/*-*- 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);

}