-/*\r
- *\r
- * bn_mont2.c\r
- *\r
- * Montgomery Modular Arithmetic Functions.\r
- *\r
- * Copyright (C) Lenka Fibikova 2000\r
- *\r
- *\r
- */\r
-\r
-\r
-#include <stdio.h>\r
-#include <stdlib.h>\r
-#include <assert.h>\r
-\r
-#include "bn.h"\r
-#include "bn_modfs.h"\r
-#include "bn_mont2.h"\r
-\r
-#define BN_mask_word(x, m) ((x->d[0]) & (m))\r
-\r
-BN_MONTGOMERY *BN_mont_new()\r
-{\r
- BN_MONTGOMERY *ret;\r
-\r
- ret=(BN_MONTGOMERY *)malloc(sizeof(BN_MONTGOMERY));\r
-\r
- if (ret == NULL) return NULL;\r
-\r
- if ((ret->p = BN_new()) == NULL)\r
- {\r
- free(ret);\r
- return NULL;\r
- }\r
-\r
- return ret;\r
-}\r
-\r
-\r
-void BN_mont_clear_free(BN_MONTGOMERY *mont)\r
-{\r
- if (mont == NULL) return;\r
-\r
- if (mont->p != NULL) BN_clear_free(mont->p);\r
-\r
- mont->p_num_bytes = 0;\r
- mont->R_num_bits = 0;\r
- mont->p_inv_b_neg = 0;\r
-}\r
-\r
-int BN_to_mont(BIGNUM *x, BN_MONTGOMERY *mont, BN_CTX *ctx)\r
-{\r
- assert(x != NULL);\r
-\r
- assert(mont != NULL);\r
- assert(mont->p != NULL);\r
-\r
- assert(ctx != NULL);\r
-\r
- if (!BN_lshift(x, x, mont->R_num_bits)) return 0;\r
- if (!BN_mod(x, x, mont->p, ctx)) return 0;\r
-\r
- return 1;\r
-}\r
-\r
-\r
-static BN_ULONG BN_mont_inv(BIGNUM *a, int e, BN_CTX *ctx)\r
-/* y = a^{-1} (mod 2^e) for an odd number a */\r
-{\r
- BN_ULONG y, exp, mask;\r
- BIGNUM *x, *xy, *x_sh;\r
- int i;\r
-\r
- assert(a != NULL && ctx != NULL);\r
- assert(e <= BN_BITS2);\r
- assert(BN_is_odd(a));\r
- assert(!BN_is_zero(a) && !a->neg);\r
-\r
-\r
- y = 1;\r
- exp = 2;\r
- mask = 3;\r
- if((x = BN_dup(a)) == NULL) return 0;\r
- if(!BN_mask_bits(x, e)) return 0;\r
-\r
- xy = ctx->bn[ctx->tos]; \r
- x_sh = ctx->bn[ctx->tos + 1]; \r
- ctx->tos += 2;\r
-\r
- if (BN_copy(xy, x) == NULL) goto err;\r
- if (!BN_lshift1(x_sh, x)) goto err;\r
-\r
-\r
- for (i = 2; i <= e; i++)\r
- {\r
- if (exp < BN_mask_word(xy, mask))\r
- {\r
- y = y + exp;\r
- if (!BN_add(xy, xy, x_sh)) goto err;\r
- }\r
-\r
- exp <<= 1;\r
- if (!BN_lshift1(x_sh, x_sh)) goto err;\r
- mask <<= 1;\r
- mask++;\r
- }\r
-\r
-\r
-#ifdef TEST\r
- if (xy->d[0] != 1) goto err;\r
-#endif\r
-\r
- if (x != NULL) BN_clear_free(x);\r
- ctx->tos -= 2;\r
- return y;\r
-\r
-\r
-err:\r
- if (x != NULL) BN_clear_free(x);\r
- ctx->tos -= 2;\r
- return 0;\r
-\r
-}\r
-\r
-int BN_mont_set(BIGNUM *p, BN_MONTGOMERY *mont, BN_CTX *ctx)\r
-{\r
- assert(p != NULL && ctx != NULL);\r
- assert(mont != NULL);\r
- assert(mont->p != NULL);\r
- assert(!BN_is_zero(p) && !p->neg);\r
-\r
-\r
- mont->p_num_bytes = p->top;\r
