callback; /* 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) ? MP_YES : MP_NO) mp_bool mp_iseven(const mp_int *a) MP_WUR; mp_bool mp_isodd(const mp_int *a) MP_WUR; #define mp_isneg(a) (((a)->sign != MP_ZPOS) ? MP_YES : MP_NO) /* 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_mag32(const mp_int *a) MP_WUR; uint64_t mp_get_mag64(const mp_int *a) MP_WUR; /* get integer, set integer (long) */ #define mp_get_l(a) (sizeof (long) == 8 ? (long)mp_get_i64(a) : (long)mp_get_i32(a)) #define mp_set_l(a, b) (sizeof (long) == 8 ? mp_set_i64((a), (b)) : mp_set_i32((a), (int32_t)(b))) /* get integer, set integer (unsigned long) */ #define mp_get_ul(a) (sizeof (long) == 8 ? (unsigned long)mp_get_u64(a) : (unsigned long)mp_get_u32(a)) #define mp_set_ul(a, b) (sizeof (long) == 8 ? mp_set_u64((a), (b)) : mp_set_u32((a), (uint32_t)(b))) #define mp_get_magl(a) (sizeof (long) == 8 ? (unsigned long)mp_get_mag64(a) : (unsigned long)mp_get_mag32(a)) /* 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; /* get integer, set integer and init with integer (deprecated) */ MP_DEPRECATED(mp_get_mag32/mp_get_u32) unsigned long mp_get_int(const mp_int *a) MP_WUR; MP_DEPRECATED(mp_get_magl/mp_get_ul) unsigned long mp_get_long(const mp_int *a) MP_WUR; MP_DEPRECATED(mp_get_mag64/mp_get_u64) unsigned long long mp_get_long_long(const mp_int *a) MP_WUR; MP_DEPRECATED(mp_set_u32) mp_err mp_set_int(mp_int *a, unsigned long b); MP_DEPRECATED(mp_set_ul) mp_err mp_set_long(mp_int *a, unsigned long b); MP_DEPRECATED(mp_set_u64) mp_err mp_set_long_long(mp_int *a, unsigned long long b); MP_DEPRECATED(mp_init_u32) mp_err mp_init_set_int(mp_int *a, unsigned long 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); /* import binary data */ mp_err mp_import(mp_int *rop, size_t count, int order, size_t size, int endian, size_t nails, const void *op) MP_WUR; /* export binary data */ mp_err mp_export(void *rop, size_t *countp, int order, size_t size, int 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; /* makes a pseudo-random small int of a given size */ MP_DEPRECATED(mp_rand) mp_err mp_rand_digit(mp_digit *r) 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)); #ifdef MP_PRNG_ENABLE_LTM_RNG # warning MP_PRNG_ENABLE_LTM_RNG has been deprecated, use mp_rand_source instead. /* 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 <--- */ /* 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 */ MP_DEPRECATED(s_mp_get_bit) int mp_get_bit(const mp_int *a, int b) MP_WUR; /* c = a XOR b (two complement) */ MP_DEPRECATED(mp_xor) mp_err mp_tc_xor(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; mp_err mp_xor(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* c = a OR b (two complement) */ MP_DEPRECATED(mp_or) mp_err mp_tc_or(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; mp_err mp_or(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* c = a AND b (two complement) */ MP_DEPRECATED(mp_and) mp_err mp_tc_and(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; 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_DEPRECATED(mp_signed_rsh) mp_err mp_tc_div_2d(const mp_int *a, int b, mp_int *c) MP_WUR; 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 */ mp_err mp_sqr(const mp_int *a, mp_int *b) MP_WUR; /* 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; /* ---> 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; /* Increment "a" by one like "a++". Changes input! */ mp_err mp_incr(mp_int *a) MP_WUR; /* c = a - b */ mp_err mp_sub_d(const mp_int *a, mp_digit b, mp_int *c) MP_WUR; /* Decrement "a" by one like "a--". Changes input! */ mp_err mp_decr(mp_int *a) 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; /* a/3 => 3c + d == a */ mp_err mp_div_3(const mp_int *a, mp_int *c, mp_digit *d) MP_WUR; /* c = a**b */ mp_err mp_expt_d(const mp_int *a, mp_digit b, mp_int *c) MP_WUR; MP_DEPRECATED(mp_expt_d) mp_err mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast) MP_WUR; /* c = a mod b, 0 <= c < b */ mp_err mp_mod_d(const mp_int *a, mp_digit