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Copy pathotrv4_idake_deniable.pv.out
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otrv4_idake_deniable.pv.out
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Linear part:
ec_mul(x,ec_mul(y,ec_base)) = ec_mul(y,ec_mul(x,ec_base))
Completing equations...
Completed equations:
ec_mul(x,ec_mul(y,ec_base)) = ec_mul(y,ec_mul(x,ec_base))
Convergent part:
Completing equations...
Completed equations:
Biprocess:
{1}new h1: eddsa_private_key;
{2}new f1: ec_scalar;
{3}let H1: ec_point = ec_mul(eddsa_scalar(h1),ec_base) in
{4}let F1: ec_point = ec_mul(f1,ec_base) in
{5}let cp1: eddsa_signature = eddsa_sign(h1,(H1,F1)) in
{6}new h2: eddsa_private_key;
{7}new f2: ec_scalar;
{8}let H2: ec_point = ec_mul(eddsa_scalar(h2),ec_base) in
{9}let F2: ec_point = ec_mul(f2,ec_base) in
{10}let cp2: eddsa_signature = eddsa_sign(h2,(H2,F2)) in
{11}out(c, (cp1,cp2));
(
{12}!
{13}new y_68: ec_scalar;
{14}let Y: ec_point = ec_mul(y_68,ec_base) in
{15}out(c, Y);
{16}new x_69: ec_scalar;
{17}let X: ec_point = ec_mul(x_69,ec_base) in
{18}let ta: bitstring = (zero,cp2,cp1,Y,X,id2,id1) in
{19}let ka: bitstring = kdf(usageSharedSecret,ec_point_as_bits(ec_mul(x_69,Y))) in
{20}let ssid_a: bitstring = kdf(usageSSID,ka) in
{21}out(c, ssid_a);
{22}let priv_a: ec_scalar = choice[eddsa_scalar(h1),y_68] in
{23}let pub_a: ec_point = choice[Y,H1] in
{24}new r_70: coins;
{25}let sigma_a: ring_signature = internal_ring_sign(priv_a,F2,pub_a,ta,r_70) in
{26}out(c, sigma_a);
{27}let tb: bitstring = (one,cp2,cp1,Y,X,id2,id1) in
{28}let kb: bitstring = kdf(usageSharedSecret,ec_point_as_bits(ec_mul(y_68,X))) in
{29}let ssid_b: bitstring = kdf(usageSSID,kb) in
{30}out(c, ssid_b);
{31}let priv_b: ec_scalar = choice[eddsa_scalar(h2),x_69] in
{32}let pub_b: ec_point = choice[X,H2] in
{33}new r_71: coins;
{34}let sigma_b: ring_signature = internal_ring_sign(priv_b,F1,pub_b,tb,r_71) in
{35}new z: ec_scalar;
{36}let Z: ec_point = ec_mul(z,ec_base) in
{37}let kmac: bitstring = kdf(usageMACKey,kb) in
{38}let Z_mac: bitstring = kdf(usageAuthenticator,(kmac,ec_point_as_bits(Z))) in
{39}out(c, (sigma_b,Z,Z_mac));
{40}out(c, (ka,kb))
) | (
{41}phase 1;
{42}out(c, (h1,f1,h2,f2))
)
-- Observational equivalence
Termination warning: v_7539 <> v_7540 && attacker2_tag_p1(v_7538,v_7539) && attacker2_tag_p1(v_7538,v_7540) -> bad
Selecting 0
Termination warning: v_7542 <> v_7543 && attacker2_tag_p1(v_7542,v_7541) && attacker2_tag_p1(v_7543,v_7541) -> bad
Selecting 0
Termination warning: v_7546 <> v_7547 && attacker2_ring_signature_p1(v_7545,v_7546) && attacker2_ring_signature_p1(v_7545,v_7547) -> bad
Selecting 0
Termination warning: v_7549 <> v_7550 && attacker2_ring_signature_p1(v_7549,v_7548) && attacker2_ring_signature_p1(v_7550,v_7548) -> bad
Selecting 0
Termination warning: v_7553 <> v_7554 && attacker2_identity_p1(v_7552,v_7553) && attacker2_identity_p1(v_7552,v_7554) -> bad
Selecting 0
Termination warning: v_7556 <> v_7557 && attacker2_identity_p1(v_7556,v_7555) && attacker2_identity_p1(v_7557,v_7555) -> bad
Selecting 0
Termination warning: v_7560 <> v_7561 && attacker2_eddsa_signature_p1(v_7559,v_7560) && attacker2_eddsa_signature_p1(v_7559,v_7561) -> bad
Selecting 0
Termination warning: v_7563 <> v_7564 && attacker2_eddsa_signature_p1(v_7563,v_7562) && attacker2_eddsa_signature_p1(v_7564,v_7562) -> bad
Selecting 0