- mont->R_num_bits = (mont->p_num_bytes) * BN_BITS2;\r
-\r
- if (BN_copy(mont->p, p) == NULL);\r
- \r
- mont->p_inv_b_neg = BN_mont_inv(p, BN_BITS2, ctx);\r
- mont->p_inv_b_neg = 0 - mont->p_inv_b_neg;\r
-\r
- return 1;\r
-}\r
-\r
-static int BN_cpy_mul_word(BIGNUM *ret, BIGNUM *a, BN_ULONG w)\r
-/* ret = a * w */\r
-{\r
- if (BN_copy(ret, a) == NULL) return 0;\r
-\r
- if (!BN_mul_word(ret, w)) return 0;\r
-\r
- return 1;\r
-}\r
-\r
-\r
-int BN_mont_red(BIGNUM *y, BN_MONTGOMERY *mont, BN_CTX *ctx)\r
-/* yR^{-1} (mod p) */\r
-{\r
- int i;\r
- BIGNUM *up, *p;\r
- BN_ULONG u;\r
-\r
- assert(y != NULL && mont != NULL && ctx != NULL);\r
- assert(mont->p != NULL);\r
- assert(BN_cmp(y, mont->p) < 0);\r
- assert(!y->neg);\r
-\r
-\r
- if (BN_is_zero(y)) return 1;\r
-\r
- p = mont->p;\r
- up = ctx->bn[ctx->tos]; \r
- ctx->tos += 1;\r
-\r
-\r
- for (i = 0; i < mont->p_num_bytes; i++)\r
- {\r
- u = (y->d[0]) * mont->p_inv_b_neg; /* u = y_0 * p' */\r
-\r
- if (!BN_cpy_mul_word(up, p, u)) goto err; /* up = u * p */\r
-\r
- if (!BN_add(y, y, up)) goto err; \r
-#ifdef TEST\r
- if (y->d[0]) goto err;\r
-#endif\r
- if (!BN_rshift(y, y, BN_BITS2)) goto err; /* y = (y + up)/b */\r
- }\r
-\r
-\r
- if (BN_cmp(y, mont->p) >= 0) \r
- {\r
- if (!BN_sub(y, y, mont->p)) goto err;\r
- }\r
-\r
- ctx->tos -= 1;\r
- return 1;\r
-\r
-err:\r
- ctx->tos -= 1;\r
- return 0;\r
-\r
-}\r
-\r
-\r
-int BN_mont_mod_mul(BIGNUM *r, BIGNUM *x, BIGNUM *y, BN_MONTGOMERY *mont, BN_CTX *ctx)\r
-/* r = x * y mod p */\r
-/* r != x && r! = y !!! */\r
-{\r
- BIGNUM *xiy, *up;\r
- BN_ULONG u;\r
- int i;\r
- \r
-\r
- assert(r != x && r != y);\r
- assert(r != NULL && x != NULL && y != NULL && mont != NULL && ctx != NULL);\r
- assert(mont->p != NULL);\r
- assert(BN_cmp(x, mont->p) < 0);\r
- assert(BN_cmp(y, mont->p) < 0);\r
- assert(!x->neg);\r
- assert(!y->neg);\r
-\r
- if (BN_is_zero(x) || BN_is_zero(y))\r
- {\r
- if (!BN_zero(r)) return 0;\r
- return 1;\r
- }\r
-\r
-\r
-\r
- xiy = ctx->bn[ctx->tos]; \r
- up = ctx->bn[ctx->tos + 1]; \r
- ctx->tos += 2;\r
-\r
- if (!BN_zero(r)) goto err;\r
-\r
- for (i = 0; i < x->top; i++)\r
- {\r
- u = (r->d[0] + x->d[i] * y->d[0]) * mont->p_inv_b_neg;\r
-\r
- if (!BN_cpy_mul_word(xiy, y, x->d[i])) goto err;\r
- if (!BN_cpy_mul_word(up, mont->p, u)) goto err;\r
-\r
- if (!BN_add(r, r, xiy)) goto err;\r
- if (!BN_add(r, r, up)) goto err;\r
-\r
-#ifdef TEST\r
- if (r->d[0]) goto err;\r
-#endif\r
- if (!BN_rshift(r, r, BN_BITS2)) goto err; \r
- }\r
-\r
- for (i = x->top; i < mont->p_num_bytes; i++)\r
