Replace GFp ladder implementation with ladd-2002-it-4 from EFD
The EFD database does not state that the "ladd-2002-it-3" algorithm assumes X1 != 0. Consequently the current implementation, based on it, fails to compute correctly if the affine x coordinate of the scalar multiplication input point is 0. We replace this implementation using the alternative algorithm based on Eq. (9) and (10) from the same paper, which being derived from the additive relation of (6) does not incur in this problem, but costs one extra field multiplication. The EFD entry for this algorithm is at https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-ladd-2002-it-4 and the code to implement it was generated with tooling. Regression tests add one positive test for each named curve that has such a point. The `SharedSecret` was generated independently from the OpenSSL codebase with sage. This bug was originally reported by Dmitry Belyavsky on the openssl-users maling list: https://mta.openssl.org/pipermail/openssl-users/2018-August/008540.html Co-authored-by: Billy Brumley <bbrumley@gmail.com> Reviewed-by: Andy Polyakov <appro@openssl.org> Reviewed-by: Tim Hudson <tjh@openssl.org> (Merged from https://github.com/openssl/openssl/pull/7000)
This commit is contained in:
Nicola Tuveri
Matt Caswell
parent
e97be71804
commit
5d92b853f6
2 changed files with 270 additions and 30 deletions
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@ -1483,10 +1483,10 @@ int ec_GFp_simple_ladder_pre(const EC_GROUP *group,
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}
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/*-
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* Differential addition-and-doubling using Eq. (8) and (10) from Izu-Takagi
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* Differential addition-and-doubling using Eq. (9) and (10) from Izu-Takagi
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* "A fast parallel elliptic curve multiplication resistant against side channel
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* attacks", as described at
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* https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-ladd-2002-it-3
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* https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-ladd-2002-it-4
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*/
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int ec_GFp_simple_ladder_step(const EC_GROUP *group,
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EC_POINT *r, EC_POINT *s,
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@ -1511,39 +1511,42 @@ int ec_GFp_simple_ladder_step(const EC_GROUP *group,
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|| !group->meth->field_mul(group, t2, r->X, s->Z, ctx)
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|| !group->meth->field_mul(group, t3, r->Z, s->X, ctx)
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|| !group->meth->field_mul(group, t4, group->a, t1, ctx)
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|| !BN_mod_sub_quick(t4, t0, t4, group->field)
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|| !BN_mod_add_quick(t5, t3, t2, group->field)
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|| !group->meth->field_sqr(group, t4, t4, ctx)
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|| !group->meth->field_mul(group, t5, t1, t5, ctx)
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|| !BN_mod_lshift_quick(t0, group->b, 2, group->field)
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|| !group->meth->field_mul(group, t5, t0, t5, ctx)
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|| !BN_mod_sub_quick(t5, t4, t5, group->field)
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|| !BN_mod_add_quick(t0, t0, t4, group->field)
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|| !BN_mod_add_quick(t4, t3, t2, group->field)
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|| !group->meth->field_mul(group, t0, t4, t0, ctx)
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|| !group->meth->field_sqr(group, t1, t1, ctx)
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|| !BN_mod_lshift_quick(t7, group->b, 2, group->field)
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|| !group->meth->field_mul(group, t1, t7, t1, ctx)
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|| !BN_mod_lshift1_quick(t0, t0, group->field)
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|| !BN_mod_add_quick(t0, t1, t0, group->field)
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|| !BN_mod_sub_quick(t1, t2, t3, group->field)
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|| !group->meth->field_sqr(group, t1, t1, ctx)
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|| !group->meth->field_mul(group, t3, t1, p->X, ctx)
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|| !group->meth->field_mul(group, t0, p->Z, t0, ctx)
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/* s->X coord output */
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|| !group->meth->field_mul(group, s->X, t5, p->Z, ctx)