Termination warning: v_7567 <> v_7568 && attacker2_eddsa_private_key_p1(v_7566,v_7567) && attacker2_eddsa_private_key_p1(v_7566,v_7568) -> bad
Selecting 0
Termination warning: v_7570 <> v_7571 && attacker2_eddsa_private_key_p1(v_7570,v_7569) && attacker2_eddsa_private_key_p1(v_7571,v_7569) -> bad
Selecting 0
Termination warning: v_7574 <> v_7575 && attacker2_ec_scalar_p1(v_7573,v_7574) && attacker2_ec_scalar_p1(v_7573,v_7575) -> bad
Selecting 0
Termination warning: v_7577 <> v_7578 && attacker2_ec_scalar_p1(v_7577,v_7576) && attacker2_ec_scalar_p1(v_7578,v_7576) -> bad
Selecting 0
Termination warning: v_7581 <> v_7582 && attacker2_ec_point_p1(v_7580,v_7581) && attacker2_ec_point_p1(v_7580,v_7582) -> bad
Selecting 0
Termination warning: v_7584 <> v_7585 && attacker2_ec_point_p1(v_7584,v_7583) && attacker2_ec_point_p1(v_7585,v_7583) -> bad
Selecting 0
Termination warning: v_7588 <> v_7589 && attacker2_coins_p1(v_7587,v_7588) && attacker2_coins_p1(v_7587,v_7589) -> bad
Selecting 0
Termination warning: v_7591 <> v_7592 && attacker2_coins_p1(v_7591,v_7590) && attacker2_coins_p1(v_7592,v_7590) -> bad
Selecting 0
Termination warning: v_7595 <> v_7596 && attacker2_channel_p1(v_7594,v_7595) && attacker2_channel_p1(v_7594,v_7596) -> bad
Selecting 0
Termination warning: v_7598 <> v_7599 && attacker2_channel_p1(v_7598,v_7597) && attacker2_channel_p1(v_7599,v_7597) -> bad
Selecting 0
Termination warning: v_7602 <> v_7603 && attacker2_bool_p1(v_7601,v_7602) && attacker2_bool_p1(v_7601,v_7603) -> bad
Selecting 0
Termination warning: v_7605 <> v_7606 && attacker2_bool_p1(v_7605,v_7604) && attacker2_bool_p1(v_7606,v_7604) -> bad
Selecting 0
Termination warning: v_7609 <> v_7610 && attacker2_bitstring_p1(v_7608,v_7609) && attacker2_bitstring_p1(v_7608,v_7610) -> bad
Selecting 0
Termination warning: v_7612 <> v_7613 && attacker2_bitstring_p1(v_7612,v_7611) && attacker2_bitstring_p1(v_7613,v_7611) -> bad
Selecting 0
Completing...
200 rules inserted. The rule base contains 200 rules. 334 rules in the queue.
400 rules inserted. The rule base contains 400 rules. 143 rules in the queue.
Termination warning: v_7539 <> v_7540 && attacker2_tag_p1(v_7538,v_7539) && attacker2_tag_p1(v_7538,v_7540) -> bad
Selecting 0
Termination warning: v_7542 <> v_7543 && attacker2_tag_p1(v_7542,v_7541) && attacker2_tag_p1(v_7543,v_7541) -> bad
Selecting 0
Termination warning: v_7546 <> v_7547 && attacker2_ring_signature_p1(v_7545,v_7546) && attacker2_ring_signature_p1(v_7545,v_7547) -> bad
Selecting 0
Termination warning: v_7549 <> v_7550 && attacker2_ring_signature_p1(v_7549,v_7548) && attacker2_ring_signature_p1(v_7550,v_7548) -> bad
Selecting 0
Termination warning: v_7553 <> v_7554 && attacker2_identity_p1(v_7552,v_7553) && attacker2_identity_p1(v_7552,v_7554) -> bad
Selecting 0
Termination warning: v_7556 <> v_7557 && attacker2_identity_p1(v_7556,v_7555) && attacker2_identity_p1(v_7557,v_7555) -> bad
Selecting 0
Termination warning: v_7560 <> v_7561 && attacker2_eddsa_signature_p1(v_7559,v_7560) && attacker2_eddsa_signature_p1(v_7559,v_7561) -> bad
Selecting 0
Termination warning: v_7563 <> v_7564 && attacker2_eddsa_signature_p1(v_7563,v_7562) && attacker2_eddsa_signature_p1(v_7564,v_7562) -> bad
Selecting 0
Termination warning: v_7567 <> v_7568 && attacker2_eddsa_private_key_p1(v_7566,v_7567) && attacker2_eddsa_private_key_p1(v_7566,v_7568) -> bad
Selecting 0
Termination warning: v_7570 <> v_7571 && attacker2_eddsa_private_key_p1(v_7570,v_7569) && attacker2_eddsa_private_key_p1(v_7571,v_7569) -> bad
