diff options
Diffstat (limited to 'source4/heimdal/lib/hcrypto/imath/imath.c')
| -rw-r--r--[-rwxr-xr-x] | source4/heimdal/lib/hcrypto/imath/imath.c | 283 |
1 files changed, 184 insertions, 99 deletions
diff --git a/source4/heimdal/lib/hcrypto/imath/imath.c b/source4/heimdal/lib/hcrypto/imath/imath.c index 4487029f78..d8e170aedd 100755..100644 --- a/source4/heimdal/lib/hcrypto/imath/imath.c +++ b/source4/heimdal/lib/hcrypto/imath/imath.c @@ -1,8 +1,8 @@ /* Name: imath.c Purpose: Arbitrary precision integer arithmetic routines. - Author: M. J. Fromberger <http://www.dartmouth.edu/~sting/> - Info: $Id: imath.c 22648 2008-02-25 07:37:57Z lha $ + Author: M. J. Fromberger <http://spinning-yarns.org/michael/> + Info: $Id: imath.c 645 2008-08-03 04:00:30Z sting $ Copyright (C) 2002-2007 Michael J. Fromberger, All Rights Reserved. @@ -53,6 +53,7 @@ const mp_result MP_RANGE = -3; /* argument out of range */ const mp_result MP_UNDEF = -4; /* result undefined */ const mp_result MP_TRUNC = -5; /* output truncated */ const mp_result MP_BADARG = -6; /* invalid null argument */ +const mp_result MP_MINERR = -6; const mp_sign MP_NEG = 1; /* value is strictly negative */ const mp_sign MP_ZPOS = 0; /* value is non-negative */ @@ -65,7 +66,7 @@ static const char *s_error_msg[] = { "argument out of range", "result undefined", "output truncated", - "invalid null argument", + "invalid argument", NULL }; @@ -97,14 +98,7 @@ static const double s_log2[] = { 0.218104292, 0.215338279, 0.212746054, 0.210309918, /* 24 25 26 27 */ 0.208014598, 0.205846832, 0.203795047, 0.201849087, /* 28 29 30 31 */ 0.200000000, 0.198239863, 0.196561632, 0.194959022, /* 32 33 34 35 */ - 0.193426404, 0.191958720, 0.190551412, 0.189200360, /* 36 37 38 39 */ - 0.187901825, 0.186652411, 0.185449023, 0.184288833, /* 40 41 42 43 */ - 0.183169251, 0.182087900, 0.181042597, 0.180031327, /* 44 45 46 47 */ - 0.179052232, 0.178103594, 0.177183820, 0.176291434, /* 48 49 50 51 */ - 0.175425064, 0.174583430, 0.173765343, 0.172969690, /* 52 53 54 55 */ - 0.172195434, 0.171441601, 0.170707280, 0.169991616, /* 56 57 58 59 */ - 0.169293808, 0.168613099, 0.167948779, 0.167300179, /* 60 61 62 63 */ - 0.166666667 + 0.193426404, /* 36 */ }; /* }}} */ @@ -130,31 +124,38 @@ memcpy(q__,p__,i__);}while(0) #define REV(T, A, N) \ do{T *u_=(A),*v_=u_+(N)-1;while(u_<v_){T xch=*u_;*u_++=*v_;*v_--=xch;}}while(0) -#if TRACEABLE_CLAMP -#define CLAMP(Z) s_clamp(Z) -#else #define CLAMP(Z) \ do{mp_int z_=(Z);mp_size uz_=MP_USED(z_);mp_digit *dz_=MP_DIGITS(z_)+uz_-1;\ while(uz_ > 1 && (*dz_-- == 0)) --uz_;MP_USED(z_)=uz_;}while(0) -#endif +/* Select min/max. Do not provide expressions for which multiple + evaluation would be problematic, e.g. x++ */ #define MIN(A, B) ((B)<(A)?(B):(A)) #define MAX(A, B) ((B)>(A)?