diff options
Diffstat (limited to 'moon-abe/pbc-0.5.14/arith/ternary_extension_field.c')
| -rw-r--r-- | moon-abe/pbc-0.5.14/arith/ternary_extension_field.c | 950 |
1 files changed, 0 insertions, 950 deletions
diff --git a/moon-abe/pbc-0.5.14/arith/ternary_extension_field.c b/moon-abe/pbc-0.5.14/arith/ternary_extension_field.c deleted file mode 100644 index 3c79e3bd..00000000 --- a/moon-abe/pbc-0.5.14/arith/ternary_extension_field.c +++ /dev/null @@ -1,950 +0,0 @@ -/* $GF(3^m) = GF(3)[x]/(x^m + x^t + 2)$ - $GF(3^{2*m}) = GF(3^m)[x]/(x^2 + 1)$ - $GF(3^{3*m}) = GF(3^m)[x]/(x^3 - x -1)$ - $GF(3^{6*m}) = GF(3^{2*m})[x]/(x^3 - x -1)$ - - The "gf3_*" functions are for $GF(3)$. - The "gf3m_*" functions are for $GF(3^m)$. - The "gf32m_*" functions are for $GF(3^{2*m})$. - The "gf33m_*" functions are for $GF(3^{3*m})$ and $GF(3^{6*m})$. - - (gf3m field_t).data is a pointer of struct params - (gf3m element_t).data is a pointer of unsigned long - (gf32m element_t).data is gf32m_ptr - (gf33m element_t).data is gf33m_ptr */ - -#include <stdlib.h> -#include <string.h> -#include <stdarg.h> -#include <stdio.h> -#include <stdint.h> -#include <gmp.h> -#include "pbc_utils.h" -#include "pbc_memory.h" -#include "pbc_field.h" - -typedef unsigned long gf3; - -typedef struct { /* private data of $GF(3^m)$ */ - unsigned int len; /* the number of native machine integers required to represent one GF(3^m) element */ - unsigned int m; /* the irreducible polynomial is $x^m + x^t + 2$ */ - unsigned int t; /* the irreducible polynomial is $x^m + x^t + 2$ */ - element_ptr p; /* $p$ is the irreducible polynomial. */ -} params; - -typedef struct { - element_t _0, _1; -} gf32m_s; - -typedef gf32m_s *gf32m_ptr; - -typedef struct { - element_t _0, _1, _2; -} gf33m_s; - -typedef gf33m_s *gf33m_ptr; - -#define W (sizeof(unsigned long)*8) /* number of GF(3) elements in one processor integer */ -#define PARAM(e) ((params *)e->field->data) -#define LEN(e) (PARAM(e)->len) -#define SIZE(e) (LEN(e) * 2 * sizeof(unsigned long)) -#define DATA1(e) ((unsigned long*)e->data) -#define DATA2(e) ((unsigned long*)e->data + LEN(e)) -#define GF32M(e) ((gf32m_s *)e->data) -#define GF33M(e) ((gf33m_s *)e->data) -#define BASE(e) ((field_ptr)e->field->data) -#define print(e) {printf(#e": "); element_out_str(stdout, 10, e); printf("\n");} - -static size_t gf3m_out_str(FILE *stream, int base, element_t e) { - if (base != 10 && base != 16) - pbc_die("only support base 10 and base 16"); - size_t size = 0; - unsigned i; - unsigned long *d = DATA1(e); - for (i = 0; i < LEN(e) * 2; i++) { - if (base == 16) - size += fprintf(stream, "0x%lx,", d[i]); - else - size += fprintf(stream, "%lu,", d[i]); - } - return size; -} - -/* $a <- 0$ */ -static void gf3m_zero(element_t a) { - memset(a->data, 0, SIZE(a)); -} - -static void gf3m_init(element_t e) { - e->data = pbc_malloc(SIZE(e)); - gf3m_zero(e); -} - -static void gf3m_clear(element_t e) { - pbc_free(e->data); -} - -/* $e <- a$ */ -static void gf3m_assign(element_t e, element_t a) { - memcpy(e->data, a->data, SIZE(a)); -} - -/* $a <- a/x$. $len$ is the number of elements in $a$ */ -static void shift_down(unsigned int len, unsigned long a[]) { - unsigned long h = 0; - const unsigned long x = 1ul << (W - 1); - int i; - for (i = len - 1; i >= 0; i--) { - unsigned long l = a[i] & 1; - a[i] >>= 1; - if (h) - a[i] |= x; - h = l; - } -} - -/* $e <- e/x$ */ -static void gf3m_shift_down(element_t e) { - shift_down(LEN(e), DATA1(e)); - shift_down(LEN(e), DATA2(e)); -} - -/* $a <- a*x$. $len$ is the number of elements in $a$ */ -static void shift_up(unsigned int len, unsigned long a[]) { - unsigned long l = 0; - const unsigned long x = 1ul << (W - 1), y = x - 1; - unsigned i; - for (i = 0; i < len; i++) { - unsigned long h = a[i] & x; - a[i] = ((a[i] & y) << 1) | l; - l = h ? 