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|| !BN_mod_sub_quick(t3, t2, t3, group->field)
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|| !group->meth->field_sqr(group, t3, t3, ctx)
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|| !BN_mod_sub_quick(s->X, t0, t3, group->field)
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/* s->Z coord output */
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|| !group->meth->field_mul(group, s->Z, t3, p->X, ctx)
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|| !group->meth->field_sqr(group, t2, r->X, ctx)
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|| !group->meth->field_sqr(group, t4, r->Z, ctx)
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|| !group->meth->field_mul(group, t1, t4, group->a, ctx)
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|| !BN_mod_add_quick(t6, r->X, r->Z, group->field)
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|| !group->meth->field_mul(group, s->Z, p->Z, t1, ctx)
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|| !group->meth->field_sqr(group, t3, r->X, ctx)
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|| !group->meth->field_sqr(group, t2, r->Z, ctx)
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|| !group->meth->field_mul(group, t4, t2, group->a, ctx)
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|| !BN_mod_add_quick(t5, r->X, r->Z, group->field)
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|| !group->meth->field_sqr(group, t5, t5, ctx)
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|| !BN_mod_sub_quick(t5, t5, t3, group->field)
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|| !BN_mod_sub_quick(t5, t5, t2, group->field)
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|| !BN_mod_sub_quick(t6, t3, t4, group->field)
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|| !group->meth->field_sqr(group, t6, t6, ctx)
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|| !BN_mod_sub_quick(t6, t6, t2, group->field)
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|| !BN_mod_sub_quick(t6, t6, t4, group->field)
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|| !BN_mod_sub_quick(t7, t2, t1, group->field)
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|| !group->meth->field_sqr(group, t7, t7, ctx)
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|| !group->meth->field_mul(group, t5, t4, t6, ctx)
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|| !group->meth->field_mul(group, t5, t0, t5, ctx)
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|| !group->meth->field_mul(group, t0, t2, t5, ctx)
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|| !group->meth->field_mul(group, t0, t7, t0, ctx)
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/* r->X coord output */
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|| !BN_mod_sub_quick(r->X, t7, t5, group->field)
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|| !BN_mod_add_quick(t2, t2, t1, group->field)
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|| !group->meth->field_sqr(group, t5, t4, ctx)
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|| !group->meth->field_mul(group, t5, t5, t0, ctx)
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|| !group->meth->field_mul(group, t6, t6, t2, ctx)
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|| !BN_mod_lshift1_quick(t6, t6, group->field)
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|| !BN_mod_sub_quick(r->X, t6, t0, group->field)
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|| !BN_mod_add_quick(t6, t3, t4, group->field)
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|| !group->meth->field_sqr(group, t3, t2, ctx)
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|| !group->meth->field_mul(group, t7, t3, t7, ctx)
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|| !group->meth->field_mul(group, t5, t5, t6, ctx)
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|| !BN_mod_lshift1_quick(t5, t5, group->field)
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/* r->Z coord output */
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|| !BN_mod_add_quick(r->Z, t5, t6, group->field))
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|| !BN_mod_add_quick(r->Z, t7, t5, group->field))
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goto err;
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ret = 1;
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@ -4364,3 +4364,240 @@ PeerKey=ALICE_cf_wap-wsg-idm-ecid-wtls9_PUB
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SharedSecret=948d3030e95cead39a1bb3d8a01c2be178517ba7
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# tests: 484
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Title=zero x-coord regression tests
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PrivateKey=ALICE_zero_prime192v1
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-----BEGIN PRIVATE KEY-----
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MDkCAQAwEwYHKoZIzj0CAQYIKoZIzj0DAQEEHzAdAgEBBBhaPNk8jG5hSG6y8tUqUoOaNNsZ3APU
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pps=
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-----END PRIVATE KEY-----