(B):(A)) + +/* Exchange lvalues A and B of type T, e.g. + SWAP(int, x, y) where x and y are variables of type int. */ #define SWAP(T, A, B) do{T t_=(A);A=(B);B=t_;}while(0) +/* Used to set up and access simple temp stacks within functions. */ #define TEMP(K) (temp + (K)) #define SETUP(E, C) \ do{if((res = (E)) != MP_OK) goto CLEANUP; ++(C);}while(0) +/* Compare value to zero. */ #define CMPZ(Z) \ (((Z)->used==1&&(Z)->digits[0]==0)?0:((Z)->sign==MP_NEG)?-1:1) +/* Multiply X by Y into Z, ignoring signs. Requires that Z have + enough storage preallocated to hold the result. */ #define UMUL(X, Y, Z) \ do{mp_size ua_=MP_USED(X),ub_=MP_USED(Y);mp_size o_=ua_+ub_;\ ZERO(MP_DIGITS(Z),o_);\ (void) s_kmul(MP_DIGITS(X),MP_DIGITS(Y),MP_DIGITS(Z),ua_,ub_);\ MP_USED(Z)=o_;CLAMP(Z);}while(0) +/* Square X into Z. Requires that Z have enough storage to hold the + result. */ #define USQR(X, Z) \ do{mp_size ua_=MP_USED(X),o_=ua_+ua_;ZERO(MP_DIGITS(Z),o_);\ (void) s_ksqr(MP_DIGITS(X),MP_DIGITS(Z),ua_);MP_USED(Z)=o_;CLAMP(Z);}while(0) @@ -194,25 +195,20 @@ static void s_free(void *ptr); necessary. Returns true if successful, false if out of memory. */ static int s_pad(mp_int z, mp_size min); -/* Normalize by removing leading zeroes (except when z = 0) */ -#if TRACEABLE_CLAMP -static void s_clamp(mp_int z); -#endif - /* Fill in a "fake" mp_int on the stack with a given value */ -static void s_fake(mp_int z, int value, mp_digit vbuf[]); +static void s_fake(mp_int z, mp_small value, mp_digit vbuf[]); /* Compare two runs of digits of given length, returns <0, 0, >0 */ static int s_cdig(mp_digit *da, mp_digit *db, mp_size len); /* Pack the unsigned digits of v into array t */ -static int s_vpack(int v, mp_digit t[]); +static int s_vpack(mp_small v, mp_digit t[]); /* Compare magnitudes of a and b, returns <0, 0, >0 */ static int s_ucmp(mp_int a, mp_int b); /* Compare magnitudes of a and v, returns <0, 0, >0 */ -static int s_vcmp(mp_int a, int v); +static int s_vcmp(mp_int a, mp_small v); /* Unsigned magnitude addition; assumes dc is big enough. Carry out is returned (no memory allocated). */ @@ -272,7 +268,7 @@ static int s_dp2k(mp_int z); static int s_isp2(mp_int z); /* Set z to 2^k. May allocate; returns false in case this fails. */ -static int s_2expt(mp_int z, int k); +static int s_2expt(mp_int z, mp_small k); /* Normalize a and b for division, returns normalization constant */ static int s_norm(mp_int a, mp_int b); @@ -410,7 +406,7 @@ mp_result mp_int_init_copy(mp_int z, mp_int old) /* {{{ mp_int_init_value(z, value) */ -mp_result mp_int_init_value(mp_int z, int value) +mp_result mp_int_init_value(mp_int z, mp_small value) { mpz_t vtmp; mp_digit vbuf[MP_VALUE_DIGITS(value)]; @@ -423,7 +419,7 @@ mp_result mp_int_init_value(mp_int z, int value) /* {{{ mp_int_set_value(z, value) */ -mp_result mp_int_set_value(mp_int z, int value) +mp_result mp_int_set_value(mp_int z, mp_small value) { mpz_t vtmp; mp_digit vbuf[MP_VALUE_DIGITS(value)]; @@ -589,12 +585,18 @@ mp_result mp_int_add(mp_int