/* 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 AWS_BN_H_ #define AWS_BN_H_ #include #include #include #include #include #include "aws_tommath_class.h" #ifndef AWS_MIN #define AWS_MIN(x,y) ((x)<(y)?(x):(y)) #endif #ifndef AWS_MAX #define AWS_MAX(x,y) ((x)>(y)?(x):(y)) #endif #ifdef __cplusplus extern "C" { /* C++ compilers don't like assigning void * to mp_digit * */ #define AWS_OPT_CAST(x) (x *) #else /* C on the other hand doesn't care */ #define AWS_OPT_CAST(x) #endif /* detect 64-bit mode if possible */ #if defined(__x86_64__) #if !(defined(AWS_MP_64BIT) && defined(AWS_MP_16BIT) && defined(AWS_MP_8BIT)) #define AWS_MP_64BIT #endif #endif /* some default configurations. * * A "mp_digit" must be able to hold AWS_DIGIT_BIT + 1 bits * A "mp_word" must be able to hold 2*AWS_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 AWS_MP_8BIT typedef unsigned char aws_mp_digit; typedef unsigned short aws_mp_word; #elif defined(AWS_MP_16BIT) typedef unsigned short aws_mp_digit; typedef unsigned long aws_mp_word; #elif defined(AWS_MP_64BIT) /* for GCC only on supported platforms */ #ifndef CRYPT typedef unsigned long long ulong64; typedef signed long long long64; #endif typedef unsigned long aws_mp_digit; typedef unsigned long aws_mp_word __attribute__ ((mode(TI))); #define AWS_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 aws_mp_digit; typedef ulong64 aws_mp_word; #ifdef AWS_MP_31BIT /* this is an extension that uses 31-bit digits */ #define AWS_DIGIT_BIT 31 #else /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */ #define AWS_DIGIT_BIT 28 #define AWS_MP_28BIT #endif #endif /* define heap macros */ #ifndef CRYPT /* default to libc stuff */ #ifndef AWS_XMALLOC #define AWS_XMALLOC malloc #define AWS_XFREE free #define AWS_XREALLOC realloc #define AWS_XCALLOC calloc #else /* prototypes for our heap functions */ extern void *AWS_XMALLOC(size_t n); extern void *AWS_XREALLOC(void *p, size_t n); extern void *AWS_XCALLOC(size_t n, size_t s); extern void AWS_XFREE(void *p); #endif #endif /* otherwise the bits per digit is calculated automatically from the size of a mp_digit */ #ifndef AWS_DIGIT_BIT #define AWS_DIGIT_BIT ((int)((AWS_CHAR_BIT * sizeof(aws_mp_digit) - 1))) /* bits per digit */ #endif #define AWS_MP_DIGIT_BIT AWS_DIGIT_BIT #define AWS_MP_MASK ((((aws_mp_digit)1)<<((aws_mp_digit)AWS_DIGIT_BIT))-((aws_mp_digit)1)) #define AWS_MP_DIGIT_MAX AWS_MP_MASK /* equalities */ #define AWS_MP_LT -1 /* less than */ #define AWS_MP_EQ 0 /* equal to */ #define AWS_MP_GT 1 /* greater than */ #define AWS_MP_ZPOS 0 /* positive integer */ #define AWS_MP_NEG 1 /* negative */ #define AWS_MP_OKAY 0 /* ok result */ #define AWS_MP_MEM -2 /* out of mem */ #define AWS_MP_VAL -3 /* invalid input */ #define AWS_MP_RANGE AWS_MP_VAL #define AWS_MP_YES 1 /* yes response */ #define AWS_MP_NO 0 /* no response */ /* Primality generation flags */ #define AWS_LTM_PRIME_BBS 0x0001 /* BBS style prime */ #define AWS_LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */ #define AWS_LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */ typedef int aws_mp_err; /* you'll have to tune these... */ extern int AWS_KARATSUBA_MUL_CUTOFF, AWS_KARATSUBA_SQR_CUTOFF, AWS_TOOM_MUL_CUTOFF, AWS_TOOM_SQR_CUTOFF; /* define this to use lower memory usage routines (exptmods mostly) */ /* #define AWS_MP_LOW_MEM */ /* default precision */ #ifndef AWS_MP_PREC #ifndef AWS_MP_LOW_MEM #define AWS_MP_PREC 32 /* default digits of precision */ #else #define AWS_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 AWS_MP_WARRAY (1 << (sizeof(aws_mp_word) * CHAR_BIT - 2 * AWS_DIGIT_BIT + 1)) /* the infamous mp_int structure */ typedef struct { int used, alloc, sign; aws_mp_digit *dp; } aws_mp_int; /* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */ typedef int aws_ltm_prime_callback(unsigned char *dst, int len, void *dat); #define AWS_JKTM_USED(m) ((m)->used) #define AWS_JKTM_DIGIT(m,k) ((m)->dp[(k)]) #define AWS_JKTM_SIGN(m) ((m)->sign) /* error code to char* string */ char *aws_mp_error_to_string(int code); /* ---> init and deinit bignum functions <--- */ /* init a bignum */ int aws_mp_init(aws_mp_int *a); /* free a bignum */ void aws_mp_clear(aws_mp_int *a); /* init a null terminated series of arguments */ int aws_mp_init_multi(aws_mp_int *mp, ...); /* clear a null terminated series of arguments */ void aws_mp_clear_multi(aws_mp_int *mp, ...); /* exchange two ints */ void aws_mp_exch(aws_mp_int *a, aws_mp_int *b); /* shrink ram required for a bignum */ int aws_mp_shrink(aws_mp_int *a); /* grow an int to a given size */ int aws_mp_grow(aws_mp_int *a, int size); /* init to a given number of digits */ int aws_mp_init_size(aws_mp_int *a, int size); /* ---> Basic Manipulations <--- */ #define aws_mp_iszero(a) (((a)->used == 0) ? AWS_MP_YES : AWS_MP_NO) #define aws_mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? AWS_MP_YES : AWS_MP_NO) #define aws_mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? AWS_MP_YES : AWS_MP_NO) /* set to zero */ void aws_mp_zero(aws_mp_int *a); /* set to a digit */ void aws_mp_set(aws_mp_int *a, aws_mp_digit b); /* set a 32-bit const */ int aws_mp_set_int(aws_mp_int *a, unsigned long b); /* get a 32-bit value */ unsigned long aws_mp_get_int(aws_mp_int *a); /* initialize and set a digit */ int aws_mp_init_set(aws_mp_int *a, aws_mp_digit b); /* initialize and set 32-bit value */ int aws_mp_init_set_int(aws_mp_int *a, unsigned long b); /* copy, b = a */ int aws_mp_copy(aws_mp_int *a, aws_mp_int *b); /* inits and copies, a = b */ int aws_mp_init_copy(aws_mp_int *a, aws_mp_int *b); /* trim unused digits */ void aws_mp_clamp(aws_mp_int *a); /* ---> digit manipulation <--- */ /* right shift by "b" digits */ void aws_mp_rshd(aws_mp_int *a, int b); /* left shift by "b" digits */ int aws_mp_lshd(aws_mp_int *a, int b); /* c = a / 2**b */ int aws_mp_div_2d(aws_mp_int *a, int b, aws_mp_int *c, aws_mp_int *d); /* b = a/2 */ int aws_mp_div_2(aws_mp_int *a, aws_mp_int *b); /* c = a * 2**b */ int aws_mp_mul_2d(aws_mp_int *a, int b, aws_mp_int *c); /* b = a*2 */ int aws_mp_mul_2(aws_mp_int *a, aws_mp_int *b); /* c = a mod 2**d */ int aws_mp_mod_2d(aws_mp_int *a, int b, aws_mp_int *c); /* computes a = 2**b */ int aws_mp_2expt(aws_mp_int *a, int b); /* Counts the number of lsbs which are zero before the first zero bit */ int aws_mp_cnt_lsb(aws_mp_int *a); /* I Love Earth! */ /* makes a pseudo-random int of a given size */ int aws_mp_rand(aws_mp_int *a, int digits); /* ---> binary operations <--- */ /* c = a XOR b */ int aws_mp_xor(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c); /* c = a OR b */ int aws_mp_or(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c); /* c = a AND b */ int aws_mp_and(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c); /* ---> Basic arithmetic <--- */ /* b = -a */ int aws_mp_neg(aws_mp_int *a, aws_mp_int *b); /* b = |a| */ int aws_mp_abs(aws_mp_int *a, aws_mp_int *b); /* compare a to b */ int aws_mp_cmp(aws_mp_int *a, aws_mp_int *b); /* compare |a| to |b| */ int aws_mp_cmp_mag(aws_mp_int *a, aws_mp_int *b); /* c = a + b */ int aws_mp_add(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c); /* c = a - b */ int aws_mp_sub(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c); /* c = a * b */ int aws_mp_mul(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c); /* b = a*a */ int aws_mp_sqr(aws_mp_int *a, aws_mp_int *b); /* a/b => cb + d == a */ int aws_mp_div(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c, aws_mp_int *d); /* c = a mod b, 0 <= c < b */ int aws_mp_mod(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c); /* ---> single digit functions <--- */ /* compare against a single digit */ int