1 : 0; - } -} - -/* $e <- e*x$ */ -static void gf3m_shift_up(element_t e) { - shift_up(LEN(e), DATA1(e)); - shift_up(LEN(e), DATA2(e)); -} - -/* return the coefficient of $x^pos$ in $e$ */ -static unsigned gf3m_get(element_t e, unsigned pos) { - unsigned long *a1 = DATA1(e), *a2 = DATA2(e); - unsigned x = pos / W; - unsigned long y = 1ul << (pos % W), v1 = a1[x] & y, v2 = a2[x] & y; - return v1 ? 1 : (v2 ? 2 : 0); -} - -/* set the coefficient of $x^pos$ as 1 */ -static void gf3m_set(element_t e, unsigned pos, unsigned value) { - unsigned long *a = DATA1(e); - /* assert value == 0, 1 or 2 */ - if (value == 2) - a = DATA2(e); - if (value) - a[pos / W] |= 1ul << (pos % W); -} - -/* $e <- a+b$ */ -static void gf3m_add(element_t e, element_t a, element_t b) { - unsigned long *e1 = DATA1(e), *e2 = DATA2(e), *a1 = DATA1(a), - *a2 = DATA2(a), *b1 = DATA1(b), *b2 = DATA2(b); - unsigned i; - for (i = 0; i < LEN(e); i++, e1++, e2++, a1++, a2++, b1++, b2++) { - unsigned long t = (*a1 | *a2) & (*b1 | *b2), c1 = t ^ (*a1 | *b1), c2 = - t ^ (*a2 | *b2); - *e1 = c1; - *e2 = c2; - } -} - -/* $e <- x-y$ */ -static void gf3m_sub(element_t e, element_t a, element_t b) { - unsigned long *e1 = DATA1(e), *e2 = DATA2(e), *a1 = DATA1(a), - *a2 = DATA2(a), *b1 = DATA2(b), *b2 = DATA1(b); - unsigned i; - for (i = 0; i < LEN(e); i++, e1++, e2++, a1++, a2++, b1++, b2++) { - unsigned long t = (*a1 | *a2) & (*b1 | *b2), c1 = t ^ (*a1 | *b1), c2 = - t ^ (*a2 | *b2); - *e1 = c1; - *e2 = c2; - } -} - -/* return 0 if $a == b$ in $GF(3^m)$, 1 otherwise. */ -static int gf3m_cmp(element_t a, element_t b) { - unsigned long *pa = DATA1(a), *pb = DATA1(b); - unsigned i; - for (i = 0; i < LEN(a) * 2; i++, pa++, pb++) - if (*pa != *pb) - return 1; - return 0; -} - -/* $a <- 1$ */ -static void gf3m_one(element_t a) { - gf3m_zero(a); - *DATA1(a) = 1; -} - -static int gf3m_is0(element_t e) { - unsigned i; - for (i = 0; i < LEN(e) * 2; i++) - if (DATA1(e)[i]) - return 0; - return 1; -} - -static int gf3m_is1(element_t e) { - unsigned i; - if (DATA1(e)[0] != 1) - return 0; - for (i = 1; i < LEN(e) * 2; i++) - if (DATA1(e)[i]) - return 0; - return 1; -} - -/* set $a$ to be a random element in $GF(3^m)$ */ -static void gf3m_random(element_t a) { - /* TODO: use uniform distribution? */ - params *c = PARAM(a); - unsigned rm = c->m % W; - const unsigned long i1 = ~0ul; - unsigned long i2 = (1ul << rm) - 1; - unsigned long *a1 = DATA1(a), *a2 = DATA2(a); - unsigned i; - for (i = 0; i < c->len - 1; i++, a1++, a2++) { /* TODO: if $RAND_MAX < i1$ ? */ - *a1 = rand() & i1; - *a2 = rand() & i1 & ~(*a1); /* assuring there is no bit that a1[x] & a2[x] == 1 */ - } - unsigned long x = rm ? i2 : i1; - *a1 = rand() & x; - *a2 = rand() & x & ~(*a1); -} - -static void swap(unsigned long *a, unsigned long *b) { - *a ^= *b; - *b ^= *a; - *a ^= *b; -} - -/* $y <- (-x)$ */ -static void gf3m_neg(element_t y, element_t x) { - unsigned long *a1 = DATA1(x), *a2 = DATA2(x), *c1 = DATA1(y), - *c2 = DATA2(y); - if (a1 == c1) { - unsigned i; - for (i = 0; i < LEN(y); i++, a1++, a2++) - swap(a1, a2); - } else { - memcpy(c1, a2, SIZE(y) / 2); - memcpy(c2, a1, SIZE(y) / 2); - } -} - -/* doing reduction - * The function returns the value of $a$ modulo $the irreducible trinomial$. - * $degree$ equals the degree of $a$. - * $2*len$ is the number of elements in $a$ */ -static void gf3m_reduct(element_t e, unsigned len, unsigned degree) { - // the $len$ argument exists because sometimes $len != p->len$ - params *p = PARAM(e); - unsigned old = p->len; - p->len = len; - element_t px; - element_init(px, e->field); - gf3m_set(px, degree, 1); - gf3m_set(px, degree - p->m + p->t, 1); - gf3m_set(px, degree - p->m, 2); - while (degree >= p->m) { - unsigned v = gf3m_get(e, degree); - if (v == 1) - gf3m_sub(e, e, px); - else if (v == 2) - gf3m_add(e, e, px); - degree--; - gf3m_shift_down(px); - } - element_clear(px); - p->len = old; -} - -/* doing multiplication of $n \in \{0,1,2\}$ and $a$ in $GF(3^m)$ - * The function sets $e <- n * a$. */ -static void gf3m_f1(element_t e, unsigned n, element_t a) { - /* assert $e$ is not $a$ */ - if (n == 0) - memset(DATA1(e), 0, SIZE(e)); - else if (n == 1) - memcpy(DATA1(e), DATA1(a), SIZE(e)); - else { - memcpy(DATA1(e), DATA2(a), SIZE(e) / 2); - memcpy(DATA2(e), DATA1(a), SIZE(e) / 2); - } -} - -/* $e <- e*x mod p(x)$ */ -static void gf3m_f2(element_t e) { - params *p = PARAM(e); - gf3m_shift_up(e); - unsigned v = gf3m_get(e, p->m); - if (v == 1) - gf3m_sub(e, e, p->p); - else if (v == 2) - gf3m_add(e, e, p->p); -} - -/* doing multiplication in GF(3^m) - * The function sets $e == a*b \in GF(3^m)$ */ -static void gf3m_mult(element_t e, element_ptr a, element_t b) { - params *p = PARAM(a); - element_t aa, t, c; - element_init(aa, a->field); - element_set(aa, a); - a = aa; // clone $a$ - element_init(t, a->field); - element_init(c, a->field); - unsigned i; - for (i = 0; i < p->m; i++) { - unsigned v = gf3m_get(b, i); - gf3m_f1(t, v, a); /* t == b[i]*a in GF(3^m) */ - gf3m_add(c, c, t); /* c += b[i]*a in GF(3^m) */ - gf3m_f2(a); /* a == a*x in GF(3^m) */ - } - element_set(e, c); - element_clear(t); - element_clear(c); - element_clear(aa); -} - -/* $e <- x^3$ */ -static void gf3m_cubic(element_t e, element_t x) { - /* TODO: faster algorithm */ - params *p = PARAM(x); - unsigned old = p->len; - unsigned len = (3 * p->m - 2 + W - 1) / W; /* length of $b1 */ - p->len = len; - element_t a; - element_init(a, x->field); - unsigned i; - for (i = 0; i < p->m; i++) { - p->len = old; - unsigned v = gf3m_get(x, i); - p->len = len; - gf3m_set(a, 3 * i, v); - } - gf3m_reduct(a, len, 3 * p->m - 3); - p->len = old; - memcpy(DATA1(e), DATA1(a), SIZE(e) / 2); - memcpy(DATA2(e), DATA1(a) + len, SIZE(e) / 2); - element_clear(a); -} - -/* multiplication modulo 3 of two elements in GF(3) - * for example, $mult(2,2) == 1$, and $mult(1,2) == 2$ */ -static unsigned gf3_mult(unsigned a, unsigned b) { - static const unsigned l[] = { 0, 1, 2, 0, 1 }; - return l[a * b]; -} - -static void gf3m_swap(element_t a, element_t b) { - unsigned long *p = DATA1(a); - a->data = b->data; - b->data = p; -} - -/* computing the inversion of an element $a$ in GF(3^m), i.e., $e <- a^{-1}$ - The algorithm is by Tim Kerins, Emanuel Popovici and William Marnane - in the paper of "Algorithms and