- {\r
- u = (r->d[0]) * mont->p_inv_b_neg;\r
-\r
- if (!BN_cpy_mul_word(up, mont->p, u)) goto err;\r
-\r
- if (!BN_add(r, r, up)) goto err;\r
-\r
-#ifdef TEST\r
- if (r->d[0]) goto err;\r
-#endif\r
- if (!BN_rshift(r, r, BN_BITS2)) goto err; \r
- }\r
-\r
-\r
- if (BN_cmp(r, mont->p) >= 0) \r
- {\r
- if (!BN_sub(r, r, mont->p)) goto err;\r
- }\r
-\r
-\r
- ctx->tos -= 2;\r
- return 1;\r
-\r
-err:\r
- ctx->tos -= 2;\r
- return 0;\r
-}\r
-\r
-int BN_mont_mod_add(BIGNUM *r, BIGNUM *x, BIGNUM *y, BN_MONTGOMERY *mont)\r
-{\r
- assert(r != NULL && x != NULL && y != NULL && mont != NULL);\r
- assert(mont->p != NULL);\r
- assert(BN_cmp(x, mont->p) < 0);\r
- assert(BN_cmp(y, mont->p) < 0);\r
- assert(!x->neg);\r
- assert(!y->neg);\r
-\r
- if (!BN_add(r, x, y)) return 0;\r
- if (BN_cmp(r, mont->p) >= 0) \r
- {\r
- if (!BN_sub(r, r, mont->p)) return 0;\r
- }\r
-\r
- return 1;\r
-}\r
-\r
-\r
-int BN_mont_mod_sub(BIGNUM *r, BIGNUM *x, BIGNUM *y, BN_MONTGOMERY *mont)\r
-{\r
- assert(r != NULL && x != NULL && y != NULL && mont != NULL);\r
- assert(mont->p != NULL);\r
- assert(BN_cmp(x, mont->p) < 0);\r
- assert(BN_cmp(y, mont->p) < 0);\r
- assert(!x->neg);\r
- assert(!y->neg);\r
-\r
- if (!BN_sub(r, x, y)) return 0;\r
- if (r->neg) \r
- {\r
- if (!BN_add(r, r, mont->p)) return 0;\r
- }\r
-\r
- return 1;\r
-}\r
-\r
-int BN_mont_mod_lshift1(BIGNUM *r, BIGNUM *x, BN_MONTGOMERY *mont)\r
-{\r
- assert(r != NULL && x != NULL && mont != NULL);\r
- assert(mont->p != NULL);\r
- assert(BN_cmp(x, mont->p) < 0);\r
- assert(!x->neg);\r
-\r
- if (!BN_lshift1(r, x)) return 0;\r
-\r
- if (BN_cmp(r, mont->p) >= 0) \r
- {\r
- if (!BN_sub(r, r, mont->p)) return 0;\r
- }\r
-\r
- return 1;\r
-}\r
-\r
-int BN_mont_mod_lshift(BIGNUM *r, BIGNUM *x, int n, BN_MONTGOMERY *mont)\r
-{\r
- int sh_nb;\r
-\r
- assert(r != NULL && x != NULL && mont != NULL);\r
- assert(mont->p != NULL);\r
- assert(BN_cmp(x, mont->p) < 0);\r
- assert(!x->neg);\r
- assert(n > 0);\r
-\r
- if (r != x)\r
- {\r
- if (BN_copy(r, x) == NULL) return 0;\r
- }\r
-\r
- while (n)\r
- {\r
- sh_nb = BN_num_bits(mont->p) - BN_num_bits(r);\r
- if (sh_nb > n) sh_nb = n;\r
-\r
- if (sh_nb)\r
- {\r
- if(!BN_lshift(r, r, sh_nb)) return 0;\r
- }\r
- else \r
- {\r
- sh_nb = 1;\r
- if (!BN_lshift1(r, r)) return 0;\r
- }\r
-\r
- if (BN_cmp(r, mont->p) >= 0) \r
- {\r
- if (!BN_sub(r, r, mont->p)) return 0;\r
- }\r
-\r
- n -= sh_nb;\r
- }\r
-\r
- return 1;\r
-}\r
+/*
+ *
+ * bn_mont2.c
+ *
+ * Montgomery Modular Arithmetic Functions.