aws_mp_cmp_d(aws_mp_int *a, aws_mp_digit b); /* c = a + b */ int aws_mp_add_d(aws_mp_int *a, aws_mp_digit b, aws_mp_int *c); /* c = a - b */ int aws_mp_sub_d(aws_mp_int *a, aws_mp_digit b, aws_mp_int *c); /* c = a * b */ int aws_mp_mul_d(aws_mp_int *a, aws_mp_digit b, aws_mp_int *c); /* a/b => cb + d == a */ int aws_mp_div_d(aws_mp_int *a, aws_mp_digit b, aws_mp_int *c, aws_mp_digit *d); /* a/3 => 3c + d == a */ int aws_mp_div_3(aws_mp_int *a, aws_mp_int *c, aws_mp_digit *d); /* c = a**b */ int aws_mp_expt_d(aws_mp_int *a, aws_mp_digit b, aws_mp_int *c); /* c = a mod b, 0 <= c < b */ int aws_mp_mod_d(aws_mp_int *a, aws_mp_digit b, aws_mp_digit *c); /* ---> number theory <--- */ /* d = a + b (mod c) */ int aws_mp_addmod(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c, aws_mp_int *d); /* d = a - b (mod c) */ int aws_mp_submod(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c, aws_mp_int *d); /* d = a * b (mod c) */ int aws_mp_mulmod(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c, aws_mp_int *d); /* c = a * a (mod b) */ int aws_mp_sqrmod(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c); /* c = 1/a (mod b) */ int aws_mp_invmod(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c); /* c = (a, b) */ int aws_mp_gcd(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c); /* produces value such that U1*a + U2*b = U3 */ int aws_mp_exteuclid(aws_mp_int *a, aws_mp_int *b, aws_mp_int *U1, aws_mp_int *U2, aws_mp_int *U3); /* c = [a, b] or (a*b)/(a, b) */ int aws_aws_mp_lcm(aws_mp_int *a, aws_mp_int *b, aws_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 aws_mp_n_root(aws_mp_int *a, aws_mp_digit b, aws_mp_int *c); /* special sqrt algo */ int aws_mp_sqrt(aws_mp_int *arg, aws_mp_int *ret); /* is number a square? */ int aws_mp_is_square(aws_mp_int *arg, int *ret); /* computes the jacobi c = (a | n) (or Legendre if b is prime) */ int aws_mp_jacobi(aws_mp_int *a, aws_mp_int *n, int *c); /* used to setup the Barrett reduction for a given modulus b */ int aws_mp_reduce_setup(aws_mp_int *a, aws_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 * aws_mp_reduce(aws_mp_abs(a)) [pseudo code]. */ int aws_mp_reduce(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c); /* setups the montgomery reduction */ int aws_mp_montgomery_setup(aws_mp_int *a, aws_mp_digit *mp); /* computes a = B**n mod b without division or multiplication useful for * normalizing numbers in a Montgomery system. */ int aws_mp_montgomery_calc_normalization(aws_mp_int *a, aws_mp_int *b); /* computes x/R == x (mod N) via Montgomery Reduction */ int aws_mp_montgomery_reduce(aws_mp_int *a, aws_mp_int *m, aws_mp_digit mp); /* returns 1 if a is a valid DR modulus */ int aws_mp_dr_is_modulus(aws_mp_int *a); /* sets the value of "d" required for aws_mp_dr_reduce */ void aws_mp_dr_setup(aws_mp_int *a, aws_mp_digit *d); /* reduces a modulo b using the Diminished Radix method */ int aws_mp_dr_reduce(aws_mp_int *a, aws_mp_int *b, aws_mp_digit mp); /* returns true if a can be reduced with aws_mp_reduce_2k */ int aws_mp_reduce_is_2k(aws_mp_int *a); /* determines k value for 2k reduction */ int aws_mp_reduce_2k_setup(aws_mp_int *a, aws_mp_digit *d); /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ int aws_mp_reduce_2k(aws_mp_int *a, aws_mp_int *n, aws_mp_digit d); /* returns true if a can be reduced with aws_mp_reduce_2k_l */ int aws_mp_reduce_is_2k_l(aws_mp_int *a); /* determines k value for 2k reduction */ int aws_mp_reduce_2k_setup_l(aws_mp_int *a, aws_mp_int *d); /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ int aws_mp_reduce_2k_l(aws_mp_int *a, aws_mp_int *n, aws_mp_int *d); /* d = a**b (mod c) */ int aws_mp_exptmod(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c, aws_mp_int *d); /* ---> Primes <--- */ /* number of primes */ #ifdef AWS_MP_8BIT #define AWS_JKTM_PRIME_SIZE 31 #else #define