--- /dev/null
+/*-*- Mode: C; c-basic-offset: 8; indent-tabs-mode: nil -*-*/
+
+/*
+ * fsprg v0.1 - (seekable) forward-secure pseudorandom generator
+ * Copyright (C) 2012 B. Poettering
+ * Contact: fsprg@point-at-infinity.org
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Lesser General Public
+ * License as published by the Free Software Foundation; either
+ * version 2.1 of the License, or (at your option) any later version.
+ *
+ * This library 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
+ * Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public
+ * License along with this library; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
+ * 02110-1301 USA
+ *
+ */
+
+#include <gcrypt.h>
+#include <string.h>
+#include <assert.h>
+
+#include "fsprg.h"
+
+#define ISVALID_SECPAR(secpar) (((secpar) % 16 == 0) && ((secpar) >= 16) && ((secpar) <= 16384))
+#define VALIDATE_SECPAR(secpar) assert(ISVALID_SECPAR(secpar));
+
+#define RND_HASH GCRY_MD_SHA256
+#define RND_GEN_P 0x01
+#define RND_GEN_Q 0x02
+#define RND_GEN_X 0x03
+
+/******************************************************************************/
+
+static void mpi_export(void *buf, size_t buflen, const gcry_mpi_t x) {
+ unsigned len;
+ size_t nwritten;
+
+ assert(gcry_mpi_cmp_ui(x, 0) >= 0);
+ len = (gcry_mpi_get_nbits(x) + 7) / 8;
+ assert(len <= buflen);
+ memset(buf, 0, buflen);
+ gcry_mpi_print(GCRYMPI_FMT_USG, buf + (buflen - len), len, &nwritten, x);
+ assert(nwritten == len);
+}
+
+static gcry_mpi_t mpi_import(const void *buf, size_t buflen) {
+ gcry_mpi_t h;
+ unsigned len;
+
+ gcry_mpi_scan(&h, GCRYMPI_FMT_USG, buf, buflen, NULL);
+ len = (gcry_mpi_get_nbits(h) + 7) / 8;
+ assert(len <= buflen);
+ assert(gcry_mpi_cmp_ui(h, 0) >= 0);
+
+ return h;
+}
+
+static void uint64_export(void *buf, size_t buflen, uint64_t x) {
+ assert(buflen == 8);
+ ((uint8_t*) buf)[0] = (x >> 56) & 0xff;
+ ((uint8_t*) buf)[1] = (x >> 48) & 0xff;
+ ((uint8_t*) buf)[2] = (x >> 40) & 0xff;
+ ((uint8_t*) buf)[3] = (x >> 32) & 0xff;
+ ((uint8_t*) buf)[4] = (x >> 24) & 0xff;
+ ((uint8_t*) buf)[5] = (x >> 16) & 0xff;
+ ((uint8_t*) buf)[6] = (x >> 8) & 0xff;
+ ((uint8_t*) buf)[7] = (x >> 0) & 0xff;
+}
+
+static uint64_t uint64_import(const void *buf, size_t buflen) {
+ assert(buflen == 8);
+ return
+ (uint64_t)(((uint8_t*) buf)[0]) << 56 |
+ (uint64_t)(((uint8_t*) buf)[1]) << 48 |
+ (uint64_t)(((uint8_t*) buf)[2]) << 40 |
+ (uint64_t)(((uint8_t*) buf)[3]) << 32 |
+ (uint64_t)(((uint8_t*) buf)[4]) << 24 |
+ (uint64_t)(((uint8_t*) buf)[5]) << 16 |
+ (uint64_t)(((uint8_t*) buf)[6]) << 8 |
+ (uint64_t)(((uint8_t*) buf)[7]) << 0;
+}
+
+/* deterministically generate from seed/idx a string of buflen pseudorandom bytes */
+static void det_randomize(void *buf, size_t buflen, const void *seed, size_t seedlen, uint32_t idx) {