a, mp_int b, mp_int c) mp_int x, y; int cmp = s_ucmp(a, b); /* magnitude comparision, sign ignored */ - /* Set x to max(a, b), y to min(a, b) to simplify later code */ - if(cmp >= 0) { - x = a; y = b; - } + /* Set x to max(a, b), y to min(a, b) to simplify later code. + A special case yields zero for equal magnitudes. + */ + if(cmp == 0) { + mp_int_zero(c); + return MP_OK; + } + else if(cmp < 0) { + x = b; y = a; + } else { - x = b; y = a; + x = a; y = b; } if(!s_pad(c, MP_USED(x))) @@ -616,7 +618,7 @@ mp_result mp_int_add(mp_int a, mp_int b, mp_int c) /* {{{ mp_int_add_value(a, value, c) */ -mp_result mp_int_add_value(mp_int a, int value, mp_int c) +mp_result mp_int_add_value(mp_int a, mp_small value, mp_int c) { mpz_t vtmp; mp_digit vbuf[MP_VALUE_DIGITS(value)]; @@ -694,7 +696,7 @@ mp_result mp_int_sub(mp_int a, mp_int b, mp_int c) /* {{{ mp_int_sub_value(a, value, c) */ -mp_result mp_int_sub_value(mp_int a, int value, mp_int c) +mp_result mp_int_sub_value(mp_int a, mp_small value, mp_int c) { mpz_t vtmp; mp_digit vbuf[MP_VALUE_DIGITS(value)]; @@ -770,7 +772,7 @@ mp_result mp_int_mul(mp_int a, mp_int b, mp_int c) /* {{{ mp_int_mul_value(a, value, c) */ -mp_result mp_int_mul_value(mp_int a, int value, mp_int c) +mp_result mp_int_mul_value(mp_int a, mp_small value, mp_int c) { mpz_t vtmp; mp_digit vbuf[MP_VALUE_DIGITS(value)]; @@ -784,7 +786,7 @@ mp_result mp_int_mul_value(mp_int a, int value, mp_int c) /* {{{ mp_int_mul_pow2(a, p2, c) */ -mp_result mp_int_mul_pow2(mp_int a, int p2, mp_int c) +mp_result mp_int_mul_pow2(mp_int a, mp_small p2, mp_int c) { mp_result res; CHECK(a != NULL && c != NULL && p2 >= 0); @@ -896,16 +898,22 @@ mp_result mp_int_div(mp_int a, mp_int b, mp_int q, mp_int r) or to overlap with the inputs. */ if((lg = s_isp2(b)) < 0) { - if(q && b != q && (res = mp_int_copy(a, q)) == MP_OK) { - qout = q; + if(q && b != q) { + if((res = mp_int_copy(a, q)) != MP_OK) + goto CLEANUP; + else + qout = q; } else { qout = TEMP(last); SETUP(mp_int_init_copy(TEMP(last), a), last); } - if(r && a != r && (res = mp_int_copy(b, r)) == MP_OK) { - rout = r; + if(r && a != r) { + if((res = mp_int_copy(b, r)) != MP_OK) + goto CLEANUP; + else + rout = r; } else { rout = TEMP(last); @@ -981,7 +989,7 @@ mp_result mp_int_mod(mp_int a, mp_int m, mp_int c) /* {{{ mp_int_div_value(a, value, q, r) */ -mp_result mp_int_div_value(mp_int a, int value, mp_int q, int *r) +mp_result mp_int_div_value(mp_int a, mp_small value, mp_int q, mp_small *r) { mpz_t vtmp, rtmp; mp_digit vbuf[MP_VALUE_DIGITS(value)]; @@ -1005,7 +1013,7 @@ mp_result mp_int_div_value(mp_int a, int value, mp_int q, int *r) /* {{{ mp_int_div_pow2(a, p2, q, r) */ -mp_result mp_int_div_pow2(mp_int a, int p2, mp_int q, mp_int r) +mp_result mp_int_div_pow2(mp_int a, mp_small p2, mp_int q, mp_int r) { mp_result res = MP_OK; @@ -1024,7 +1032,7 @@ mp_result mp_int_div_pow2(mp_int a, int