Architectures for use in FPGA", - Lecture Notes in Computer Science, 2004, Volume 3203/2004, 74-83. - Note that $U$ must have an extra bit, i.e, (_m + W - 1) // W == (_m + W) // W */ -static void gf3m_invert(element_t e, element_t a) { - struct field_s *f = a->field; - params *p = PARAM(a); - unsigned lenA = p->len; - unsigned lenS = (3 * p->m + W - 1) / W; - p->len = lenS; - element_t S, R, t, U, V, t2; - element_init(S, f); - element_init(R, f); - element_init(t, f); - memcpy(DATA1(S), DATA1(p->p), lenA * sizeof(unsigned long)); /* S = p(x) */ - memcpy(DATA1(S) + lenS, DATA1(p->p) + lenA, lenA * sizeof(unsigned long)); - memcpy(DATA1(R), DATA1(a), lenA * sizeof(unsigned long)); /* R = _clone(a) */ - memcpy(DATA1(R) + lenS, DATA1(a) + lenA, lenA * sizeof(unsigned long)); - p->len = lenA; - element_init(U, f); - gf3m_one(U); - element_init(V, f); - element_init(t2, f); - unsigned d = 0, i, r_m, s_m, q, x; - for (i = 0; i < p->m * 2; i++) { - p->len = lenS; - r_m = gf3m_get(R, p->m), s_m = gf3m_get(S, p->m); - if (r_m == 0) { - gf3m_shift_up(R); /* R = xR */ - p->len = lenA; - gf3m_f2(U); /* U = xU mod p */ - d++; - } else { - q = gf3_mult(r_m, s_m); - gf3m_f1(t, q, R); - gf3m_sub(S, S, t); /* S = S-qR */ - gf3m_shift_up(S); /* S = xS */ - p->len = lenA; - gf3m_f1(t2, q, U); - gf3m_sub(V, V, t2); /* V = V-qU */ - if (d == 0) { - gf3m_swap(S, R); - gf3m_swap(U, V); - gf3m_f2(U); /* U = xU mod p*/ - d++; - } else { - x = gf3m_get(U, 0); - if (x == 1) /* assuring x|U */ - gf3m_add(U, U, p->p); - else if (x == 2) - gf3m_sub(U, U, p->p); - gf3m_shift_down(U); /* divide U by $x$ */ - d--; - } - } - } - p->len = lenS; - r_m = gf3m_get(R, p->m); /* assume r_m is not zero */ - p->len = lenA; - if (r_m == 2) - gf3m_neg(U, U); - memcpy(e->data, U->data, lenA * 2 * sizeof(unsigned long)); - element_clear(S); - element_clear(R); - element_clear(U); - element_clear(V); - element_clear(t); - element_clear(t2); -} - -static void gf3m_sqrt(element_t e, element_t a) { - field_ptr f = e->field; - mpz_t t; - mpz_init(t); // t == (field_order + 1) / 4 - mpz_set(t, f->order); - mpz_add_ui(t, t, 1); - mpz_tdiv_q_2exp(t, t, 2); - element_pow_mpz(e, a, t); - mpz_clear(t); -} - -int gf3m_to_bytes(unsigned char *d, element_ptr e) { - unsigned long *a = DATA1(e), *b = DATA2(e); - unsigned long i, j; - for (i = 0; i < LEN(e); i++, a++, b++) { - for (j = 0; j < sizeof(unsigned long) * 8; j += 8) { - *(d++) = (unsigned char) ((*a) >> j); - *(d++) = (unsigned char) ((*b) >> j); - } - } - return SIZE(e); -} - -int gf3m_from_bytes(element_ptr e, unsigned char *d) { - unsigned long *a = DATA1(e), *b = DATA2(e); - unsigned i; - int j; - for (i = 0; i < LEN(e); i++, a++, b++, d += sizeof(unsigned long) * 2) { - *a = 0, *b = 0; - j = 2 * sizeof(unsigned long) - 2; - while (j >= 0) { - *a <<= 8, *b <<= 8; - *a += d[j]; - *b += d[j + 1]; - j -= 2; - } - } - return SIZE(e); -} - -static void field_clear_gf3m(field_t f) { - params *p = f->data; - gf3m_clear(p->p); - pbc_free(p->p); - pbc_free(p); -} - -/* initialize the finite field as $GF(3^m)$, whose irreducible polynomial is with the degree of $m$ */ -void field_init_gf3m(field_t f, unsigned m, unsigned t) { - params *p = pbc_malloc(sizeof(*p)); - p->len = (m + (W - 1) + 1) / W; /* extra one bit for $_p$ */ - p->m = m; - p->t = t; - p->p = pbc_malloc(sizeof(*(p->p))); - p->p->field = f; - p->p->data = pbc_malloc(2 * sizeof(unsigned long) * p->len); - memset(p->p->data, 0, 2 * sizeof(unsigned long) * p->len); - unsigned long *p1 = p->p->data, *p2 = p1 + p->len; - p2[0] = 1; /* _p == x^m+x^t+2 */ - unsigned int p_t = p->t; - p1[p_t / W] |= 1ul << (p_t % W); - p1[m / W] |= 1ul << (m % W); - - field_init(f); - f->field_clear = field_clear_gf3m; - f->init = gf3m_init; - f->clear = gf3m_clear; - f->set = gf3m_assign; - f->set0 = gf3m_zero; - f->set1 = gf3m_one; - f->is0 = gf3m_is0; - f->is1 = gf3m_is1; - f->add = gf3m_add; - f->sub = gf3m_sub; - f->mul = gf3m_mult; - f->cubic = gf3m_cubic; - f->invert = gf3m_invert; - f->neg = gf3m_neg; - f->random = gf3m_random; - f->cmp = gf3m_cmp; - f->sqrt = gf3m_sqrt; - f->from_bytes = gf3m_from_bytes; - f->to_bytes = gf3m_to_bytes; - f->out_str = gf3m_out_str; - f->fixed_length_in_bytes = 2 * sizeof(unsigned long) * p->len; - f->data = p; - f->name = "GF(3^m)"; - - mpz_set_ui(f->order, 3); - mpz_pow_ui(f->order, f->order, p->m); -} - -static size_t gf32m_out_str(FILE *stream, int base, element_t e) { - UNUSED_VAR(base); - element_ptr e0 = GF32M(e)->_0, e1 = GF32M(e)->_1; - size_t size = 0; - size += element_out_str(stream, base, e0); - size += element_out_str(stream, base, e1); - return size; -} - -static void gf32m_init(element_t e) { - e->data = pbc_malloc(sizeof(gf32m_s)); - gf32m_ptr p = (gf32m_ptr) e->data; - field_ptr base = BASE(e); - element_init(p->_0, base); - element_init(p->_1, base); -} - -static void gf32m_clear(element_t e) { - gf32m_ptr p = (gf32m_ptr) e->data; - element_clear(p->_0); - element_clear(p->_1); - pbc_free(e->data); -} - -static void gf32m_set0(element_t e) { - element_ptr e0 = GF32M(e)->_0, e1 = GF32M(e)->_1; - element_set0(e0); - element_set0(e1); -} - -static void gf32m_set1(element_t e) { - element_ptr e0 = GF32M(e)->_0, e1 = GF32M(e)->_1; - element_set1(e0); - element_set0(e1); -} - -static int gf32m_item_count(element_t e) { - UNUSED_VAR(e); - return 2; -} - -static element_ptr gf32m_item(element_t a, int i) { - element_ptr a0 = GF32M(a)->_0, a1 = GF32M(a)->_1; - return i == 0 ? a0 : a1; -} - -static void gf32m_assign(element_t e, element_t a) { - element_ptr a0 = GF32M(a)->_0, a1 = GF32M(a)->_1, e0 = GF32M(e)->_0, e1 = - GF32M(e)->_1; - element_set(e0, a0); - element_set(e1, a1); -} - -static void gf32m_random(element_t e) { - element_ptr e0 = GF32M(e)->_0, e1 = GF32M(e)->_1; - element_random(e0); - element_random(e1); -} - -/* return 0 if $a == b$, 1 otherwise */ -static int gf32m_cmp(element_t a, element_t b) { - element_ptr a0 = GF32M(a)->_0, a1 = GF32M(a)->_1, b0 = GF32M(b)->_0, b1 = - GF32M(b)->_1; - return element_cmp(a0, b0) || element_cmp(a1, b1); -} - -/* $c <- a+b$ */ -static void gf32m_add(element_t c, element_t a, element_t b) { - element_ptr a0 = GF32M(a)->_0, a1 = GF32M(a)->_1, b0 = GF32M(b)->_0, b1 = - GF32M(b)->_1, c0 = GF32M(c)->_0, c1 = GF32M(c)->_1; - element_add(c0, a0, b0); - element_add(c1, a1, b1); -} - -/* $c <- a-b$ */ -static void gf32m_sub(element_t c, element_t a, element_t b) { - element_ptr a0 = GF32M(a)->_0, a1 = GF32M(a)->_1, b0 = GF32M(b)->_0, b1 = - GF32M(b)->_1, c0 = GF32M(c)->_0, c1 = GF32M(c)->_1; - element_sub(c0, a0, b0); - element_sub(c1, a1, b1); -} - -/* $c <- (-a)$ */ -static void gf32m_neg(element_t c, element_t a) { - element_ptr a0 = GF32M(a)->_0, a1 = GF32M(a)->_1, c0 = GF32M(c)->_0, c1 = - GF32M(c)->_1; - element_neg(c0, a0); - element_neg(c1, a1); -} - -/* $e<- a*b$ */ -static void gf32m_mult(element_t e, element_t a, element_t b) { - element_ptr a0 = GF32M(a)->_0, a1 = GF32M(a)->_1, b0 = GF32M(b)->_0, b1 = - GF32M(b)->_1, e0 = GF32M(e)->_0, e1 = GF32M(e)->_1; - field_ptr base = BASE(a); - element_t a0b0, a1b1, t0, t1, c1; - element_init(a0b0, base); - element_init(a1b1, base); - element_init(t0, base); - element_init(t1, base); - element_init(c1, base); - element_mul(a0b0, a0, b0); - element_mul(a1b1, a1, b1); - element_add(t0, a1, a0); - element_add(t1, b1, b0); - element_mul(c1, t0, t1); // c1 == (a1+a0)*(b1+b0) - element_sub(c1, c1, a1b1); - element_sub(c1, c1, a0b0); - element_ptr c0 = a0b0; - element_sub(c0, c0, a1b1); // c0 == a0*b0 - a1*b1 - element_set(e0, c0); - element_set(e1, c1); - element_clear(a0b0); - element_clear(a1b1); - element_clear(t0); - element_clear(t1); - element_clear(c1); -} - -/* $e <- a^3$ */ -static void gf32m_cubic(element_t e, element_t a) { - element_ptr a0 = GF32M(a)->_0, a1 = GF32M(a)->_1, e0 = GF32M(e)->_0, e1 = - GF32M(e)->_1; - field_ptr base = BASE(a); - element_t c0, c1; - element_init(c0, base); - element_init(c1, base); - element_cubic(c0, a0); - element_cubic(c1, a1); - element_neg(c1, c1); // c1 == -(a1^3) - element_set(e0, c0); - element_set(e1, c1); - element_clear(c0); - element_clear(c1); -} - -void field_clear_gf32m(field_t f) { - UNUSED_VAR(f); -} - -/* initialize the finite field as $base_field[x]/(x^2 + 1)$, whose base field is $b$ */ -void field_init_gf32m(field_t f, field_t b) { - field_init(f); - f->data = b; - f->field_clear = field_clear_gf32m; - f->init = gf32m_init; - f->clear = gf32m_clear; - f->set = gf32m_assign; - f->set0 = gf32m_set0; - f->set1 = gf32m_set1; - f->random = gf32m_random; - f->cmp = gf32m_cmp; - f->add = gf32m_add; - f->sub = gf32m_sub; - f->neg = gf32m_neg; - f->mul = gf32m_mult; - f->cubic = gf32m_cubic; - f->item_count = gf32m_item_count; - f->item = gf32m_item; - f->out_str = gf32m_out_str; - mpz_pow_ui(f->order, b->order, 2); - f->name = "GF(3^{2*m})"; -} - -static size_t gf33m_out_str(FILE *stream, int base, element_t e) { - UNUSED_VAR(base); - element_ptr e0 = GF33M(e)->_0, e1 = GF33M(e)->_1, e2 = GF33M(e)->_2; - size_t size = 0; - size += element_out_str(stream, base, e0); - size += element_out_str(stream, base, e1); - size += element_out_str(stream, base, e2); - return size; -} - -static void gf33m_init(element_t e) { - e->data = pbc_malloc(sizeof(gf33m_s)); - gf33m_ptr p = (gf33m_ptr) e->data; - field_ptr base = BASE(e); - element_init(p->_0, base); - element_init(p->_1, base); - element_init(p->_2, base); -} - -static void gf33m_clear(element_t e) { - gf33m_ptr p = (gf33m_ptr) e->data; - element_clear(p->_0); - element_clear(p->_1); - element_clear(p->_2); - pbc_free(e->data); -} - -static void gf33m_set0(element_t e) { - element_ptr e0 = GF33M(e)->_0, e1 = GF33M(e)->_1, e2 = GF33M(e)->_2; - element_set0(e0); - element_set0(e1); - element_set0(e2); -} - -static void gf33m_set1(element_t e) { - element_ptr e0 = GF33M(e)->_0, e1 = GF33M(e)->_1, e2 = GF33M(e)->_2; - element_set1(e0); - element_set0(e1); - element_set0(e2); -} - -static int gf33m_item_count(element_t e) { - UNUSED_VAR(e); - return 3; -} - -static element_ptr gf33m_item(element_t a, int i) { - element_ptr a0 = GF33M(a)->_0, a1 = GF33M(a)->_1, a2 = GF33M(a)->_2; - return i == 0 ? a0 : (i == 1 ? a1 : a2); -} - -static void gf33m_assign(element_t e, element_t a) { - element_ptr a0 = GF33M(a)->_0, a1 = GF33M(a)->_1, a2 = GF33M(a)->_2, e0 = - GF33M(e)->_0, e1 = GF33M(e)->_1, e2 = GF33M(e)->_2; - element_set(e0, a0); - element_set(e1, a1); - element_set(e2, a2); -} - -static void gf33m_random(element_t e) { - element_ptr e0 = GF33M(e)->_0, e1 = GF33M(e)->_1, e2 = GF33M(e)->_2; - element_random(e0); - element_random(e1); - element_random(e2); -} - -/* return 0 if $a == b$, 1 otherwise */ -static int gf33m_cmp(element_t a, element_t b) { - element_ptr a0 = GF33M(a)->_0, a1 = GF33M(a)->_1, a2 = GF33M(a)->_2, b0 = - GF33M(b)->_0, b1 = GF33M(b)->_1, b2 = GF33M(b)->_2; - return element_cmp(a0, b0) || element_cmp(a1, b1) || element_cmp(a2, b2); -} - -/* $c <- a+b$ */ -static void gf33m_add(element_t c, element_t a, element_t b) { - element_ptr a0 = GF33M(a)->_0, a1 = GF33M(a)->_1, a2 = GF33M(a)->_2, b0 = - GF33M(b)->_0, b1 = GF33M(b)->_1, b2 = GF33M(b)->_2, c0 = - GF33M(c)->_0, c1 = GF33M(c)->_1, c2 = GF33M(c)->_2; - element_add(c0, a0, b0); - element_add(c1, a1, b1); - element_add(c2, a2, b2); -} - -/* $c <- a-b$ */ -static void gf33m_sub(element_t c, element_t a, element_t b) { - element_ptr a0 = GF33M(a)->_0, a1 = GF33M(a)->_1, a2 = GF33M(a)->_2, b0 = - GF33M(b)->_0, b1 = GF33M(b)->_1, b2 = GF33M(b)->_2, c0 = - GF33M(c)->_0, c1 = GF33M(c)->_1, c2 = GF33M(c)->_2; - element_sub(c0, a0, b0); - element_sub(c1, a1, b1); - element_sub(c2, a2, b2); -} - -/* $c <- a*b$ */ -static void gf33m_mult(element_t e, element_t a, element_t b) { - element_ptr a0 = GF33M(a)->_0, a1 = GF33M(a)->_1, a2 = GF33M(a)->_2, b0 = - GF33M(b)->_0, b1 = GF33M(b)->_1, b2 = GF33M(b)->_2, e0 = - GF33M(e)->_0, e1 = GF33M(e)->_1, e2 = GF33M(e)->_2; - field_ptr base = BASE(e); - element_t t0, t1, c1, a0b0, a1b1, a2b2; - element_init(t0, base); - element_init(t1, base); - element_init(c1, base); - element_init(a0b0, base); - element_init(a1b1, base); - element_init(a2b2, base); - element_mul(a0b0, a0, b0); - element_mul(a1b1, a1, b1); - element_mul(a2b2, a2, b2); - element_ptr d0 = a0b0; - element_add(t0, a1, a0); - element_add(t1, b1, b0); - element_t d1; - element_init(d1, base); - element_mul(d1, t0, t1); - element_sub(d1, d1, a1b1); - element_sub(d1, d1, a0b0); - element_add(t0, a2, a0); - element_add(t1, b2, b0); - element_t d2; - element_init(d2, base); - element_mul(d2, t0, t1); - element_add(d2, d2, a1b1); - element_sub(d2, d2, a2b2); - element_sub(d2, d2, a0b0); - element_add(t0, a2, a1); - element_add(t1, b2, b1); - element_t d3; - element_init(d3, base); - element_mul(d3, t0, t1); - element_sub(d3, d3, a2b2); - element_sub(d3, d3, a1b1); - element_ptr d4 = a2b2; - element_add(t0, d0, d3); - element_ptr c0 = t0; - element_add(c1, d1, d3); - element_add(c1, c1, d4); - element_add(t1, d2, d4); - element_ptr c2 = t1; - element_set(e0, c0); - element_set(e1, c1); - element_set(e2, c2); - element_clear(t0); - element_clear(t1); - element_clear(c1); - element_clear(a0b0); - element_clear(a1b1); - element_clear(a2b2); - element_clear(d1); - element_clear(d2); - element_clear(d3); -} - -/* $e <- a^3$ */ -static void gf33m_cubic(element_t e, element_t a) { - field_ptr base = BASE(a); - element_ptr a0 = GF33M(a)->_0, a1 = GF33M(a)->_1, a2 = GF33M(a)->_2, e0 = - GF33M(e)->_0, e1 = GF33M(e)->_1, e2 = GF33M(e)->_2; - element_t a03, a13, a23; - element_init(a03, base); - element_init(a13, base); - element_init(a23, base); - element_cubic(a03, a0); - element_cubic(a13, a1); - element_cubic(a23, a2); - element_add(a03, a03, a13); - element_add(a03, a03, a23); - element_ptr c0 = a03; - element_sub(a13, a13, a23); - element_ptr c1 = a13; - element_ptr c2 = a23; - element_set(e0, c0); - element_set(e1, c1); - element_set(e2, c2); - element_clear(a03); - element_clear(a13); - element_clear(a23); -} - -/* $e <- a^{-1}$ */ -static void gf33m_invert(element_t e, element_t a) { - element_ptr a0 = GF33M(a)->_0, a1 = GF33M(a)->_1, a2 = GF33M(a)->_2, e0 = - GF33M(e)->_0, e1 = GF33M(e)->_1, e2 = GF33M(e)->_2; - field_ptr base = BASE(e); - element_t a02, a12, a22; - element_init(a02, base); - element_init(a12, base); - element_init(a22, base); - element_mul(a02, a0, a0); - element_mul(a12, a1, a1); - element_mul(a22, a2, a2); - element_t v0; - element_init(v0, base); - element_sub(v0, a0, a2); // v0 == a0-a2 - element_t delta; - element_init(delta, base); - element_mul(delta, v0, a02); // delta = (a0-a2)*(a0^2), free - element_sub(v0, a1, a0); // v0 == a1-a0 - element_t c0; - element_init(c0, base); - element_mul(c0, v0, a12); // c0 == (a1-a0)*(a1^2) - element_add(delta, delta, c0); // delta = (a0-a2)*(a0^2) + (a1-a0)*(a1^2) - element_sub(v0, a2, v0); // v0 == a2-(a1-a0) = a0-a1+a2 - element_t c1; - element_init(c1, base); - element_mul(c1, v0, a22); // c1 == (a0-a1+a2)*(a2^2) - element_add(delta, delta, c1); // delta = (a0-a2)*(a0^2) + (a1-a0)*(a1^2) + (a0-a1+a2)*(a2^2) - element_invert(delta, delta); // delta = [(a0-a2)*(a0^2) + (a1-a0)*(a1^2) + (a0-a1+a2)*(a2^2)] ^ {-1} - element_add(v0, a02, a22); // v0 == a0^2+a2^2 - element_t c2; - element_init(c2, base); - element_mul(c2, a0, a2); // c2 == a0*a2 - element_sub(c0, v0, c2); // c0 == a0^2+a2^2-a0*a2 - element_add(v0, a1, a2); // v0 == a1+a2 - element_t c3; - element_init(c3, base); - element_mul(c3, a1, v0); // c3 == a1*(a1+a2) - element_sub(c0, c0, c3); // c0 == a0^2+a2^2-a0*a2-a1*(a1+a2) - element_mul(c0, c0, delta); // c0 *= delta - element_mul(c1, a0, a1); // c1 == a0*a1 - element_sub(c1, a22, c1); // c1 == a2^2-a0*a1 - element_mul(c1, c1, delta); // c1 *= delta - element_sub(c2, a12, c2); // c2 == a1^2-a0*a2 - element_sub(c2, c2, a22); // c2 == a1^2-a0*a2-a2^2 - element_mul(c2, c2, delta); // c2 *= delta - element_set(e0, c0); - element_set(e1, c1); - element_set(e2, c2); - element_clear(a02); - element_clear(a12); - element_clear(a22); - element_clear(v0); - element_clear(delta); - element_clear(c0); - element_clear(c1); - element_clear(c2); - element_clear(c3); -} - -void field_clear_gf33m(field_t f) { - UNUSED_VAR(f); -} - -/* initialize the finite field as $base_field[x]/(x^3 - x - 1)$, whose base field is $b$ */ -void field_init_gf33m(field_t f, field_t b) { - field_init(f); - f->data = b; - f->field_clear = field_clear_gf33m; - f->init = gf33m_init; - f->clear = gf33m_clear; - f->set = gf33m_assign; - f->set0 = gf33m_set0; - f->set1 = gf33m_set1; - f->random = gf33m_random; - f->cmp = gf33m_cmp; - f->add = gf33m_add; - f->sub = gf33m_sub; - f->mul = gf33m_mult; - f->cubic = gf33m_cubic; - f->invert = gf33m_invert; - f->item_count = gf33m_item_count; - f->item = gf33m_item; - f->out_str = gf33m_out_str; - mpz_pow_ui(f->order, b->order, 3); - f->name = "GF(3^{3*m})"; -} - |