+ *
+ * Copyright (C) Lenka Fibikova 2000
+ *
+ *
+ */
+
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <assert.h>
+
+#include "bn_lcl.h"
+#include "bn_mont2.h"
+
+#define BN_mask_word(x, m) ((x->d[0]) & (m))
+
+BN_MONTGOMERY *BN_mont_new()
+ {
+ BN_MONTGOMERY *ret;
+
+ ret=(BN_MONTGOMERY *)malloc(sizeof(BN_MONTGOMERY));
+
+ if (ret == NULL) return NULL;
+
+ if ((ret->p = BN_new()) == NULL)
+ {
+ free(ret);
+ return NULL;
+ }
+
+ return ret;
+ }
+
+
+void BN_mont_clear_free(BN_MONTGOMERY *mont)
+ {
+ if (mont == NULL) return;
+
+ if (mont->p != NULL) BN_clear_free(mont->p);
+
+ mont->p_num_bytes = 0;
+ mont->R_num_bits = 0;
+ mont->p_inv_b_neg = 0;
+ }
+
+
+int BN_to_mont(BIGNUM *x, BN_MONTGOMERY *mont, BN_CTX *ctx)
+ {
+ assert(x != NULL);
+
+ assert(mont != NULL);
+ assert(mont->p != NULL);
+
+ assert(ctx != NULL);
+
+ if (!BN_lshift(x, x, mont->R_num_bits)) return 0;
+ if (!BN_mod(x, x, mont->p, ctx)) return 0;
+
+ return 1;
+ }
+
+
+static BN_ULONG BN_mont_inv(BIGNUM *a, int e, BN_CTX *ctx)
+/* y = a^{-1} (mod 2^e) for an odd number a */
+ {
+ BN_ULONG y, exp, mask;
+ BIGNUM *x, *xy, *x_sh;
+ int i;
+
+ assert(a != NULL && ctx != NULL);
+ assert(e <= BN_BITS2);
+ assert(BN_is_odd(a));
+ assert(!BN_is_zero(a) && !a->neg);
+
+
+ y = 1;
+ exp = 2;
+ mask = 3;
+ if((x = BN_dup(a)) == NULL) return 0;
+ if (x->top > e/BN_BITS2)
+ if(!BN_mask_bits(x, e)) return 0;
+
+ BN_CTX_start(ctx);
+ xy = BN_CTX_get(ctx);
+ x_sh = BN_CTX_get(ctx);
+ if (x_sh == NULL) goto err;
+
+ if (BN_copy(xy, x) == NULL) goto err;
+ if (!BN_lshift1(x_sh, x)) goto err;
+
+
+ for (i = 2; i <= e; i++)
+ {
+ if (exp < BN_mask_word(xy, mask))
+ {
+ y = y + exp;
+ if (!BN_add(xy, xy, x_sh)) goto err;
+ }
+
+ exp <<= 1;
+ if (!BN_lshift1(x_sh, x_sh)) goto err;
+ mask <<= 1;
+ mask++;
+ }
+
+
+#ifdef TEST
+ if (xy->d[0] != 1) goto err;
+#endif
+
+ if (x != NULL) BN_clear_free(x);
+ BN_CTX_end(ctx);
+ return y;
+
+
+err:
+ if (x != NULL) BN_clear_free(x);
+ BN_CTX_end(ctx);
+ return 0;
+ }
+
+
+int BN_mont_set(BIGNUM *p, BN_MONTGOMERY *mont, BN_CTX *ctx)
+ {
+ assert(p != NULL && ctx != NULL);
+ assert(mont != NULL);
+ assert(mont->p != NULL);
+ assert(!BN_is_zero(p) && !p->neg);
+
+
+ mont->p_num_bytes = p->top;
+ mont->R_num_bits = (mont->p_num_bytes) * BN_BITS2;
+
+ if (BN_copy(mont->p, p) == NULL);
+