AWS_JKTM_PRIME_SIZE 256 #endif /* table of first AWS_JKTM_PRIME_SIZE primes */ extern const aws_mp_digit aws_ltm_prime_tab[]; /* result=1 if a is divisible by one of the first AWS_JKTM_PRIME_SIZE primes */ int aws_mp_prime_is_divisible(aws_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 aws_mp_prime_fermat(aws_mp_int *a, aws_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 aws_mp_prime_miller_rabin(aws_mp_int *a, aws_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 aws_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 aws_mp_prime_is_prime(aws_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 aws_mp_prime_next_prime(aws_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)?AWS_LTM_PRIME_BBS:0, cb, dat) /* makes a truly random prime of a given size (bits), * * Flags are as follows: * * AWS_LTM_PRIME_BBS - make prime congruent to 3 mod 4 * AWS_LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies AWS_LTM_PRIME_BBS) * AWS_LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero * AWS_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 aws_mp_prime_random_ex(aws_mp_int *a, int t, int size, int flags, aws_ltm_prime_callback cb, void *dat); /* ---> radix conversion <--- */ int aws_mp_count_bits(aws_mp_int *a); int aws_mp_unsigned_bin_size(aws_mp_int *a); int aws_mp_read_unsigned_bin(aws_mp_int *a, const unsigned char *b, int c); int aws_mp_to_unsigned_bin(aws_mp_int *a, unsigned char *b); int aws_mp_to_unsigned_bin_n(aws_mp_int *a, unsigned char *b, unsigned long *outlen); int aws_mp_signed_bin_size(aws_mp_int *a); int aws_mp_read_signed_bin(aws_mp_int *a, const unsigned char *b, int c); int aws_mp_to_signed_bin(aws_mp_int *a, unsigned char *b); int aws_mp_to_signed_bin_n(aws_mp_int *a, unsigned char *b, unsigned long *outlen); int aws_mp_read_radix(aws_mp_int *a, const char *str, int radix); int aws_mp_toradix(aws_mp_int *a, char *str, int radix); int aws_mp_toradix_n(aws_mp_int *a, char *str, int radix, int maxlen); int aws_mp_radix_size(aws_mp_int *a, int radix, int *size); int aws_mp_fread(aws_mp_int *a, int radix, FILE *stream); int aws_mp_fwrite(aws_mp_int *a, int radix, FILE *stream); #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) /* lowlevel functions, do not call! */ int aws_s_mp_add(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c); int aws_s_mp_sub(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c); #define aws_s_mp_mul(a, b, c) aws_s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1) int aws_fast_s_mp_mul_digs(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c, int digs); int aws_s_mp_mul_digs(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c, int digs); int aws_fast_s_mp_mul_high_digs(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c, int digs); int aws_s_mp_mul_high_digs(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c, int digs); int aws_fast_s_mp_sqr(aws_mp_int *a, aws_mp_int *b); int aws_s_mp_sqr(aws_mp_int *a, aws_mp_int *b); int aws_mp_karatsuba_mul(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c); int aws_mp_toom_mul(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c); int aws_mp_karatsuba_sqr(aws_mp_int *a, aws_mp_int *b); int aws_mp_toom_sqr(aws_mp_int *a, aws_mp_int *b); int aws_fast_mp_invmod(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c); int aws_mp_invmod_slow(aws_mp_int *a, aws_mp_int *b, aws_mp_int *c); int aws_fast_mp_montgomery_reduce(aws_mp_int *a, aws_mp_int *m, aws_mp_digit mp); int aws_mp_exptmod_fast(aws_mp_int *G, aws_mp_int *X, aws_mp_int *P, aws_mp_int *Y, int mode); int aws_s_mp_exptmod(aws_mp_int *G, aws_mp_int *X, aws_mp_int *P, aws_mp_int *Y, int mode); void aws_bn_reverse(unsigned char *s, int len); extern const char *aws_mp_s_rmap; #ifdef __cplusplus } #endif #endif /* $Source$ */ /* $Revision: 0.39 $ */ /* $Date: 2006-04-06 19:49:59 +0000 $ */