Diff: math/numtheory/fp_invmod.c

Revision:

4:cbaf466d717d

Parent:

0:35aa5be3b78d

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/math/numtheory/fp_invmod.c	Tue Jun 10 14:23:09 2014 +0000
@@ -0,0 +1,207 @@
+/* TomsFastMath, a fast ISO C bignum library.
+ * 
+ * This project is meant to fill in where LibTomMath
+ * falls short.  That is speed ;-)
+ *
+ * This project is public domain and free for all purposes.
+ * 
+ * Tom St Denis, tomstdenis@gmail.com
+ */
+#include <tfm.h>
+
+static int fp_invmod_slow (fp_int * a, fp_int * b, fp_int * c)
+{
+  fp_int  x, y, u, v, A, B, C, D;
+  int     res;
+
+  /* b cannot be negative */
+  if (b->sign == FP_NEG || fp_iszero(b) == 1) {
+    return FP_VAL;
+  }
+
+  /* init temps */
+  fp_init(&x);    fp_init(&y);
+  fp_init(&u);    fp_init(&v);
+  fp_init(&A);    fp_init(&B);
+  fp_init(&C);    fp_init(&D);
+
+  /* x = a, y = b */
+  if ((res = fp_mod(a, b, &x)) != FP_OKAY) {
+      return res;
+  }
+  fp_copy(b, &y);
+
+  /* 2. [modified] if x,y are both even then return an error! */
+  if (fp_iseven (&x) == 1 && fp_iseven (&y) == 1) {
+    return FP_VAL;
+  }
+
+  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
+  fp_copy (&x, &u);
+  fp_copy (&y, &v);
+  fp_set (&A, 1);
+  fp_set (&D, 1);
+
+top:
+  /* 4.  while u is even do */
+  while (fp_iseven (&u) == 1) {
+    /* 4.1 u = u/2 */
+    fp_div_2 (&u, &u);
+
+    /* 4.2 if A or B is odd then */
+    if (fp_isodd (&A) == 1 || fp_isodd (&B) == 1) {
+      /* A = (A+y)/2, B = (B-x)/2 */
+      fp_add (&A, &y, &A);
+      fp_sub (&B, &x, &B);
+    }
+    /* A = A/2, B = B/2 */
+    fp_div_2 (&A, &A);
+    fp_div_2 (&B, &B);
+  }
+
+  /* 5.  while v is even do */
+  while (fp_iseven (&v) == 1) {
+    /* 5.1 v = v/2 */
+    fp_div_2 (&v, &v);
+
+    /* 5.2 if C or D is odd then */
+    if (fp_isodd (&C) == 1 || fp_isodd (&D) == 1) {
+      /* C = (C+y)/2, D = (D-x)/2 */
+      fp_add (&C, &y, &C);
+      fp_sub (&D, &x, &D);
+    }
+    /* C = C/2, D = D/2 */
+    fp_div_2 (&C, &C);
+    fp_div_2 (&D, &D);
+  }
+
+  /* 6.  if u >= v then */
+  if (fp_cmp (&u, &v) != FP_LT) {
+    /* u = u - v, A = A - C, B = B - D */
+    fp_sub (&u, &v, &u);
+    fp_sub (&A, &C, &A);
+    fp_sub (&B, &D, &B);
+  } else {
+    /* v - v - u, C = C - A, D = D - B */
+    fp_sub (&v, &u, &v);
+    fp_sub (&C, &A, &C);
+    fp_sub (&D, &B, &D);
+  }
+
+  /* if not zero goto step 4 */
+  if (fp_iszero (&u) == 0)
+    goto top;
+
+  /* now a = C, b = D, gcd == g*v */
+
+  /* if v != 1 then there is no inverse */
+  if (fp_cmp_d (&v, 1) != FP_EQ) {
+    return FP_VAL;
+  }
+
+  /* if its too low */
+  while (fp_cmp_d(&C, 0) == FP_LT) {
+      fp_add(&C, b, &C);
+  }
+  
+  /* too big */
+  while (fp_cmp_mag(&C, b) != FP_LT) {
+      fp_sub(&C, b, &C);
+  }
+  
+  /* C is now the inverse */
+  fp_copy(&C, c);
+  return FP_OKAY;
+}
+
+/* c = 1/a (mod b) for odd b only */
+int fp_invmod(fp_int *a, fp_int *b, fp_int *c)
+{
+  fp_int  x, y, u, v, B, D;
+  int     neg;
+
+  /* 2. [modified] b must be odd   */
+  if (fp_iseven (b) == FP_YES) {
+    return fp_invmod_slow(a,b,c);
+  }
+
+  /* init all our temps */
+  fp_init(&x);  fp_init(&y);
+  fp_init(&u);  fp_init(&v);
+  fp_init(&B);  fp_init(&D);
+
+  /* x == modulus, y == value to invert */
+  fp_copy(b, &x);
+
+  /* we need y = |a| */
+  fp_abs(a, &y);
+
+  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
+  fp_copy(&x, &u);
+  fp_copy(&y, &v);
+  fp_set (&D, 1);
+
+top:
+  /* 4.  while u is even do */
+  while (fp_iseven (&u) == FP_YES) {
+    /* 4.1 u = u/2 */
+    fp_div_2 (&u, &u);
+
+    /* 4.2 if B is odd then */
+    if (fp_isodd (&B) == FP_YES) {
+      fp_sub (&B, &x, &B);
+    }
+    /* B = B/2 */
+    fp_div_2 (&B, &B);
+  }
+
+  /* 5.  while v is even do */
+  while (fp_iseven (&v) == FP_YES) {
+    /* 5.1 v = v/2 */
+    fp_div_2 (&v, &v);
+
+    /* 5.2 if D is odd then */
+    if (fp_isodd (&D) == FP_YES) {
+      /* D = (D-x)/2 */
+      fp_sub (&D, &x, &D);
+    }
+    /* D = D/2 */
+    fp_div_2 (&D, &D);
+  }
+
+  /* 6.  if u >= v then */
+  if (fp_cmp (&u, &v) != FP_LT) {
+    /* u = u - v, B = B - D */
+    fp_sub (&u, &v, &u);
+    fp_sub (&B, &D, &B);
+  } else {
+    /* v - v - u, D = D - B */
+    fp_sub (&v, &u, &v);
+    fp_sub (&D, &B, &D);
+  }
+
+  /* if not zero goto step 4 */
+  if (fp_iszero (&u) == FP_NO) {
+    goto top;
+  }
+
+  /* now a = C, b = D, gcd == g*v */
+
+  /* if v != 1 then there is no inverse */
+  if (fp_cmp_d (&v, 1) != FP_EQ) {
+    return FP_VAL;
+  }
+
+  /* b is now the inverse */
+  neg = a->sign;
+  while (D.sign == FP_NEG) {
+    fp_add (&D, b, &D);
+  }
+  fp_copy (&D, c);
+  c->sign = neg;
+  return FP_OKAY;
+}
+
+/* $Source: /cvs/libtom/tomsfastmath/src/numtheory/fp_invmod.c,v $ */
+/* $Revision: 1.1 $ */
+/* $Date: 2007/01/24 21:25:19 $ */