p2, mp_int q, mp_int r) /* {{{ mp_int_expt(a, b, c) */ -mp_result mp_int_expt(mp_int a, int b, mp_int c) +mp_result mp_int_expt(mp_int a, mp_small b, mp_int c) { mpz_t t; mp_result res; @@ -1058,7 +1066,7 @@ mp_result mp_int_expt(mp_int a, int b, mp_int c) /* {{{ mp_int_expt_value(a, b, c) */ -mp_result mp_int_expt_value(int a, int b, mp_int c) +mp_result mp_int_expt_value(mp_small a, mp_small b, mp_int c) { mpz_t t; mp_result res; @@ -1149,7 +1157,7 @@ int mp_int_compare_zero(mp_int z) /* {{{ mp_int_compare_value(z, value) */ -int mp_int_compare_value(mp_int z, int value) +int mp_int_compare_value(mp_int z, mp_small value) { mp_sign vsign = (value < 0) ? MP_NEG : MP_ZPOS; int cmp; @@ -1224,7 +1232,7 @@ mp_result mp_int_exptmod(mp_int a, mp_int b, mp_int m, mp_int c) /* {{{ mp_int_exptmod_evalue(a, value, m, c) */ -mp_result mp_int_exptmod_evalue(mp_int a, int value, mp_int m, mp_int c) +mp_result mp_int_exptmod_evalue(mp_int a, mp_small value, mp_int m, mp_int c) { mpz_t vtmp; mp_digit vbuf[MP_VALUE_DIGITS(value)]; @@ -1238,7 +1246,7 @@ mp_result mp_int_exptmod_evalue(mp_int a, int value, mp_int m, mp_int c) /* {{{ mp_int_exptmod_bvalue(v, b, m, c) */ -mp_result mp_int_exptmod_bvalue(int value, mp_int b, +mp_result mp_int_exptmod_bvalue(mp_small value, mp_int b, mp_int m, mp_int c) { mpz_t vtmp; @@ -1555,11 +1563,45 @@ mp_result mp_int_egcd(mp_int a, mp_int b, mp_int c, /* }}} */ +/* {{{ mp_int_lcm(a, b, c) */ + +mp_result mp_int_lcm(mp_int a, mp_int b, mp_int c) +{ + mpz_t lcm; + mp_result res; + + CHECK(a != NULL && b != NULL && c != NULL); + + /* Since a * b = gcd(a, b) * lcm(a, b), we can compute + lcm(a, b) = (a / gcd(a, b)) * b. + + This formulation insures everything works even if the input + variables share space. + */ + if((res = mp_int_init(&lcm)) != MP_OK) + return res; + if((res = mp_int_gcd(a, b, &lcm)) != MP_OK) + goto CLEANUP; + if((res = mp_int_div(a, &lcm, &lcm, NULL)) != MP_OK) + goto CLEANUP; + if((res = mp_int_mul(&lcm, b, &lcm)) != MP_OK) + goto CLEANUP; + + res = mp_int_copy(&lcm, c); + + CLEANUP: + mp_int_clear(&lcm); + + return res; +} + +/* }}} */ + /* {{{ mp_int_divisible_value(a, v) */ -int mp_int_divisible_value(mp_int a, int v) +int mp_int_divisible_value(mp_int a, mp_small v) { - int rem = 0; + mp_small rem = 0; if(mp_int_div_value(a, v, NULL, &rem) != MP_OK) return 0; @@ -1580,61 +1622,87 @@ int mp_int_is_pow2(mp_int z) /* }}} */ -/* {{{ mp_int_sqrt(a, c) */ +/* {{{ mp_int_root(a, b, c) */ -mp_result mp_int_sqrt(mp_int a, mp_int c) +/* Implementation of Newton's root finding method, based loosely on a + patch contributed by Hal Finkel <half@halssoftware.com> + modified by M. J. Fromberger. + */ +mp_result mp_int_root(mp_int a, mp_small b, mp_int c) { mp_result res = MP_OK; - mpz_t temp[2]; + mpz_t temp[5]; int last = 0; + int flips = 0; - CHECK(a != NULL && c != NULL); + CHECK(a != NULL && c != NULL && b > 