--- /dev/null
+/* -*-c-*-
+ *
+ * $Id: share.c,v 1.1 2000/06/17 12:09:38 mdw Exp $
+ *
+ * Shamir's secret sharing
+ *
+ * (c) 2000 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------*
+ *
+ * This file is part of Catacomb.
+ *
+ * Catacomb is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * Catacomb is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb; if not, write to the Free
+ * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+/*----- Revision history --------------------------------------------------*
+ *
+ * $Log: share.c,v $
+ * Revision 1.1 2000/06/17 12:09:38 mdw
+ * Shamir's secret sharing system.
+ *
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include "grand.h"
+#include "mp.h"
+#include "mpint.h"
+#include "mpmont.h"
+#include "mprand.h"
+#include "pgen.h"
+#include "rabin.h"
+#include "share.h"
+
+/*----- Main code ---------------------------------------------------------*/
+
+/* --- @share_create@ --- *
+ *
+ * Arguments: @share *s@ = pointer to share context to initialize
+ * @unsigned t, n@ = threshold parameters for the system
+ *
+ * Returns: ---
+ *
+ * Use: Initializes a sharing context.
+ */
+
+void share_create(share *s, unsigned t, unsigned n)
+{
+ s->t = t;
+ s->n = n;
+ s->i = 0;
+ s->s = 0;
+ s->p = 0;
+ s->v = 0;
+}
+
+/* --- @share_destroy@ --- *
+ *
+ * Arguments: @share *s@ = pointer to share context to destroy
+ *
+ * Returns: ---
+ *
+ * Use: Disposes of a sharing context. All memory is freed, all
+ * integers are dropped.
+ */
+
+void share_destroy(share *s)
+{
+ unsigned n;
+ unsigned i;
+
+ /* --- Dispose of the share vector --- */
+
+ if (s->v) {
+ if (s->i)
+ n = s->i;
+ else if (s->n)
+ n = s->n;
+ else
+ n = s->t;
+ for (i = 0; i < n; i++) {
+ if (s->v[i].y)
+ mp_drop(s->v[i].y);
+ }
+ xfree(s->v);
+ }
+
+ /* --- Other stuff --- */
+
+ if (s->p)
+ mp_drop(s->p);
+ if (s->s)
+ mp_drop(s->s);
+}
+
+/* --- @share_mkshares@ --- *
+ *
+ * Arguments: @share *s@ = pointer to share context to fill in
+ * @grand *r@ = pointer to random number source
+ *
+ * Returns: ---
+ *
+ * Use: Generates @c->n@ secret shares, such that any @c->t@ of them
+ * may be used to recover the secret.
+ *
+ * The context structure is expected to be mostly filled in. In
+ * particular, @t@, @n@ and @s@ must be initialized. If @p@ is
+ * zero, a prime number of appropriate size is generated
+ * automatically. If @v@ is zero, a vector of appropriate size
+ * is allocated. You should use the macro @SHARE_INIT@ or
+ * @share_create@ to construct sharing contexts.