b, mp_digit *c) MP_WUR; /* ---> 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; /* 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_n_root(const mp_int *a, mp_digit b, mp_int *c) MP_WUR; MP_DEPRECATED(mp_n_root_ex) mp_err mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast) 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, mp_bool *ret) MP_WUR; /* computes the jacobi c = (a | n) (or Legendre if b is prime) */ MP_DEPRECATED(mp_kronecker) mp_err mp_jacobi(const mp_int *a, const mp_int *n, int *c) 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 */ mp_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 */ mp_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 */ mp_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; /* ---> Primes <--- */ /* number of primes */ #ifdef MP_8BIT # define PRIVATE_MP_PRIME_TAB_SIZE 31 #else # define PRIVATE_MP_PRIME_TAB_SIZE 256 #endif #define PRIME_SIZE (MP_DEPRECATED_PRAGMA("PRIME_SIZE has been made internal") PRIVATE_MP_PRIME_TAB_SIZE) /* table of first PRIME_SIZE primes */ MP_DEPRECATED(internal) extern const mp_digit ltm_prime_tab[PRIVATE_MP_PRIME_TAB_SIZE]; /* result=1 if a is divisible by one of the first PRIME_SIZE primes */ MP_DEPRECATED(mp_prime_is_prime) mp_err mp_prime_is_divisible(const mp_int *a, mp_bool *result) MP_WUR; /* 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, mp_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, mp_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, mp_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, mp_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, mp_bool *result) MP_WUR; /* 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 */ mp_err mp_prime_next_prime(mp_int *a, int t, int bbs_style) MP_WUR; /* 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_DEPRECATED_PRAGMA("mp_prime_random has been deprecated, use mp_prime_rand instead") mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?MP_PRIME_BBS:0, cb, dat)) /* 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_DEPRECATED(mp_prime_rand) mp_err mp_prime_random_ex(mp_int *a, int t, int size, int flags, private_mp_prime_callback cb, void *dat) MP_WUR; mp_err mp_prime_rand(mp_int *a, int t, int size, int flags) MP_WUR; /* Integer logarithm to integer base */ mp_err mp_ilogb(const mp_int *a, mp_digit base, mp_int *c) MP_WUR; /* ---> radix conversion <--- */ int mp_count_bits(const mp_int *a) MP_WUR; int mp_unsigned_bin_size(const mp_int *a) MP_WUR; mp_err mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c) MP_WUR; mp_err mp_to_unsigned_bin(const mp_int *a, unsigned char *b) MP_WUR; mp_err mp_to_unsigned_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen) MP_WUR; int mp_signed_bin_size(const mp_int *a) MP_WUR; mp_err mp_read_signed_bin(mp_int *a, const unsigned char *b, int c) MP_WUR; mp_err mp_to_signed_bin(const mp_int *a, unsigned char *b) MP_WUR; mp_err mp_to_signed_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen) MP_WUR; mp_err mp_read_radix(mp_int *a, const char *str, int radix) MP_WUR; mp_err mp_toradix(const mp_int *a, char *str, int radix) MP_WUR; mp_err mp_toradix_n(const mp_int *a, char *str, int radix, int maxlen) MP_WUR; mp_err mp_radix_size(const mp_int *a, int radix, int *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_read_raw(mp, str, len) (MP_DEPRECATED_PRAGMA("replaced by mp_read_signed_bin") mp_read_signed_bin((mp), (str), (len))) #define mp_raw_size(mp) (MP_DEPRECATED_PRAGMA("replaced by mp_signed_bin_size") mp_signed_bin_size(mp)) #define mp_toraw(mp, str) (MP_DEPRECATED_PRAGMA("replaced by mp_to_signed_bin") mp_to_signed_bin((mp), (str))) #define mp_read_mag(mp, str, len) (MP_DEPRECATED_PRAGMA("replaced by mp_read_unsigned_bin") mp_read_unsigned_bin((mp), (str), (len)) #define mp_mag_size(mp) (MP_DEPRECATED_PRAGMA("replaced by mp_unsigned_bin_size") mp_unsigned_bin_size(mp)) #define mp_tomag(mp, str) (MP_DEPRECATED_PRAGMA("replaced by mp_to_unsigned_bin") 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