hostap/src/eap_common/eap_pwd_common.c

/*
 * EAP server/peer: EAP-pwd shared routines
 * Copyright (c) 2010, Dan Harkins <dharkins@lounge.org>
 *
 * This software may be distributed under the terms of the BSD license.
 * See README for more details.
 */

#include "includes.h"
#include "common.h"
#include "utils/const_time.h"
#include "crypto/sha256.h"
#include "crypto/crypto.h"
#include "eap_defs.h"
#include "eap_pwd_common.h"

#define MAX_ECC_PRIME_LEN 66


/* The random function H(x) = HMAC-SHA256(0^32, x) */
struct crypto_hash * eap_pwd_h_init(void)
{
	u8 allzero[SHA256_MAC_LEN];
	os_memset(allzero, 0, SHA256_MAC_LEN);
	return crypto_hash_init(CRYPTO_HASH_ALG_HMAC_SHA256, allzero,
				SHA256_MAC_LEN);
}


void eap_pwd_h_update(struct crypto_hash *hash, const u8 *data, size_t len)
{
	crypto_hash_update(hash, data, len);
}


void eap_pwd_h_final(struct crypto_hash *hash, u8 *digest)
{
	size_t len = SHA256_MAC_LEN;
	crypto_hash_finish(hash, digest, &len);
}


/* a counter-based KDF based on NIST SP800-108 */
static int eap_pwd_kdf(const u8 *key, size_t keylen, const u8 *label,
		       size_t labellen, u8 *result, size_t resultbitlen)
{
	struct crypto_hash *hash;
	u8 digest[SHA256_MAC_LEN];
	u16 i, ctr, L;
	size_t resultbytelen, len = 0, mdlen;

	resultbytelen = (resultbitlen + 7) / 8;
	ctr = 0;
	L = htons(resultbitlen);
	while (len < resultbytelen) {
		ctr++;
		i = htons(ctr);
		hash = crypto_hash_init(CRYPTO_HASH_ALG_HMAC_SHA256,
					key, keylen);
		if (hash == NULL)
			return -1;
		if (ctr > 1)
			crypto_hash_update(hash, digest, SHA256_MAC_LEN);
		crypto_hash_update(hash, (u8 *) &i, sizeof(u16));
		crypto_hash_update(hash, label, labellen);
		crypto_hash_update(hash, (u8 *) &L, sizeof(u16));
		mdlen = SHA256_MAC_LEN;
		if (crypto_hash_finish(hash, digest, &mdlen) < 0)
			return -1;
		if ((len + mdlen) > resultbytelen)
			os_memcpy(result + len, digest, resultbytelen - len);
		else
			os_memcpy(result + len, digest, mdlen);
		len += mdlen;
	}

	/* since we're expanding to a bit length, mask off the excess */
	if (resultbitlen % 8) {
		u8 mask = 0xff;
		mask <<= (8 - (resultbitlen % 8));
		result[resultbytelen - 1] &= mask;
	}

	return 0;
}


EAP_PWD_group * get_eap_pwd_group(u16 num)
{
	EAP_PWD_group *grp;

	grp = os_zalloc(sizeof(EAP_PWD_group));
	if (!grp)
		return NULL;
	grp->group = crypto_ec_init(num);
	if (!grp->group) {
		wpa_printf(MSG_INFO, "EAP-pwd: unable to create EC group");
		os_free(grp);
		return NULL;
	}

	grp->group_num = num;
	wpa_printf(MSG_INFO, "EAP-pwd: provisioned group %d", num);

	return grp;
}


static void buf_shift_right(u8 *buf, size_t len, size_t bits)
{
	size_t i;
	for (i = len - 1; i > 0; i--)
		buf[i] = (buf[i - 1] << (8 - bits)) | (buf[i] >> bits);
	buf[0] >>= bits;
}