+ */
+
+void share_mkshares(share *s, grand *r)
+{
+ mp **v;
+ unsigned i;
+ mp *u;
+ mpmont mm;
+
+ /* --- If there's no prime, construct one --- */
+
+ if (!s->p) {
+ pgen_filterctx pf;
+ rabin pr;
+ mp *p;
+ unsigned bits = (mp_octets(s->s) + 1) * 8;
+
+ pf.step = 2;
+ p = mprand(MP_NEW, bits, r, 1);
+ s->p = pgen("p", p, p, 0, 0, 0, pgen_filter, &pf,
+ rabin_iters(bits), pgen_test, &pr);
+ }
+
+ /* --- Construct the coefficients --- */
+
+ mpmont_create(&mm, s->p);
+ v = xmalloc(s->t * sizeof(mp *));
+ for (i = 0; i < s->t - 1; i++)
+ v[i] = mprand_range(MP_NEW, s->p, r, 0);
+ v[s->t - 1] = mpmont_mul(&mm, MP_NEW, s->s, mm.r2);
+
+ /* --- Construct the shares --- */
+
+ if (!s->v)
+ s->v = xmalloc(s->n * sizeof(share_pt));
+
+ u = mp_copy(mm.r);
+ for (i = 0; i < s->n; i++) {
+ mp *m = MP_ZERO;
+ unsigned j;
+
+ /* --- Evaluate the polynomial at %$x = i + 1$% --- */
+
+ for (j = 0; j < s->t; j++) {
+ m = mpmont_mul(&mm, m, m, u);
+ m = mp_add(m, m, v[j]);
+ if (MP_CMP(m, >=, s->p))
+ m = mp_sub(m, m, s->p);
+ }
+
+ /* --- Reduce the final result --- */
+
+ s->v[i].x = i;
+ s->v[i].y = mpmont_reduce(&mm, m, m);
+
+ /* --- Compute the next point in Montgomery space --- */
+
+ u = mp_add(u, u, mm.r);
+ if (MP_CMP(u, >=, s->p))
+ u = mp_sub(u, u, s->p);
+ }
+ mpmont_destroy(&mm);
+
+ /* --- Dispose of various bits of old rubbish --- */
+
+ for (i = 0; i < s->t; i++)
+ mp_drop(v[i]);
+ mp_drop(u);
+ xfree(v);
+}
+
+/* --- @share_add@ --- *
+ *
+ * Arguments: @share *s@ = pointer to sharing context
+ * @unsigned x@ = which share number this is
+ * @mp *y@ = the share value
+ *
+ * Returns: Number of shares required before recovery may be performed.
+ *
+ * Use: Adds a share to the context. The context must have been
+ * initialized with the correct prime @p@ and threshold @t@.
+ */
+
+unsigned share_add(share *s, unsigned x, mp *y)
+{
+ /* --- If no vector has been allocated, create one --- */
+
+ if (!s->v) {
+ s->v = xmalloc(s->t * sizeof(share_pt));
+ s->i = 0;
+ }
+
+ assert(((void)"Share context is full", s->i < s->t));
+
+ /* --- Store the share in the vector --- */
+
+ s->v[s->i].x = x;
+ s->v[s->i].y = mp_copy(y);
+ s->i++;
+
+ /* --- Done --- */
+
+ return (s->t - s->i);
+}
+
+/* --- @share_combine@ --- *
+ *
+ * Arguments: @share *s@ = pointer to share context
+ *
+ * Returns: The secret, as a multiprecision integer.
+ *
+ * Use: Reconstructs a secret, given enough shares.
+ */
+
+mp *share_combine(share *s)
+{
+ mp *a = MP_ZERO;
+ mpmont mm;
+ unsigned i, j;
+ mp *ii = MP_NEW, *jj = MP_NEW;
+ mp *m = MP_NEW;
+
+ /* --- Sanity checking --- */
+
+ assert(((void)"Not enough shares yet", s->i == s->t));
+
+ /* --- Initialization --- */
+
+ mpmont_create(&mm, s->p);
+
+ /* --- Grind through the shares --- */
+
+ for (i = 0; i < s->t; i++) {
+ mp *c = mp_copy(mm.r);
+
+ ii = mp_fromuint(ii, s->v[i].x + 1);
+ for (j = 0; j < s->t; j++) {
+ if (i == j)
+ continue;
+ jj = mp_fromuint(jj, s->v[j].x + 1);