0); - /* The square root of a negative value does not exist in the integers. */ - if(MP_SIGN(a) == MP_NEG) - return MP_UNDEF; + if(b == 1) { + return mp_int_copy(a, c); + } + if(MP_SIGN(a) == MP_NEG) { + if(b % 2 == 0) + return MP_UNDEF; /* root does not exist for negative a with even b */ + else + flips = 1; + } SETUP(mp_int_init_copy(TEMP(last), a), last); + SETUP(mp_int_init_copy(TEMP(last), a), last); + SETUP(mp_int_init(TEMP(last)), last); + SETUP(mp_int_init(TEMP(last)), last); SETUP(mp_int_init(TEMP(last)), last); + (void) mp_int_abs(TEMP(0), TEMP(0)); + (void) mp_int_abs(TEMP(1), TEMP(1)); + for(;;) { - if((res = mp_int_sqr(TEMP(0), TEMP(1))) != MP_OK) + if((res = mp_int_expt(TEMP(1), b, TEMP(2))) != MP_OK) goto CLEANUP; - if(mp_int_compare_unsigned(a, TEMP(1)) == 0) break; + if(mp_int_compare_unsigned(TEMP(2), TEMP(0)) <= 0) + break; - if((res = mp_int_copy(a, TEMP(1))) != MP_OK) + if((res = mp_int_sub(TEMP(2), TEMP(0), TEMP(2))) != MP_OK) goto CLEANUP; - if((res = mp_int_div(TEMP(1), TEMP(0), TEMP(1), NULL)) != MP_OK) + if((res = mp_int_expt(TEMP(1), b - 1, TEMP(3))) != MP_OK) goto CLEANUP; - if((res = mp_int_add(TEMP(0), TEMP(1), TEMP(1))) != MP_OK) + if((res = mp_int_mul_value(TEMP(3), b, TEMP(3))) != MP_OK) goto CLEANUP; - if((res = mp_int_div_pow2(TEMP(1), 1, TEMP(1), NULL)) != MP_OK) + if((res = mp_int_div(TEMP(2), TEMP(3), TEMP(4), NULL)) != MP_OK) + goto CLEANUP; + if((res = mp_int_sub(TEMP(1), TEMP(4), TEMP(4))) != MP_OK) goto CLEANUP; - if(mp_int_compare_unsigned(TEMP(0), TEMP(1)) == 0) break; - if((res = mp_int_sub_value(TEMP(0), 1, TEMP(0))) != MP_OK) goto CLEANUP; - if(mp_int_compare_unsigned(TEMP(0), TEMP(1)) == 0) break; - - if((res = mp_int_copy(TEMP(1), TEMP(0))) != MP_OK) goto CLEANUP; + if(mp_int_compare_unsigned(TEMP(1), TEMP(4)) == 0) { + if((res = mp_int_sub_value(TEMP(4), 1, TEMP(4))) != MP_OK) + goto CLEANUP; + } + if((res = mp_int_copy(TEMP(4), TEMP(1))) != MP_OK) + goto CLEANUP; } - res = mp_int_copy(TEMP(0), c); + if((res = mp_int_copy(TEMP(1), c)) != MP_OK) + goto CLEANUP; + + /* If the original value of a was negative, flip the output sign. */ + if(flips) + (void) mp_int_neg(c, c); /* cannot fail */ CLEANUP: while(--last >= 0) mp_int_clear(TEMP(last)); - - return res; + + return res; } /* }}} */ /* {{{ mp_int_to_int(z, out) */ -mp_result mp_int_to_int(mp_int z, int *out) +mp_result mp_int_to_int(mp_int z, mp_small *out) { - unsigned int uv = 0; + mp_usmall uv = 0; mp_size uz; mp_digit *dz; mp_sign sz; @@ -1643,8 +1711,8 @@ mp_result mp_int_to_int(mp_int z, int *out) /* Make sure the value is representable as an int */ sz = MP_SIGN(z); - if((sz == MP_ZPOS && mp_int_compare_value(z, INT_MAX) > 0) || - mp_int_compare_value(z, INT_MIN) < 0) + if((sz == MP_ZPOS && mp_int_compare_value(z, MP_SMALL_MAX) > 0) || + mp_int_compare_value(z, MP_SMALL_MIN) < 0) return MP_RANGE; uz = MP_USED(z); @@ -1657,13 +1725,46 @@ mp_result mp_int_to_int(mp_int z, int *out) } if(out) - *out = (sz == MP_NEG) ? -(int)uv : (int)uv; + *out = (sz == MP_NEG) ? -(mp_small)uv : (mp_small)uv; return MP_OK; } /* }}} */ +/* {{{ mp_int_to_uint(z, *out) */ + +mp_result mp_int_to_uint(mp_int z, mp_usmall *out) +{ + mp_usmall uv = 0; + mp_size uz; + mp_digit *dz; + mp_sign sz; + + CHECK(z != NULL); + + /* Make sure the value is representable as an int */ + sz = MP_SIGN(z); + if(!(sz == MP_ZPOS && mp_int_compare_value(z, UINT_MAX) <= 0)) + return MP_RANGE; + + uz = MP_USED(z); + dz = MP_DIGITS(z) + uz - 1; + + while(uz > 0) { + uv <<= MP_DIGIT_BIT/2; + uv = (uv << (MP_DIGIT_BIT/2)) | *dz--; + --uz; + } + + if(out) + *out = uv; + + return MP_OK; +} + +/* }}} */ + /* {{{ mp_int_to_string(z, radix, str, limit) */ mp_result mp_int_to_string(mp_int z, mp_size radix, @@ -1769,7 +1870,7 @@ mp_result mp_int_read_cstring(mp_int z, mp_size radix, const char *str, char **e return MP_RANGE; /* Skip leading whitespace */ - while(isspace((unsigned char)*str)) + while(isspace((int)*str)) ++str; /* Handle leading sign tag (+/-, positive default) */ @@ -2091,26 +2192,9 @@ static int s_pad(mp_int z, mp_size min) /* }}} */ -/* {{{ s_clamp(z) */ - -#if TRACEABLE_CLAMP -static void s_clamp(mp_int z) -{ - mp_size uz = MP_USED(z); - mp_digit *zd = MP_DIGITS(z) + uz - 1; - - while(uz > 1 && (*zd-- == 0)) - --uz; - - MP_USED(z) = uz; -} -#endif - -/* }}} */ - /* {{{ s_fake(z, value, vbuf) */ -static void s_fake(mp_int z, int value, mp_digit vbuf[]) +static void s_fake(mp_int z, mp_small value, mp_digit vbuf[]) { mp_size uv = (mp_size) s_vpack(value, vbuf); @@ -2142,9 +2226,9 @@ static int s_cdig(mp_digit *da, mp_digit *db, mp_size len) /* {{{ s_vpack(v, t[]) */ -static int s_vpack(int v, mp_digit t[]) +static int s_vpack(mp_small v, mp_digit t[]) { - unsigned int uv = (unsigned int)((v < 0) ? -v : v); + mp_usmall uv = (mp_usmall) ((v < 0) ? -v : v); int ndig = 0; if(uv == 0) @@ -2180,7 +2264,7 @@ static int s_ucmp(mp_int a, mp_int b) /* {{{ s_vcmp(a, v) */ -static int s_vcmp(mp_int a, int v) +static int s_vcmp(mp_int a, mp_small v) { mp_digit vdig[MP_VALUE_DIGITS(v)]; int ndig = 0; @@ -2814,7 +2898,7 @@ static int s_isp2(mp_int z) /* {{{ s_2expt(z, k) */ -static int s_2expt(mp_int z, int k) +static int s_2expt(mp_int z, mp_small k) { mp_size ndig, rest; mp_digit *dz; @@ -3100,12 +3184,13 @@ static mp_result s_udiv(mp_int a, mp_int b) /* {{{ s_outlen(z, r) */ -/* Precondition: 2 <= r < 64 */ static int s_outlen(mp_int z, mp_size r) { mp_result bits; double raw; + assert(r >= MP_MIN_RADIX && r <= MP_MAX_RADIX); + bits = mp_int_count_bits(z); raw = (double)bits * s_log2[r]; @@ -3135,7 +3220,7 @@ static int s_ch2val(char c, int r) if(isdigit((unsigned char) c)) out = c - '0'; else if(r > 10 && isalpha((unsigned char) c)) - out = toupper((unsigned char)c) - 'A' + 10; + out = toupper(c) - 'A' + 10; else return -1; |