+ mont->p_inv_b_neg = BN_mont_inv(p, BN_BITS2, ctx);
+ if (!mont->p_inv_b_neg) return 0;
+ mont->p_inv_b_neg = 0 - mont->p_inv_b_neg;
+
+ return 1;
+ }
+
+
+#ifdef BN_LLONG
+#define cpy_mul_add(r, b, a, w, c) { \
+ BN_ULLONG t; \
+ t = (BN_ULLONG)w * (a) + (b) + (c); \
+ (r)= Lw(t); \
+ (c)= Hw(t); \
+ }
+
+BN_ULONG BN_mul_add_rshift(BN_ULONG *r, BN_ULONG *a, int num, BN_ULONG w)
+/* r = (r + a * w) >> BN_BITS2 */
+ {
+ BN_ULONG c = 0;
+
+ mul_add(r[0], a[0], w, c);
+ if (--num == 0) return c;
+ a++;
+
+ for (;;)
+ {
+ cpy_mul_add(r[0], r[1], a[0], w, c);
+ if (--num == 0) break;
+ cpy_mul_add(r[1], r[2], a[1], w, c);
+ if (--num == 0) break;
+ cpy_mul_add(r[2], r[3], a[2], w, c);
+ if (--num == 0) break;
+ cpy_mul_add(r[3], r[4], a[3], w, c);
+ if (--num == 0) break;
+ a += 4;
+ r += 4;
+ }
+
+ return c;
+ }
+#else
+
+#define cpy_mul_add(r, b, a, bl, bh, c) { \
+ BN_ULONG l,h; \
+ \
+ h=(a); \
+ l=LBITS(h); \
+ h=HBITS(h); \
+ mul64(l,h,(bl),(bh)); \
+ \
+ /* non-multiply part */ \
+ l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
+ (c)=(b); \
+ l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
+ (c)=h&BN_MASK2; \
+ (r)=l; \
+ }
+
+static BN_ULONG BN_mul_add_rshift(BN_ULONG *r, BN_ULONG *a, int num, BN_ULONG w)
+/* ret = (ret + a * w) << shift * BN_BITS2 */
+ {
+ BN_ULONG c = 0;
+ BN_ULONG bl, bh;
+
+ bl = LBITS(w);
+ bh = HBITS(w);
+
+ mul_add(r[0], a[0], bl, bh, c);
+ if (--num == 0) return c;
+ a++;
+
+ for (;;)
+ {
+ cpy_mul_add(r[0], r[1], a[0], bl, bh, c);
+ if (--num == 0) break;
+ cpy_mul_add(r[1], r[2], a[1], bl, bh, c);
+ if (--num == 0) break;
+ cpy_mul_add(r[2], r[3], a[2], bl, bh, c);
+ if (--num == 0) break;
+ cpy_mul_add(r[3], r[4], a[3], bl, bh, c);
+ if (--num == 0) break;
+ a += 4;
+ r += 4;
+ }
+ return c;
+ }
+#endif /* BN_LLONG */
+
+
+
+int BN_mont_red(BIGNUM *y, BN_MONTGOMERY *mont)
+/* yR^{-1} (mod p) */
+ {
+ BIGNUM *p;
+ BN_ULONG c;
+ int i, max;
+
+ assert(y != NULL && mont != NULL);
+ assert(mont->p != NULL);
+ assert(BN_cmp(y, mont->p) < 0);
+ assert(!y->neg);
+
+
+ if (BN_is_zero(y)) return 1;
+
+ p = mont->p;
+ max = mont->p_num_bytes;
+
+ if (bn_wexpand(y, max) == NULL) return 0;
+ for (i = y->top; i < max; i++) y->d[i] = 0;
+ y->top = max;
+
+ /* r = [r + (y_0 * p') * p] / b */
+ for (i = 0; i < max; i++)
+ {