+ gcry_md_hd_t hd, hd2;
+ size_t olen, cpylen;
+ uint32_t ctr;
+
+ olen = gcry_md_get_algo_dlen(RND_HASH);
+ gcry_md_open(&hd, RND_HASH, 0);
+ gcry_md_write(hd, seed, seedlen);
+ gcry_md_putc(hd, (idx >> 24) & 0xff);
+ gcry_md_putc(hd, (idx >> 16) & 0xff);
+ gcry_md_putc(hd, (idx >> 8) & 0xff);
+ gcry_md_putc(hd, (idx >> 0) & 0xff);
+
+ for (ctr = 0; buflen; ctr++) {
+ gcry_md_copy(&hd2, hd);
+ gcry_md_putc(hd2, (ctr >> 24) & 0xff);
+ gcry_md_putc(hd2, (ctr >> 16) & 0xff);
+ gcry_md_putc(hd2, (ctr >> 8) & 0xff);
+ gcry_md_putc(hd2, (ctr >> 0) & 0xff);
+ gcry_md_final(hd2);
+ cpylen = (buflen < olen) ? buflen : olen;
+ memcpy(buf, gcry_md_read(hd2, RND_HASH), cpylen);
+ gcry_md_close(hd2);
+ buf += cpylen;
+ buflen -= cpylen;
+ }
+ gcry_md_close(hd);
+}
+
+/* deterministically generate from seed/idx a prime of length `bits' that is 3 (mod 4) */
+static gcry_mpi_t genprime3mod4(int bits, const void *seed, size_t seedlen, uint32_t idx) {
+ size_t buflen = bits / 8;
+ uint8_t buf[buflen];
+ gcry_mpi_t p;
+
+ assert(bits % 8 == 0);
+ assert(buflen > 0);
+
+ det_randomize(buf, buflen, seed, seedlen, idx);
+ buf[0] |= 0xc0; /* set upper two bits, so that n=pq has maximum size */
+ buf[buflen - 1] |= 0x03; /* set lower two bits, to have result 3 (mod 4) */
+
+ p = mpi_import(buf, buflen);
+ while (gcry_prime_check(p, 0))
+ gcry_mpi_add_ui(p, p, 4);
+
+ return p;
+}
+
+/* deterministically generate from seed/idx a quadratic residue (mod n) */
+static gcry_mpi_t gensquare(const gcry_mpi_t n, const void *seed, size_t seedlen, uint32_t idx, unsigned secpar) {
+ size_t buflen = secpar / 8;
+ uint8_t buf[buflen];
+ gcry_mpi_t x;
+
+ det_randomize(buf, buflen, seed, seedlen, idx);
+ buf[0] &= 0x7f; /* clear upper bit, so that we have x < n */
+ x = mpi_import(buf, buflen);
+ assert(gcry_mpi_cmp(x, n) < 0);
+ gcry_mpi_mulm(x, x, x, n);
+ return x;
+}
+
+/* compute 2^m (mod phi(p)), for a prime p */
+static gcry_mpi_t twopowmodphi(uint64_t m, const gcry_mpi_t p) {
+ gcry_mpi_t phi, r;
+ int n;
+
+ phi = gcry_mpi_new(0);
+ gcry_mpi_sub_ui(phi, p, 1);
+
+ /* count number of used bits in m */
+ for (n = 0; ((uint64_t)1 << n) <= m; n++)
+ ;
+
+ r = gcry_mpi_new(0);
+ gcry_mpi_set_ui(r, 1);
+ while (n) { /* square and multiply algorithm for fast exponentiation */
+ n--;
+ gcry_mpi_mulm(r, r, r, phi);
+ if (m & ((uint64_t)1 << n)) {
+ gcry_mpi_add(r, r, r);
+ if (gcry_mpi_cmp(r, phi) >= 0)
+ gcry_mpi_sub(r, r, phi);
+ }
+ }
+
+ gcry_mpi_release(phi);
+ return r;
+}
+
+/* Decompose $x \in Z_n$ into $(xp,xq) \in Z_p \times Z_q$ using Chinese Remainder Theorem */
+static void CRT_decompose(gcry_mpi_t *xp, gcry_mpi_t *xq, const gcry_mpi_t x, const gcry_mpi_t p, const gcry_mpi_t q) {
+ *xp = gcry_mpi_new(0);
+ *xq = gcry_mpi_new(0);
+ gcry_mpi_mod(*xp, x, p);
+ gcry_mpi_mod(*xq, x, q);