+ if (s->v[j].x >= s->v[i].x)
+ m = mp_sub(m, jj, ii);
+ else {
+ m = mp_sub(m, ii, jj);
+ m = mp_sub(m, s->p, m);
+ }
+ jj = mpmont_mul(&mm, jj, jj, mm.r2);
+ mp_gcd(0, 0, &m, s->p, m);
+ m = mpmont_mul(&mm, m, m, mm.r2);
+ m = mpmont_mul(&mm, m, m, jj);
+ c = mpmont_mul(&mm, c, c, m);
+ }
+ m = mpmont_mul(&mm, m, s->v[i].y, mm.r2);
+ c = mpmont_mul(&mm, c, c, m);
+ a = mp_add(a, a, c);
+ mp_drop(c);
+ }
+
+ a = mpmont_reduce(&mm, a, a);
+ s->s = mp_copy(a);
+ mp_drop(ii);
+ if (jj)
+ mp_drop(jj);
+ mp_drop(m);
+ mpmont_destroy(&mm);
+ return (a);
+}
+
+/*----- Test rig ----------------------------------------------------------*/
+
+#ifdef TEST_RIG
+
+#include "fibrand.h"
+
+static int verify(grand *r)
+{
+ unsigned n = r->ops->range(r, 16) + 8;
+ unsigned t = r->ops->range(r, n - 1) + 1;
+ unsigned len = r->ops->range(r, 160);
+
+ share_pt *v = xmalloc(t * sizeof(share_pt));
+ unsigned *p = xmalloc(n * sizeof(unsigned));
+ mp *sec = mprand(MP_NEW, len, r, 0);
+ share s;
+ mp *pp;
+ mp *ss;
+ unsigned i;
+
+ int ok = 1;
+
+ for (i = 0; i < n; i++)
+ p[i] = i;
+ for (i = 0; i < t; i++) {
+ unsigned long j = r->ops->range(r, n - i);
+ unsigned x = p[i];
+ p[i] = p[i + j];
+ p[i + j] = x;
+ }
+
+ share_create(&s, t, n);
+ s.s = mp_copy(sec);
+ share_mkshares(&s, r);
+ for (i = 0; i < t; i++) {
+ v[i].x = s.v[p[i]].x;
+ v[i].y = mp_copy(s.v[p[i]].y);
+ }
+ pp = mp_copy(s.p);
+ share_destroy(&s);
+
+ assert(mparena_count(MPARENA_GLOBAL) == t + 2);
+
+ share_create(&s, t, n);
+ s.p = pp;
+ for (i = 0; i < t; i++) {
+ share_add(&s, v[i].x, v[i].y);
+ }
+ ss = share_combine(&s);
+ share_destroy(&s);
+
+ if (MP_CMP(sec, !=, ss)) {
+ ok = 0;
+ fprintf(stderr, "\nbad recombination of shares\n");
+ };
+
+ mp_drop(sec);
+ mp_drop(ss);
+
+ for (i = 0; i < t; i++)
+ mp_drop(v[i].y);
+
+ xfree(v);
+ xfree(p);
+
+ assert(mparena_count(MPARENA_GLOBAL) == 0);
+ return (ok);
+}
+
+int main(void)
+{
+ grand *r = fibrand_create(0);
+ unsigned i;
+ int ok = 1;
+
+ fputs("share: ", stdout);
+ for (i = 0; i < 40; i++) {
+ if (!verify(r))
+ ok = 0;
+ fputc('.', stdout);
+ fflush(stdout);
+ }
+
+ if (ok)
+ fputs(" ok\n", stdout);
+ else
+ fputs(" failed\n", stdout);
+ return (ok ? EXIT_SUCCESS : EXIT_FAILURE);
+}
+
+#endif
+
+/*----- That's all, folks -------------------------------------------------*/
--- /dev/null
+/* -*-c-*-
+ *
+ * $Id: share.h,v 1.1 2000/06/17 12:09:38 mdw Exp $
+ *
+ * Shamir's secret sharing
+ *
+ * (c) 2000 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------*
+ *
+ * This file is part of Catacomb.
+ *
+ * Catacomb is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * Catacomb is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb; if not, write to the Free
+ * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+/*----- Revision history --------------------------------------------------*
+ *
+ * $Log: share.h,v $
+ * Revision 1.1 2000/06/17 12:09:38 mdw
+ * Shamir's secret sharing system.