+ c = BN_mul_add_rshift(y->d, p->d, max, ((y->d[0]) * mont->p_inv_b_neg) & BN_MASK2);
+ y->d[max - 1] = c;
+ }
+
+ while (y->d[y->top - 1] == 0) y->top--;
+
+ if (BN_cmp(y, p) >= 0)
+ {
+ if (!BN_sub(y, y, p)) return 0;
+ }
+
+ return 1;
+ }
+
+
+int BN_mont_mod_mul(BIGNUM *r_, BIGNUM *x, BIGNUM *y, BN_MONTGOMERY *mont, BN_CTX *ctx)
+/* r = x * y mod p */
+/* r != x && r! = y !!! */
+ {
+ BN_ULONG c;
+ BIGNUM *p;
+ int i, j, max;
+ BIGNUM *r;
+
+ assert(r_!= NULL && x != NULL && y != NULL && mont != NULL);
+ assert(mont->p != NULL);
+ assert(BN_cmp(x, mont->p) < 0);
+ assert(BN_cmp(y, mont->p) < 0);
+ assert(!x->neg);
+ assert(!y->neg);
+
+ if (BN_is_zero(x) || BN_is_zero(y))
+ {
+ if (!BN_zero(r)) return 0;
+ return 1;
+ }
+
+ if (r_ == x || r_ == y)
+ {
+ BN_CTX_start(ctx);
+ r = BN_CTX_get(ctx);
+ }
+ else
+ r = r_;
+
+ p = mont->p;
+ max = mont->p_num_bytes;
+
+ /* for multiplication we need at most max + 2 words
+ the last one --- max + 3 --- is only as a backstop
+ for incorrect input
+ */
+ if (bn_wexpand(r, max + 3) == NULL) goto err;
+ for (i = 0; i < max + 3; i++) r->d[i] = 0;
+ r->top = max + 2;
+
+ for (i = 0; i < x->top; i++)
+ {
+ /* r = r + (r_0 + x_i * y_0) * p' * p */
+ c = bn_mul_add_words(r->d, p->d, max, \
+ ((r->d[0] + x->d[i] * y->d[0]) * mont->p_inv_b_neg) & BN_MASK2);
+ if (c)
+ {
+ if (((r->d[max] += c) & BN_MASK2) < c)
+ if (((r->d[max + 1] ++) & BN_MASK2) == 0) goto err;
+ }
+
+ /* r = (r + x_i * y) / b */
+ c = BN_mul_add_rshift(r->d, y->d, y->top, x->d[i]);
+ for(j = y->top; j <= max + 1; j++) r->d[j - 1] = r->d[j];
+ if (c)
+ {
+ if (((r->d[y->top - 1] += c) & BN_MASK2) < c)
+ {
+ j = y->top;
+ while (((++ (r->d[j]) ) & BN_MASK2) == 0)
+ j++;
+ if (j > max) goto err;
+ }
+ }
+ r->d[max + 1] = 0;
+ }
+
+ for (i = x->top; i < max; i++)
+ {
+ /* r = (r + r_0 * p' * p) / b */
+ c = BN_mul_add_rshift(r->d, p->d, max, ((r->d[0]) * mont->p_inv_b_neg) & BN_MASK2);
+ j = max - 1;
+ r->d[j] = c + r->d[max];
+ if (r->d[j++] < c) r->d[j] = r->d[++j] + 1;
+ else r->d[j] = r->d[++j];
+ r->d[max + 1] = 0;
+ }
+
+ while (r->d[r->top - 1] == 0) r->top--;
+
+ if (BN_cmp(r, mont->p) >= 0)
+ {
+ if (!BN_sub(r, r, mont->p)) goto err;
+ }
+
+ if (r != r_)
+ {
+ if (!BN_copy(r_, r)) goto err;
+ BN_CTX_end(ctx);
+ }
+
+ return 1;
+
+ err:
+ if (r != r_)
+ BN_CTX_end(ctx);
+ return 0;
+ }
projects / openssl.git / blobdiff