+}
+
+/* Compose $(xp,xq) \in Z_p \times Z_q$ into $x \in Z_n$ using Chinese Remainder Theorem */
+static void CRT_compose(gcry_mpi_t *x, const gcry_mpi_t xp, const gcry_mpi_t xq, const gcry_mpi_t p, const gcry_mpi_t q) {
+ gcry_mpi_t a, u;
+
+ a = gcry_mpi_new(0);
+ u = gcry_mpi_new(0);
+ *x = gcry_mpi_new(0);
+ gcry_mpi_subm(a, xq, xp, q);
+ gcry_mpi_invm(u, p, q);
+ gcry_mpi_mulm(a, a, u, q); /* a = (xq - xp) / p (mod q) */
+ gcry_mpi_mul(*x, p, a);
+ gcry_mpi_add(*x, *x, xp); /* x = p * ((xq - xp) / p mod q) + xp */
+ gcry_mpi_release(a);
+ gcry_mpi_release(u);
+}
+
+static void initialize_libgcrypt(void) {
+ const char *p;
+ if (gcry_control(GCRYCTL_INITIALIZATION_FINISHED_P))
+ return;
+
+ p = gcry_check_version("1.4.5");
+ assert(p);
+
+ /* Turn off "secmem". Clients which whish to make use of this
+ * feature should initialize the library manually */
+ gcry_control(GCRYCTL_DISABLE_SECMEM);
+ gcry_control(GCRYCTL_INITIALIZATION_FINISHED, 0);
+}
+
+/******************************************************************************/
+
+size_t FSPRG_mskinbytes(unsigned _secpar) {
+ VALIDATE_SECPAR(_secpar);
+ return 2 + 2 * (_secpar / 2) / 8; /* to store header,p,q */
+}
+
+size_t FSPRG_mpkinbytes(unsigned _secpar) {
+ VALIDATE_SECPAR(_secpar);
+ return 2 + _secpar / 8; /* to store header,n */
+}
+
+size_t FSPRG_stateinbytes(unsigned _secpar) {
+ VALIDATE_SECPAR(_secpar);
+ return 2 + 2 * _secpar / 8 + 8; /* to store header,n,x,epoch */
+}
+
+static void store_secpar(void *buf, uint16_t secpar) {
+ secpar = secpar / 16 - 1;
+ ((uint8_t*) buf)[0] = (secpar >> 8) & 0xff;
+ ((uint8_t*) buf)[1] = (secpar >> 0) & 0xff;
+}
+
+static uint16_t read_secpar(const void *buf) {
+ uint16_t secpar;
+ secpar =
+ (uint16_t)(((uint8_t*) buf)[0]) << 8 |
+ (uint16_t)(((uint8_t*) buf)[1]) << 0;
+ return 16 * (secpar + 1);
+}
+
+void FSPRG_GenMK(void *msk, void *mpk, const void *seed, size_t seedlen, unsigned _secpar) {
+ uint8_t iseed[FSPRG_RECOMMENDED_SEEDLEN];
+ gcry_mpi_t n, p, q;
+ uint16_t secpar;
+
+ VALIDATE_SECPAR(_secpar);
+ secpar = _secpar;
+
+ initialize_libgcrypt();
+
+ if (!seed) {
+ gcry_randomize(iseed, FSPRG_RECOMMENDED_SEEDLEN, GCRY_STRONG_RANDOM);
+ seed = iseed;
+ seedlen = FSPRG_RECOMMENDED_SEEDLEN;
+ }
+
+ p = genprime3mod4(secpar / 2, seed, seedlen, RND_GEN_P);
+ q = genprime3mod4(secpar / 2, seed, seedlen, RND_GEN_Q);
+
+ if (msk) {
+ store_secpar(msk + 0, secpar);
+ mpi_export(msk + 2 + 0 * (secpar / 2) / 8, (secpar / 2) / 8, p);
+ mpi_export(msk + 2 + 1 * (secpar / 2) / 8, (secpar / 2) / 8, q);
+ }
+
+ if (mpk) {
+ n = gcry_mpi_new(0);
+ gcry_mpi_mul(n, p, q);
+ assert(gcry_mpi_get_nbits(n) == secpar);
+
+ store_secpar(mpk + 0, secpar);
+ mpi_export(mpk + 2, secpar / 8, n);
+
+ gcry_mpi_release(n);
+ }
+
+ gcry_mpi_release(p);
+ gcry_mpi_release(q);