+ *
+ */
+
+/*----- Notes on the sharing system ---------------------------------------*
+ *
+ * Shamir's secret-sharing system is based on polynomial interpolation modulo
+ * a prime number. It is `perfect' in that fewer participants than the
+ * threshold can derive no information about the secret by pooling their
+ * shares, and `ideal' in that the shares are the same size as the secret.
+ *
+ * This implementation stays close to the definition, in order to support
+ * other schemes for (e.g.) threshold cryptography. It is, however, rather
+ * slow.
+ */
+
+#ifndef CATACOMB_SHARE_H
+#define CATACOMB_SHARE_H
+
+#ifdef __cplusplus
+ extern "C" {
+#endif
+
+/*----- Header files ------------------------------------------------------*/
+
+#ifndef CATACOMB_GRAND_H
+# include "grand.h"
+#endif
+
+#ifndef CATACOMB_MP_H
+# include "mp.h"
+#endif
+
+/*----- Data structures ---------------------------------------------------*/
+
+/* --- A secret sharing context --- */
+
+typedef struct share_pt {
+ unsigned x; /* Index of this share */
+ mp *y; /* Payload of this share */
+} share_pt;
+
+typedef struct share {
+ unsigned t; /* Threshold */
+ unsigned n; /* The number of shares to make */
+ unsigned i; /* Next free slot in the vector */
+ mp *s; /* The secret */
+ mp *p; /* Modulus for arithmetic */
+ share_pt *v; /* Vector of share information */
+} share;
+
+#define SHARE_INIT(t, n) { t, n, 0, 0, 0, 0 }
+
+/*----- Functions provided ------------------------------------------------*/
+
+/* --- @share_create@ --- *
+ *
+ * Arguments: @share *s@ = pointer to share context to initialize
+ * @unsigned t, n@ = threshold parameters for the system
+ *
+ * Returns: ---
+ *
+ * Use: Initializes a sharing context.
+ */
+
+extern void share_create(share */*s*/, unsigned /*t*/, unsigned /*n*/);
+
+/* --- @share_destroy@ --- *
+ *
+ * Arguments: @share *s@ = pointer to share context to destroy
+ *
+ * Returns: ---
+ *
+ * Use: Disposes of a sharing context. All memory is freed, all
+ * integers are dropped.
+ */
+
+extern void share_destroy(share */*s*/);
+
+/* --- @share_mkshares@ --- *
+ *
+ * Arguments: @share *s@ = pointer to share context to fill in
+ * @grand *r@ = pointer to random number source
+ *
+ * Returns: ---
+ *
+ * Use: Generates @c->n@ secret shares, such that any @c->t@ of them
+ * may be used to recover the secret.
+ *
+ * The context structure is expected to be mostly filled in. In
+ * particular, @t@, @n@ and @s@ must be initialized. If @p@ is
+ * zero, a prime number of appropriate size is generated
+ * automatically. If @v@ is zero, a vector of appropriate size
+ * is allocated. You should use the macro @SHARE_INIT@ or
+ * @share_create@ to construct sharing contexts.
+ */
+
+extern void share_mkshares(share */*s*/, grand */*r*/);
+
+/* --- @share_add@ --- *
+ *
+ * Arguments: @share *s@ = pointer to sharing context
+ * @unsigned x@ = which share number this is
+ * @mp *y@ = the share value
+ *
+ * Returns: Number of shares required before recovery may be performed.
+ *
+ * Use: Adds a share to the context. The context must have been
+ * initialized with the correct prime @p@ and threshold @t@.
+ */
+
+extern unsigned share_add(share */*s*/, unsigned /*x*/, mp */*y*/);
+
+/* --- @share_combine@ --- *
+ *
+ * Arguments: @share *s@ = pointer to share context
+ *
+ * Returns: The secret, as a multiprecision integer.
+ *
+ * Use: Reconstructs a secret, given enough shares.
+ */
+
+extern mp *share_combine(share */*s*/);
+
+/*----- That's all, folks -------------------------------------------------*/
+
+#ifdef __cplusplus
+ }
+#endif
+
+#endif
projects / u / mdw / catacomb / commitdiff