/*
 * compute a "random" secret point on an elliptic curve based
 * on the password and identities.
 */
int compute_password_element(EAP_PWD_group *grp, u16 num,
			     const u8 *password, size_t password_len,
			     const u8 *id_server, size_t id_server_len,
			     const u8 *id_peer, size_t id_peer_len,
			     const u8 *token)
{
	struct crypto_bignum *qr = NULL, *qnr = NULL, *one = NULL;
	struct crypto_bignum *qr_or_qnr = NULL;
	u8 qr_bin[MAX_ECC_PRIME_LEN];
	u8 qnr_bin[MAX_ECC_PRIME_LEN];
	u8 qr_or_qnr_bin[MAX_ECC_PRIME_LEN];
	u8 x_bin[MAX_ECC_PRIME_LEN];
	struct crypto_bignum *tmp1 = NULL, *tmp2 = NULL, *pm1 = NULL;
	struct crypto_hash *hash;
	unsigned char pwe_digest[SHA256_MAC_LEN], *prfbuf = NULL, ctr;
	int ret = 0, check, res;
	u8 found = 0; /* 0 (false) or 0xff (true) to be used as const_time_*
		       * mask */
	size_t primebytelen = 0, primebitlen;
	struct crypto_bignum *x_candidate = NULL, *cofactor = NULL;
	const struct crypto_bignum *prime;
	u8 mask, found_ctr = 0, is_odd = 0;

	if (grp->pwe)
		return -1;

	os_memset(x_bin, 0, sizeof(x_bin));

	prime = crypto_ec_get_prime(grp->group);
	cofactor = crypto_bignum_init();
	grp->pwe = crypto_ec_point_init(grp->group);
	tmp1 = crypto_bignum_init();
	pm1 = crypto_bignum_init();
	one = crypto_bignum_init_set((const u8 *) "\x01", 1);
	if (!cofactor || !grp->pwe || !tmp1 || !pm1 || !one) {
		wpa_printf(MSG_INFO, "EAP-pwd: unable to create bignums");
		goto fail;
	}

	if (crypto_ec_cofactor(grp->group, cofactor) < 0) {
		wpa_printf(MSG_INFO, "EAP-pwd: unable to get cofactor for "
			   "curve");
		goto fail;
	}
	primebitlen = crypto_ec_prime_len_bits(grp->group);
	primebytelen = crypto_ec_prime_len(grp->group);
	if ((prfbuf = os_malloc(primebytelen)) == NULL) {
		wpa_printf(MSG_INFO, "EAP-pwd: unable to malloc space for prf "
			   "buffer");
		goto fail;
	}
	if (crypto_bignum_sub(prime, one, pm1) < 0)
		goto fail;

	/* get a random quadratic residue and nonresidue */
	while (!qr || !qnr) {
		if (crypto_bignum_rand(tmp1, prime) < 0)
			goto fail;
		res = crypto_bignum_legendre(tmp1, prime);
		if (!qr && res == 1) {
			qr = tmp1;
			tmp1 = crypto_bignum_init();
		} else if (!qnr && res == -1) {
			qnr = tmp1;
			tmp1 = crypto_bignum_init();
		}
		if (!tmp1)
			goto fail;
	}
	if (crypto_bignum_to_bin(qr, qr_bin, sizeof(qr_bin),
				 primebytelen) < 0 ||
	    crypto_bignum_to_bin(qnr, qnr_bin, sizeof(qnr_bin),
				 primebytelen) < 0)
		goto fail;

	os_memset(prfbuf, 0, primebytelen);
	ctr = 0;

	/*
	 * Run through the hunting-and-pecking loop 40 times to mask the time
	 * necessary to find PWE. The odds of PWE not being found in 40 loops is
	 * roughly 1 in 1 trillion.
	 */
	while (ctr < 40) {
		ctr++;

		/*
		 * compute counter-mode password value and stretch to prime
		 *    pwd-seed = H(token | peer-id | server-id | password |
		 *		   counter)
		 */
		hash = eap_pwd_h_init();
		if (hash == NULL)
			goto fail;
		eap_pwd_h_update(hash, token, sizeof(u32));
		eap_pwd_h_update(hash, id_peer, id_peer_len);
		eap_pwd_h_update(hash, id_server, id_server_len);
		eap_pwd_h_update(hash, password, password_len);
		eap_pwd_h_update(hash, &ctr, sizeof(ctr));
		eap_pwd_h_final(hash, pwe_digest);

		is_odd = const_time_select_u8(
			found, is_odd, pwe_digest[SHA256_MAC_LEN - 1] & 0x01);
		if (eap_pwd_kdf(pwe_digest, SHA256_MAC_LEN,
				(u8 *) "EAP-pwd Hunting And Pecking",
				os_strlen("EAP-pwd Hunting And Pecking"),
				prfbuf, primebitlen) < 0)
			goto fail;
		if (primebitlen % 8)
			buf_shift_right(prfbuf, primebytelen,
					8 - primebitlen % 8);