+}
+
+void FSPRG_GenState0(void *state, const void *mpk, const void *seed, size_t seedlen) {
+ gcry_mpi_t n, x;
+ uint16_t secpar;
+
+ initialize_libgcrypt();
+
+ secpar = read_secpar(mpk + 0);
+ n = mpi_import(mpk + 2, secpar / 8);
+ x = gensquare(n, seed, seedlen, RND_GEN_X, secpar);
+
+ memcpy(state, mpk, 2 + secpar / 8);
+ mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, x);
+ memset(state + 2 + 2 * secpar / 8, 0, 8);
+
+ gcry_mpi_release(n);
+ gcry_mpi_release(x);
+}
+
+void FSPRG_Evolve(void *state) {
+ gcry_mpi_t n, x;
+ uint16_t secpar;
+ uint64_t epoch;
+
+ initialize_libgcrypt();
+
+ secpar = read_secpar(state + 0);
+ n = mpi_import(state + 2 + 0 * secpar / 8, secpar / 8);
+ x = mpi_import(state + 2 + 1 * secpar / 8, secpar / 8);
+ epoch = uint64_import(state + 2 + 2 * secpar / 8, 8);
+
+ gcry_mpi_mulm(x, x, x, n);
+ epoch++;
+
+ mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, x);
+ uint64_export(state + 2 + 2 * secpar / 8, 8, epoch);
+
+ gcry_mpi_release(n);
+ gcry_mpi_release(x);
+}
+
+uint64_t FSPRG_GetEpoch(const void *state) {
+ uint16_t secpar;
+ secpar = read_secpar(state + 0);
+ return uint64_import(state + 2 + 2 * secpar / 8, 8);
+}
+
+void FSPRG_Seek(void *state, uint64_t epoch, const void *msk, const void *seed, size_t seedlen) {
+ gcry_mpi_t p, q, n, x, xp, xq, kp, kq, xm;
+ uint16_t secpar;
+
+ initialize_libgcrypt();
+
+ secpar = read_secpar(msk + 0);
+ p = mpi_import(msk + 2 + 0 * (secpar / 2) / 8, (secpar / 2) / 8);
+ q = mpi_import(msk + 2 + 1 * (secpar / 2) / 8, (secpar / 2) / 8);
+
+ n = gcry_mpi_new(0);
+ gcry_mpi_mul(n, p, q);
+
+ x = gensquare(n, seed, seedlen, RND_GEN_X, secpar);
+ CRT_decompose(&xp, &xq, x, p, q); /* split (mod n) into (mod p) and (mod q) using CRT */
+
+ kp = twopowmodphi(epoch, p); /* compute 2^epoch (mod phi(p)) */
+ kq = twopowmodphi(epoch, q); /* compute 2^epoch (mod phi(q)) */
+
+ gcry_mpi_powm(xp, xp, kp, p); /* compute x^(2^epoch) (mod p) */
+ gcry_mpi_powm(xq, xq, kq, q); /* compute x^(2^epoch) (mod q) */
+
+ CRT_compose(&xm, xp, xq, p, q); /* combine (mod p) and (mod q) to (mod n) using CRT */
+
+ store_secpar(state + 0, secpar);
+ mpi_export(state + 2 + 0 * secpar / 8, secpar / 8, n);
+ mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, xm);
+ uint64_export(state + 2 + 2 * secpar / 8, 8, epoch);
+
+ gcry_mpi_release(p);
+ gcry_mpi_release(q);
+ gcry_mpi_release(n);
+ gcry_mpi_release(x);
+ gcry_mpi_release(xp);
+ gcry_mpi_release(xq);
+ gcry_mpi_release(kp);
+ gcry_mpi_release(kq);
+ gcry_mpi_release(xm);
+}
+
+void FSPRG_GetKey(const void *state, void *key, size_t keylen, uint32_t idx) {
+ uint16_t secpar;
+
+ initialize_libgcrypt();
+
+ secpar = read_secpar(state + 0);
+ det_randomize(key, keylen, state + 2, 2 * secpar / 8 + 8, idx);
+}
~ianmdlvl / elogind.git / blobdiff