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1 /**************************************************************
2 *
3 * curvegen.c
4 *
5 * CM curve generator.
6 *
7 * Compile with:
8 *
9 * % cc -O curvegen.c tools.c giants.c ellproj.c -lm -o curvegen
10 *
11 * Updates:
12 * 27 Sep 98 REC - Creation
13 *
14 *
15 * c. 1998 Perfectly Scientific, Inc.
16 * All Rights Reserved.
17 *
18 *
19 *************************************************************/
20
21 /* include files */
22
23 #include <stdio.h>
24 #include <math.h>
25 #include <stdlib.h>
26 #include <time.h>
27 #ifdef _WIN32
28
29 #include <process.h>
30
31 #endif
32
33 #include <string.h>
34 #include "giants.h"
35 #include "tools.h"
36
37 #define DCOUNT 27
38
39 int disc12[DCOUNT] = {-3, -4, -7, -8, -11, -19, -43, -67, -163, -15, -20, -24, -35, -40, -51, -52, -88, -91, -115, -123, -148, -187, -232, -235, -267, -403, -427}; /* All discriminants of class number 1,2. */
40
41 /**************************************************************
42 *
43 * Main Function
44 *
45 **************************************************************/
46
47 #define CM_SHORTS 4096
48
49 main(int argc, char **argv) {
50 giant p = newgiant(CM_SHORTS);
51 giant u = newgiant(CM_SHORTS);
52 giant v = newgiant(CM_SHORTS);
53 giant g[6];
54 giant plus_order = newgiant(CM_SHORTS);
55 giant minus_order = newgiant(CM_SHORTS);
56 giant a = newgiant(CM_SHORTS);
57 giant b = newgiant(CM_SHORTS);
58 int d, dc, olen, k;
59
60 init_tools(CM_SHORTS); /* Basic algorithms. */
61 printf("Give base prime p:\n"); fflush(stdout);
62 gin(p);
63 for(dc=0; dc < 6; dc++) g[dc] = newgiant(CM_SHORTS);
64 for(dc = 0; dc < DCOUNT; dc++) {
65 d = disc12[dc];
66 /* Next, seek representation 4N = u^2 + |d| v^2. */
67 if(cornacchia4(p, d, u, v) == 0) continue;
68 /* Here, (u,v) give the quadratic representation of 4p. */
69 printf("D: %d\n", d); fflush(stdout);
70 gtog(u, g[0]);
71 switch(d) {
72 case -3: olen = 3; /* Six orders: p + 1 +- g[0,1,2]. */
73 gtog(u, g[1]); gtog(v, g[2]);
74 addg(g[2], g[2]); addg(v, g[2]); /* g[2] := 3v. */
75 addg(g[2], g[1]); gshiftright(1, g[1]); /* g[1] = (u + 3v)/2. */
76 subg(u, g[2]); gshiftright(1, g[2]); absg(g[2]); /* g[2] = |u-3v|/2. */
77 break;
78 case -4: olen = 2; /* Four orders: p + 1 +- g[0,1]. */
79 gtog(v, g[1]); addg(g[1], g[1]); /* g[1] = 2v. */
80 break;
81 default: olen = 1; /* Two orders: p + 1 +- g[0]. */
82 }
83 for(k=0; k < olen; k++) {
84 gtog(p, plus_order); iaddg(1, plus_order);
85 gtog(p, minus_order); iaddg(1, minus_order);
86 addg(g[k], plus_order);
87 subg(g[k], minus_order);
88 printf("curve orders: \n");
89 printf("(%d) ", prime_probable(plus_order));
90 gout(plus_order);
91 printf("(%d) ", prime_probable(minus_order));
92 gout(minus_order);
93 }
94 }
95 }
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