		crypto_bignum_deinit(x_candidate, 1);
		x_candidate = crypto_bignum_init_set(prfbuf, primebytelen);
		if (!x_candidate) {
			wpa_printf(MSG_INFO,
				   "EAP-pwd: unable to create x_candidate");
			goto fail;
		}

		if (crypto_bignum_cmp(x_candidate, prime) >= 0)
			continue;

		wpa_hexdump_key(MSG_DEBUG, "EAP-pwd: x_candidate",
				prfbuf, primebytelen);
		const_time_select_bin(found, x_bin, prfbuf, primebytelen,
				      x_bin);

		/*
		 * compute y^2 using the equation of the curve
		 *
		 *      y^2 = x^3 + ax + b
		 */
		crypto_bignum_deinit(tmp2, 1);
		tmp2 = crypto_ec_point_compute_y_sqr(grp->group, x_candidate);
		if (!tmp2)
			goto fail;

		/*
		 * mask tmp2 so doing legendre won't leak timing info
		 *
		 * tmp1 is a random number between 1 and p-1
		 */
		if (crypto_bignum_rand(tmp1, pm1) < 0 ||
		    crypto_bignum_mulmod(tmp2, tmp1, prime, tmp2) < 0 ||
		    crypto_bignum_mulmod(tmp2, tmp1, prime, tmp2) < 0)
			goto fail;

		/*
		 * Now tmp2 (y^2) is masked, all values between 1 and p-1
		 * are equally probable. Multiplying by r^2 does not change
		 * whether or not tmp2 is a quadratic residue, just masks it.
		 *
		 * Flip a coin, multiply by the random quadratic residue or the
		 * random quadratic nonresidue and record heads or tails.
		 */
		mask = const_time_eq_u8(crypto_bignum_is_odd(tmp1), 1);
		check = const_time_select_s8(mask, 1, -1);
		const_time_select_bin(mask, qr_bin, qnr_bin, primebytelen,
				      qr_or_qnr_bin);
		crypto_bignum_deinit(qr_or_qnr, 1);
		qr_or_qnr = crypto_bignum_init_set(qr_or_qnr_bin, primebytelen);
		if (!qr_or_qnr ||
		    crypto_bignum_mulmod(tmp2, qr_or_qnr, prime, tmp2) < 0)
			goto fail;

		/*
		 * Now it's safe to do legendre, if check is 1 then it's
		 * a straightforward test (multiplying by qr does not
		 * change result), if check is -1 then it's the opposite test
		 * (multiplying a qr by qnr would make a qnr).
		 */
		res = crypto_bignum_legendre(tmp2, prime);
		if (res == -2)
			goto fail;
		mask = const_time_eq(res, check);
		found_ctr = const_time_select_u8(found, found_ctr, ctr);
		found |= mask;
	}
	if (found == 0) {
		wpa_printf(MSG_INFO,
			   "EAP-pwd: unable to find random point on curve for group %d, something's fishy",
			   num);
		goto fail;
	}

	/*
	 * We know x_candidate is a quadratic residue so set it here.
	 */
	crypto_bignum_deinit(x_candidate, 1);
	x_candidate = crypto_bignum_init_set(x_bin, primebytelen);
	if (!x_candidate ||
	    crypto_ec_point_solve_y_coord(grp->group, grp->pwe, x_candidate,
					  is_odd) != 0) {
		wpa_printf(MSG_INFO, "EAP-pwd: Could not solve for y");
		goto fail;
	}

	/*
	 * If there's a solution to the equation then the point must be on the
	 * curve so why check again explicitly? OpenSSL code says this is
	 * required by X9.62. We're not X9.62 but it can't hurt just to be sure.
	 */
	if (!crypto_ec_point_is_on_curve(grp->group, grp->pwe)) {
		wpa_printf(MSG_INFO, "EAP-pwd: point is not on curve");
		goto fail;
	}

	if (!crypto_bignum_is_one(cofactor)) {
		/* make sure the point is not in a small sub-group */
		if (crypto_ec_point_mul(grp->group, grp->pwe, cofactor,
					grp->pwe) != 0) {
			wpa_printf(MSG_INFO,
				   "EAP-pwd: cannot multiply generator by order");
			goto fail;
		}
		if (crypto_ec_point_is_at_infinity(grp->group, grp->pwe)) {
			wpa_printf(MSG_INFO, "EAP-pwd: point is at infinity");
			goto fail;
		}
	}
	wpa_printf(MSG_DEBUG, "EAP-pwd: found a PWE in %02d tries", found_ctr);