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PublicKey=BOB_zero_prime192v1_PUB
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-----BEGIN PUBLIC KEY-----
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MEkwEwYHKoZIzj0CAQYIKoZIzj0DAQEDMgAEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAe2hWBe5g
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DLNj216pEvK7XjoKLg5gNg8S
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-----END PUBLIC KEY-----
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# ECDH Alice with Bob peer
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Derive=ALICE_zero_prime192v1
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PeerKey=BOB_zero_prime192v1_PUB
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SharedSecret=baaffd49a8399d2ad52cbbe24d47b67afb4b3cf436f1cd65
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PrivateKey=ALICE_zero_prime192v2
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-----BEGIN PRIVATE KEY-----
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MDkCAQAwEwYHKoZIzj0CAQYIKoZIzj0DAQIEHzAdAgEBBBj1AIQMJ7jqYIKCvxYAS+qKMmKmH0to
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41k=
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-----END PRIVATE KEY-----
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PublicKey=BOB_zero_prime192v2_PUB
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-----BEGIN PUBLIC KEY-----
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MEkwEwYHKoZIzj0CAQYIKoZIzj0DAQIDMgAEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAB4Gj7Qqt
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2wx/jwFlKgvE4rnd50LspdMk
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-----END PUBLIC KEY-----
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# ECDH Alice with Bob peer
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Derive=ALICE_zero_prime192v2
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PeerKey=BOB_zero_prime192v2_PUB
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SharedSecret=b8f200a4b87064f2e8600685ca3e69b8e661a117aabc770b
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PrivateKey=ALICE_zero_prime192v3
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-----BEGIN PRIVATE KEY-----
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MDkCAQAwEwYHKoZIzj0CAQYIKoZIzj0DAQMEHzAdAgEBBBh/maLQMSlea9BfLqGy5NPuK0YAH/cz
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GqI=
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-----END PRIVATE KEY-----
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PublicKey=BOB_zero_prime192v3_PUB
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-----BEGIN PUBLIC KEY-----
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MEkwEwYHKoZIzj0CAQYIKoZIzj0DAQMDMgAEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAZEzb63e2
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3MKatRLR9Y1M5JEdI9jwMocI
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-----END PUBLIC KEY-----
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# ECDH Alice with Bob peer
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Derive=ALICE_zero_prime192v3
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PeerKey=BOB_zero_prime192v3_PUB
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SharedSecret=b5de857d355bc5b9e270a4c290ea9728d764d8b243ff5d8d
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PrivateKey=ALICE_zero_prime239v1
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-----BEGIN PRIVATE KEY-----
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MD8CAQAwEwYHKoZIzj0CAQYIKoZIzj0DAQQEJTAjAgEBBB5pYWzRYI+c6O7NXCt0H2kw8XRL3rhe
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4MrJT8j++CI=
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-----END PRIVATE KEY-----
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PublicKey=BOB_zero_prime239v1_PUB
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-----BEGIN PUBLIC KEY-----
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MFUwEwYHKoZIzj0CAQYIKoZIzj0DAQQDPgAEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
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Ox02uwNNLFuvDRn5ip8TxvW0W22R7UzJa9Av6/nh
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-----END PUBLIC KEY-----
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# ECDH Alice with Bob peer
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Derive=ALICE_zero_prime239v1
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PeerKey=BOB_zero_prime239v1_PUB
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SharedSecret=6b6206408bd05d42daa2cd224c401a1230b44e184f17b82f385f22dac215
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PrivateKey=ALICE_zero_prime239v2
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-----BEGIN PRIVATE KEY-----
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MD8CAQAwEwYHKoZIzj0CAQYIKoZIzj0DAQUEJTAjAgEBBB5l8bB7Cpmr7vyx9FiOT2wEF3YOFbDG
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bmRr3Vi/xr4=
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-----END PRIVATE KEY-----
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PublicKey=BOB_zero_prime239v2_PUB