Selecting 0
Termination warning: v_7574 <> v_7575 && attacker2_ec_scalar_p1(v_7573,v_7574) && attacker2_ec_scalar_p1(v_7573,v_7575) -> bad
Selecting 0
Termination warning: v_7577 <> v_7578 && attacker2_ec_scalar_p1(v_7577,v_7576) && attacker2_ec_scalar_p1(v_7578,v_7576) -> bad
Selecting 0
Termination warning: v_7581 <> v_7582 && attacker2_ec_point_p1(v_7580,v_7581) && attacker2_ec_point_p1(v_7580,v_7582) -> bad
Selecting 0
Termination warning: v_7584 <> v_7585 && attacker2_ec_point_p1(v_7584,v_7583) && attacker2_ec_point_p1(v_7585,v_7583) -> bad
Selecting 0
Termination warning: v_7588 <> v_7589 && attacker2_coins_p1(v_7587,v_7588) && attacker2_coins_p1(v_7587,v_7589) -> bad
Selecting 0
Termination warning: v_7591 <> v_7592 && attacker2_coins_p1(v_7591,v_7590) && attacker2_coins_p1(v_7592,v_7590) -> bad
Selecting 0
Termination warning: v_7595 <> v_7596 && attacker2_channel_p1(v_7594,v_7595) && attacker2_channel_p1(v_7594,v_7596) -> bad
Selecting 0
Termination warning: v_7598 <> v_7599 && attacker2_channel_p1(v_7598,v_7597) && attacker2_channel_p1(v_7599,v_7597) -> bad
Selecting 0
Termination warning: v_7602 <> v_7603 && attacker2_bool_p1(v_7601,v_7602) && attacker2_bool_p1(v_7601,v_7603) -> bad
Selecting 0
Termination warning: v_7605 <> v_7606 && attacker2_bool_p1(v_7605,v_7604) && attacker2_bool_p1(v_7606,v_7604) -> bad
Selecting 0
Termination warning: v_7609 <> v_7610 && attacker2_bitstring_p1(v_7608,v_7609) && attacker2_bitstring_p1(v_7608,v_7610) -> bad
Selecting 0
Termination warning: v_7612 <> v_7613 && attacker2_bitstring_p1(v_7612,v_7611) && attacker2_bitstring_p1(v_7613,v_7611) -> bad
Selecting 0
600 rules inserted. The rule base contains 594 rules. 208 rules in the queue.
Termination warning: v_32298 <> v_32299 && attacker2_tag(v_32297,v_32298) && attacker2_tag_p1(v_32297,v_32299) -> bad
Selecting 0
Termination warning: v_32315 <> v_32317 && attacker2_tag(v_32315,v_32316) && attacker2_tag_p1(v_32317,v_32316) -> bad
Selecting 0
Termination warning: v_32334 <> v_32335 && attacker2_ring_signature(v_32333,v_32334) && attacker2_ring_signature_p1(v_32333,v_32335) -> bad
Selecting 0
Termination warning: v_32347 <> v_32349 && attacker2_ring_signature(v_32347,v_32348) && attacker2_ring_signature_p1(v_32349,v_32348) -> bad
Selecting 0
Termination warning: v_32362 <> v_32363 && attacker2_identity(v_32361,v_32362) && attacker2_identity_p1(v_32361,v_32363) -> bad
Selecting 0
Termination warning: v_32364 <> v_32366 && attacker2_identity(v_32364,v_32365) && attacker2_identity_p1(v_32366,v_32365) -> bad
Selecting 0
Termination warning: v_32368 <> v_32369 && attacker2_eddsa_signature(v_32367,v_32368) && attacker2_eddsa_signature_p1(v_32367,v_32369) -> bad
Selecting 0
Termination warning: v_32375 <> v_32377 && attacker2_eddsa_signature(v_32375,v_32376) && attacker2_eddsa_signature_p1(v_32377,v_32376) -> bad
Selecting 0
Termination warning: v_32384 <> v_32385 && attacker2_eddsa_private_key(v_32383,v_32384) && attacker2_eddsa_private_key_p1(v_32383,v_32385) -> bad
Selecting 0
Termination warning: v_32386 <> v_32388 && attacker2_eddsa_private_key(v_32386,v_32387) && attacker2_eddsa_private_key_p1(v_32388,v_32387) -> bad
Selecting 0
Termination warning: v_32390 <> v_32391 && attacker2_ec_scalar(v_32389,v_32390) && attacker2_ec_scalar_p1(v_32389,v_32391) -> bad
Selecting 0
Termination warning: v_32395 <> v_32397 && attacker2_ec_scalar(v_32395,v_32396) && attacker2_ec_scalar_p1(v_32397,v_32396) -> bad