	if (0) {
 fail:
		crypto_ec_point_deinit(grp->pwe, 1);
		grp->pwe = NULL;
		ret = 1;
	}
	/* cleanliness and order.... */
	crypto_bignum_deinit(cofactor, 1);
	crypto_bignum_deinit(x_candidate, 1);
	crypto_bignum_deinit(pm1, 0);
	crypto_bignum_deinit(tmp1, 1);
	crypto_bignum_deinit(tmp2, 1);
	crypto_bignum_deinit(qr, 1);
	crypto_bignum_deinit(qnr, 1);
	crypto_bignum_deinit(qr_or_qnr, 1);
	crypto_bignum_deinit(one, 0);
	bin_clear_free(prfbuf, primebytelen);
	os_memset(qr_bin, 0, sizeof(qr_bin));
	os_memset(qnr_bin, 0, sizeof(qnr_bin));
	os_memset(qr_or_qnr_bin, 0, sizeof(qr_or_qnr_bin));
	os_memset(pwe_digest, 0, sizeof(pwe_digest));

	return ret;
}


int compute_keys(EAP_PWD_group *grp, const struct crypto_bignum *k,
		 const struct crypto_bignum *peer_scalar,
		 const struct crypto_bignum *server_scalar,
		 const u8 *confirm_peer, const u8 *confirm_server,
		 const u32 *ciphersuite, u8 *msk, u8 *emsk, u8 *session_id)
{
	struct crypto_hash *hash;
	u8 mk[SHA256_MAC_LEN], *cruft;
	u8 msk_emsk[EAP_MSK_LEN + EAP_EMSK_LEN];
	size_t prime_len, order_len;

	prime_len = crypto_ec_prime_len(grp->group);
	order_len = crypto_ec_order_len(grp->group);

	cruft = os_malloc(prime_len);
	if (!cruft)
		return -1;

	/*
	 * first compute the session-id = TypeCode | H(ciphersuite | scal_p |
	 *	scal_s)
	 */
	session_id[0] = EAP_TYPE_PWD;
	hash = eap_pwd_h_init();
	if (hash == NULL) {
		os_free(cruft);
		return -1;
	}
	eap_pwd_h_update(hash, (const u8 *) ciphersuite, sizeof(u32));
	crypto_bignum_to_bin(peer_scalar, cruft, order_len, order_len);
	eap_pwd_h_update(hash, cruft, order_len);
	crypto_bignum_to_bin(server_scalar, cruft, order_len, order_len);
	eap_pwd_h_update(hash, cruft, order_len);
	eap_pwd_h_final(hash, &session_id[1]);

	/* then compute MK = H(k | confirm-peer | confirm-server) */
	hash = eap_pwd_h_init();
	if (hash == NULL) {
		os_free(cruft);
		return -1;
	}
	crypto_bignum_to_bin(k, cruft, prime_len, prime_len);
	eap_pwd_h_update(hash, cruft, prime_len);
	os_free(cruft);
	eap_pwd_h_update(hash, confirm_peer, SHA256_MAC_LEN);
	eap_pwd_h_update(hash, confirm_server, SHA256_MAC_LEN);
	eap_pwd_h_final(hash, mk);

	/* stretch the mk with the session-id to get MSK | EMSK */
	if (eap_pwd_kdf(mk, SHA256_MAC_LEN,
			session_id, SHA256_MAC_LEN + 1,
			msk_emsk, (EAP_MSK_LEN + EAP_EMSK_LEN) * 8) < 0) {
		return -1;
	}

	os_memcpy(msk, msk_emsk, EAP_MSK_LEN);
	os_memcpy(emsk, msk_emsk + EAP_MSK_LEN, EAP_EMSK_LEN);

	return 1;
}


static int eap_pwd_element_coord_ok(const struct crypto_bignum *prime,
				    const u8 *buf, size_t len)
{
	struct crypto_bignum *val;
	int ok = 1;

	val = crypto_bignum_init_set(buf, len);
	if (!val || crypto_bignum_is_zero(val) ||
	    crypto_bignum_cmp(val, prime) >= 0)
		ok = 0;
	crypto_bignum_deinit(val, 0);
	return ok;
}


struct crypto_ec_point * eap_pwd_get_element(EAP_PWD_group *group,
					     const u8 *buf)
{
	struct crypto_ec_point *element;
	const struct crypto_bignum *prime;
	size_t prime_len;
	struct crypto_bignum *cofactor = NULL;

	prime = crypto_ec_get_prime(group->group);
	prime_len = crypto_ec_prime_len(group->group);

