/*-*- 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 */ /* * See "Practical Secure Logging: Seekable Sequential Key Generators" * by G. A. Marson, B. Poettering for details: * * http://eprint.iacr.org/2013/397 */ #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); memzero(buf, 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; } _pure_ 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; (1ULL << 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); memzero(state + 2 + 2 * secpar / 8, 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); }