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-----BEGIN PUBLIC KEY-----
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MFUwEwYHKoZIzj0CAQYIKoZIzj0DAQUDPgAEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
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IOg3VJGQ89d1GWg4Igxcj5xpDmJiP8tv+e4mxt5U
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-----END PUBLIC KEY-----
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# ECDH Alice with Bob peer
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Derive=ALICE_zero_prime239v2
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PeerKey=BOB_zero_prime239v2_PUB
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SharedSecret=772c2819c960c78f28f21f6542b7409294fad1f84567c44c4b7678dc0e42
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PrivateKey=ALICE_zero_prime239v3
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-----BEGIN PRIVATE KEY-----
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MD8CAQAwEwYHKoZIzj0CAQYIKoZIzj0DAQYEJTAjAgEBBB5HF5FABzUOTYMZg9UdZTx/oRERm/fU
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M/+otKzpLjA=
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-----END PRIVATE KEY-----
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PublicKey=BOB_zero_prime239v3_PUB
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-----BEGIN PUBLIC KEY-----
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MFUwEwYHKoZIzj0CAQYIKoZIzj0DAQYDPgAEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
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AsZ4u6r3qQI78EYBpiSgWjqNpoeShjr5piecMBWj
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-----END PUBLIC KEY-----
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# ECDH Alice with Bob peer
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Derive=ALICE_zero_prime239v3
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PeerKey=BOB_zero_prime239v3_PUB
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SharedSecret=56a71f5dd1611e8032c3e2d8224d86e5e8c2fc6480d74c0e282282decd43
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PrivateKey=ALICE_zero_prime256v1
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-----BEGIN PRIVATE KEY-----
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MEECAQAwEwYHKoZIzj0CAQYIKoZIzj0DAQcEJzAlAgEBBCDXhMb6aR4JR2+l2tmgYqP0r8S4jtym
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yH++awvF2nGhhg==
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-----END PRIVATE KEY-----
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PublicKey=BOB_zero_prime256v1_PUB
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-----BEGIN PUBLIC KEY-----
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MFkwEwYHKoZIzj0CAQYIKoZIzj0DAQcDQgAEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
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AABmSFx4Di+D1yQzvV2EoGu2VBwq8x2uhxcov4VqF0+T9A==
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-----END PUBLIC KEY-----
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# ECDH Alice with Bob peer
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Derive=ALICE_zero_prime256v1
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PeerKey=BOB_zero_prime256v1_PUB
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SharedSecret=c4f5607deb8501f1a4ba23fce4122a4343a17ada2c86a9c8e0d03d92d4a4c84c
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PrivateKey=ALICE_zero_secp112r2
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-----BEGIN PRIVATE KEY-----
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MCwCAQAwEAYHKoZIzj0CAQYFK4EEAAcEFTATAgEBBA4hh3tRkG3tnA0496ffMw==
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-----END PRIVATE KEY-----
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PublicKey=BOB_zero_secp112r2_PUB
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-----BEGIN PUBLIC KEY-----
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MDIwEAYHKoZIzj0CAQYFK4EEAAcDHgAEAAAAAAAAAAAAAAAAAAAS5eEOWDV/Wk7w4djyDQ==
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-----END PUBLIC KEY-----
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# ECDH Alice with Bob peer
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Derive=ALICE_zero_secp112r2
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PeerKey=BOB_zero_secp112r2_PUB
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SharedSecret=958cc1cb425713678830a4d7d95e
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PrivateKey=ALICE_zero_secp128r1
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-----BEGIN PRIVATE KEY-----
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MC4CAQAwEAYHKoZIzj0CAQYFK4EEABwEFzAVAgEBBBCykSzic/h3T2K6SkSP1SGt
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-----END PRIVATE KEY-----
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PublicKey=BOB_zero_secp128r1_PUB
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-----BEGIN PUBLIC KEY-----
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MDYwEAYHKoZIzj0CAQYFK4EEABwDIgAEAAAAAAAAAAAAAAAAAAAAAABya8M5aeOpNG3z799IdHc=
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-----END PUBLIC KEY-----
