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From 22ac3dfebf7b25a3aae02f9b4f69025bb4173137 Mon Sep 17 00:00:00 2001
From: Dan Harkins <dharkins@lounge.org>
Date: Fri, 25 May 2018 21:40:04 +0300
Subject: [PATCH] EAP-pwd: Mask timing of PWE derivation
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.
Signed-off-by: Dan Harkins <dharkins@lounge.org>
---
src/eap_common/eap_pwd_common.c | 171 ++++++++++++++++++++++++--------
1 file changed, 130 insertions(+), 41 deletions(-)
--- a/src/eap_common/eap_pwd_common.c
+++ b/src/eap_common/eap_pwd_common.c
@@ -112,18 +112,25 @@ int compute_password_element(EAP_PWD_gro
const u8 *id_peer, size_t id_peer_len,
const u8 *token)
{
+ struct crypto_bignum *qr = NULL, *qnr = NULL, *one = NULL;
+ struct crypto_bignum *tmp1 = NULL, *tmp2 = NULL, *pm1 = NULL;
struct crypto_hash *hash;
unsigned char pwe_digest[SHA256_MAC_LEN], *prfbuf = NULL, ctr;
- int is_odd, ret = 0;
+ int is_odd, ret = 0, check, found = 0;
size_t primebytelen, primebitlen;
struct crypto_bignum *x_candidate = NULL, *rnd = NULL, *cofactor = NULL;
+ const struct crypto_bignum *prime;
if (grp->pwe)
return -1;
+ prime = crypto_ec_get_prime(grp->group);
cofactor = crypto_bignum_init();
grp->pwe = crypto_ec_point_init(grp->group);
- if (!cofactor || !grp->pwe) {
+ 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;
}
@@ -140,15 +147,36 @@ int compute_password_element(EAP_PWD_gro
"buffer");
goto fail;
}
+ if (crypto_bignum_sub(prime, one, pm1) < 0)
+ goto fail;
+
+ /* get a random quadratic residue and nonresidue */
+ while (!qr || !qnr) {
+ int res;
+
+ 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;
+ }
+
os_memset(prfbuf, 0, primebytelen);
ctr = 0;
- while (1) {
- if (ctr > 30) {
- wpa_printf(MSG_INFO, "EAP-pwd: unable to find random "
- "point on curve for group %d, something's "
- "fishy", num);
- goto fail;
- }
+
+ /*
+ * 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++;
/*
@@ -199,58 +227,113 @@ int compute_password_element(EAP_PWD_gro
x_candidate) < 0)
goto fail;
- if (crypto_bignum_cmp(x_candidate,
- crypto_ec_get_prime(grp->group)) >= 0)
+ if (crypto_bignum_cmp(x_candidate, prime) >= 0)
continue;
wpa_hexdump(MSG_DEBUG, "EAP-pwd: x_candidate",
prfbuf, primebytelen);
/*
- * need to unambiguously identify the solution, if there is
- * one...
+ * compute y^2 using the equation of the curve
+ *
+ * y^2 = x^3 + ax + b
*/
- is_odd = crypto_bignum_is_odd(rnd);
+ tmp2 = crypto_ec_point_compute_y_sqr(grp->group, x_candidate);
+ if (!tmp2)
+ goto fail;
/*
- * solve the quadratic equation, if it's not solvable then we
- * don't have a point
+ * mask tmp2 so doing legendre won't leak timing info
+ *
+ * tmp1 is a random number between 1 and p-1
*/
- if (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");
- continue;
- }
+ 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;
+
/*
- * 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.
+ * 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.
*/
- if (!crypto_ec_point_is_on_curve(grp->group, grp->pwe)) {
- wpa_printf(MSG_INFO, "EAP-pwd: point is not on curve");
- continue;
+ if (crypto_bignum_is_odd(tmp1)) {
+ crypto_bignum_mulmod(tmp2, qr, prime, tmp2);
+ check = 1;
+ } else {
+ crypto_bignum_mulmod(tmp2, qnr, prime, tmp2);
+ check = -1;
}
- 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");
+ /*
+ * 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).
+ */
+ if (crypto_bignum_legendre(tmp2, prime) == check) {
+ if (found == 1)
+ continue;
+
+ /* need to unambiguously identify the solution */
+ is_odd = crypto_bignum_is_odd(rnd);
+
+ /*
+ * We know x_candidate is a quadratic residue so set
+ * it here.
+ */
+ if (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");
continue;
}
- if (crypto_ec_point_is_at_infinity(grp->group,
- grp->pwe)) {
- wpa_printf(MSG_INFO, "EAP-pwd: point is at "
- "infinity");
+
+ /*
+ * 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");
continue;
}
+
+ 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");
+ continue;
+ }
+ if (crypto_ec_point_is_at_infinity(grp->group,
+ grp->pwe)) {
+ wpa_printf(MSG_INFO,
+ "EAP-pwd: point is at infinity");
+ continue;
+ }
+ }
+ wpa_printf(MSG_DEBUG,
+ "EAP-pwd: found a PWE in %d tries", ctr);
+ found = 1;
}
- /* if we got here then we have a new generator. */
- break;
}
- wpa_printf(MSG_DEBUG, "EAP-pwd: found a PWE in %d tries", ctr);
+ 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;
+ }
if (0) {
fail:
crypto_ec_point_deinit(grp->pwe, 1);
@@ -261,6 +344,12 @@ int compute_password_element(EAP_PWD_gro
crypto_bignum_deinit(cofactor, 1);
crypto_bignum_deinit(x_candidate, 1);
crypto_bignum_deinit(rnd, 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(one, 0);
os_free(prfbuf);
return ret;
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