Selecting 0
Termination warning: v_32402 <> v_32403 && attacker2_ec_point(v_32401,v_32402) && attacker2_ec_point_p1(v_32401,v_32403) -> bad
Selecting 0
Termination warning: v_32410 <> v_32412 && attacker2_ec_point(v_32410,v_32411) && attacker2_ec_point_p1(v_32412,v_32411) -> bad
Selecting 0
Termination warning: v_32420 <> v_32421 && attacker2_coins(v_32419,v_32420) && attacker2_coins_p1(v_32419,v_32421) -> bad
Selecting 0
Termination warning: v_32422 <> v_32424 && attacker2_coins(v_32422,v_32423) && attacker2_coins_p1(v_32424,v_32423) -> bad
Selecting 0
Termination warning: v_32426 <> v_32427 && attacker2_channel(v_32425,v_32426) && attacker2_channel_p1(v_32425,v_32427) -> bad
Selecting 0
Termination warning: v_32428 <> v_32430 && attacker2_channel(v_32428,v_32429) && attacker2_channel_p1(v_32430,v_32429) -> bad
Selecting 0
Termination warning: v_32432 <> v_32433 && attacker2_bool(v_32431,v_32432) && attacker2_bool_p1(v_32431,v_32433) -> bad
Selecting 0
Termination warning: v_32436 <> v_32438 && attacker2_bool(v_32436,v_32437) && attacker2_bool_p1(v_32438,v_32437) -> bad
Selecting 0
Termination warning: v_32442 <> v_32443 && attacker2_bitstring(v_32441,v_32442) && attacker2_bitstring_p1(v_32441,v_32443) -> bad
Selecting 0
Termination warning: v_32535 <> v_32537 && attacker2_bitstring(v_32535,v_32536) && attacker2_bitstring_p1(v_32537,v_32536) -> bad
Selecting 0
Termination warning: v_33130 <> v_33131 && attacker2_channel(v_33129,v_33130) && attacker2_channel(v_33129,v_33131) -> bad
Selecting 0
Termination warning: v_33132 <> v_33134 && attacker2_channel(v_33132,v_33133) && attacker2_channel(v_33134,v_33133) -> bad
Selecting 0
800 rules inserted. The rule base contains 782 rules. 367 rules in the queue.
1000 rules inserted. The rule base contains 978 rules. 400 rules in the queue.
1200 rules inserted. The rule base contains 1174 rules. 532 rules in the queue.
1400 rules inserted. The rule base contains 1370 rules. 590 rules in the queue.
1600 rules inserted. The rule base contains 1570 rules. 658 rules in the queue.
1800 rules inserted. The rule base contains 1770 rules. 600 rules in the queue.
2000 rules inserted. The rule base contains 1970 rules. 563 rules in the queue.
2200 rules inserted. The rule base contains 2170 rules. 511 rules in the queue.
2400 rules inserted. The rule base contains 2370 rules. 484 rules in the queue.
2600 rules inserted. The rule base contains 2570 rules. 435 rules in the queue.
2800 rules inserted. The rule base contains 2770 rules. 357 rules in the queue.
3000 rules inserted. The rule base contains 2960 rules. 370 rules in the queue.
3200 rules inserted. The rule base contains 3118 rules. 280 rules in the queue.
3400 rules inserted. The rule base contains 3318 rules. 239 rules in the queue.
3600 rules inserted. The rule base contains 3476 rules. 205 rules in the queue.
3800 rules inserted. The rule base contains 3660 rules. 188 rules in the queue.
4000 rules inserted. The rule base contains 3844 rules. 174 rules in the queue.
4200 rules inserted. The rule base contains 4036 rules. 198 rules in the queue.
4400 rules inserted. The rule base contains 4232 rules. 218 rules in the queue.
4600 rules inserted. The rule base contains 4432 rules. 168 rules in the queue.
4800 rules inserted. The rule base contains 4618 rules. 57 rules in the queue.
RESULT Observational equivalence is true (bad not derivable).