	/* RFC 5931, 2.8.5.2.2: 0 < x,y < p */
	if (!eap_pwd_element_coord_ok(prime, buf, prime_len) ||
	    !eap_pwd_element_coord_ok(prime, buf + prime_len, prime_len)) {
		wpa_printf(MSG_INFO, "EAP-pwd: Invalid coordinate in element");
		return NULL;
	}

	element = crypto_ec_point_from_bin(group->group, buf);
	if (!element) {
		wpa_printf(MSG_INFO, "EAP-pwd: EC point from element failed");
		return NULL;
	}

	/* RFC 5931, 2.8.5.2.2: on curve and not the point at infinity */
	if (!crypto_ec_point_is_on_curve(group->group, element) ||
	    crypto_ec_point_is_at_infinity(group->group, element)) {
		wpa_printf(MSG_INFO, "EAP-pwd: Invalid element");
		goto fail;
	}

	cofactor = crypto_bignum_init();
	if (!cofactor || crypto_ec_cofactor(group->group, cofactor) < 0) {
		wpa_printf(MSG_INFO,
			   "EAP-pwd: Unable to get cofactor for curve");
		goto fail;
	}

	if (!crypto_bignum_is_one(cofactor)) {
		struct crypto_ec_point *point;
		int ok = 1;

		/* check to ensure peer's element is not in a small sub-group */
		point = crypto_ec_point_init(group->group);
		if (!point ||
		    crypto_ec_point_mul(group->group, element,
					cofactor, point) != 0 ||
		    crypto_ec_point_is_at_infinity(group->group, point))
			ok = 0;
		crypto_ec_point_deinit(point, 0);

		if (!ok) {
			wpa_printf(MSG_INFO,
				   "EAP-pwd: Small sub-group check on peer element failed");
			goto fail;
		}
	}

out:
	crypto_bignum_deinit(cofactor, 0);
	return element;
fail:
	crypto_ec_point_deinit(element, 0);
	element = NULL;
	goto out;
}


struct crypto_bignum * eap_pwd_get_scalar(EAP_PWD_group *group, const u8 *buf)
{
	struct crypto_bignum *scalar;
	const struct crypto_bignum *order;
	size_t order_len;

	order = crypto_ec_get_order(group->group);
	order_len = crypto_ec_order_len(group->group);

	/* RFC 5931, 2.8.5.2: 1 < scalar < r */
	scalar = crypto_bignum_init_set(buf, order_len);
	if (!scalar || crypto_bignum_is_zero(scalar) ||
	    crypto_bignum_is_one(scalar) ||
	    crypto_bignum_cmp(scalar, order) >= 0) {
		wpa_printf(MSG_INFO, "EAP-pwd: received scalar is invalid");
		crypto_bignum_deinit(scalar, 0);
		scalar = NULL;
	}

	return scalar;
}


int eap_pwd_get_rand_mask(EAP_PWD_group *group, struct crypto_bignum *_rand,
			  struct crypto_bignum *_mask,
			  struct crypto_bignum *scalar)
{
	const struct crypto_bignum *order;
	int count;

	order = crypto_ec_get_order(group->group);

	/* Select two random values rand,mask such that 1 < rand,mask < r and
	 * rand + mask mod r > 1. */
	for (count = 0; count < 100; count++) {
		if (crypto_bignum_rand(_rand, order) == 0 &&
		    !crypto_bignum_is_zero(_rand) &&
		    crypto_bignum_rand(_mask, order) == 0 &&
		    !crypto_bignum_is_zero(_mask) &&
		    crypto_bignum_add(_rand, _mask, scalar) == 0 &&
		    crypto_bignum_mod(scalar, order, scalar) == 0 &&
		    !crypto_bignum_is_zero(scalar) &&
		    !crypto_bignum_is_one(scalar))
			return 0;
	}

	wpa_printf(MSG_INFO, "EAP-pwd: unable to get randomness");
	return -1;
}