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# ECDH Alice with Bob peer
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Derive=ALICE_zero_secp128r1
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PeerKey=BOB_zero_secp128r1_PUB
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SharedSecret=5235d452066f126cd7e99eea00fd3068
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PrivateKey=ALICE_zero_secp160r1
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-----BEGIN PRIVATE KEY-----
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MDMCAQAwEAYHKoZIzj0CAQYFK4EEAAgEHDAaAgEBBBUACoRnbig69XLlh5VcRexpbbn5zwA=
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-----END PRIVATE KEY-----
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PublicKey=BOB_zero_secp160r1_PUB
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-----BEGIN PUBLIC KEY-----
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MD4wEAYHKoZIzj0CAQYFK4EEAAgDKgAEAAAAAAAAAAAAAAAAAAAAAAAAAAAG/w1po29wYlxlygXs
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MGfbiGg5ng==
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-----END PUBLIC KEY-----
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# ECDH Alice with Bob peer
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Derive=ALICE_zero_secp160r1
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PeerKey=BOB_zero_secp160r1_PUB
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SharedSecret=9ccd0ab8d093b6acdb3fe14c3736a0dfe61a4666
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PrivateKey=ALICE_zero_secp160r2
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-----BEGIN PRIVATE KEY-----
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MDMCAQAwEAYHKoZIzj0CAQYFK4EEAB4EHDAaAgEBBBUAQFGxInSw1eAvd45E9TUdbXtJGnA=
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-----END PRIVATE KEY-----
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PublicKey=BOB_zero_secp160r2_PUB
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-----BEGIN PUBLIC KEY-----
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MD4wEAYHKoZIzj0CAQYFK4EEAB4DKgAEAAAAAAAAAAAAAAAAAAAAAAAAAAAZtSBSZqfmXp47v5z2
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ZZZl2JFxDg==
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-----END PUBLIC KEY-----
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# ECDH Alice with Bob peer
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Derive=ALICE_zero_secp160r2
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PeerKey=BOB_zero_secp160r2_PUB
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SharedSecret=303e0a282ac86f463fe834cb51b0057be42ed5ab
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PrivateKey=ALICE_zero_secp384r1
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-----BEGIN PRIVATE KEY-----
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ME4CAQAwEAYHKoZIzj0CAQYFK4EEACIENzA1AgEBBDD6kgzKbg28zbQyVTdC0IdHbm0UCQt2Rdbi
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VVHJeYRSnNpFOiFLaOsGOmwoeZzj6jc=
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-----END PRIVATE KEY-----
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PublicKey=BOB_zero_secp384r1_PUB
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-----BEGIN PUBLIC KEY-----
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MHYwEAYHKoZIzj0CAQYFK4EEACIDYgAEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
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AAAAAAAAAAAAAAAAAAAAPPme8E9RpepjC6P5+WDdWToUyb45/SvSFdO0sIqq+Gu/kn8sRuUqsG+3
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QriFDlIe
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-----END PUBLIC KEY-----
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# ECDH Alice with Bob peer
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Derive=ALICE_zero_secp384r1
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PeerKey=BOB_zero_secp384r1_PUB
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SharedSecret=b1cfeaeef51dfd487d3a8b2849f1592e04d63f2d2c88b310a6290ebfe5399f5ffe954eabd0619231393e56c35b242986
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PrivateKey=ALICE_zero_secp521r1
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-----BEGIN PRIVATE KEY-----
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MGACAQAwEAYHKoZIzj0CAQYFK4EEACMESTBHAgEBBEIAbddDLMUWbAsY7l3vbNDmntXuAUcDYPg5
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w/cgUwSCIvrV9MBeSG8AWqT16riHmHlsn+XI5PAJM6eij3JDahnu9Mo=
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-----END PRIVATE KEY-----
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PublicKey=BOB_zero_secp521r1_PUB
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-----BEGIN PUBLIC KEY-----
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MIGbMBAGByqGSM49AgEGBSuBBAAjA4GGAAQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA0g7J/qa1d8ENJsobtEb0CymeZIsa
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1Qiq0GiJb+4/jmFLxjBU1Xcr8Bpl1BLgvKqOll0vXTMtfzn4RtRArgAfT4c=
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-----END PUBLIC KEY-----
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# ECDH Alice with Bob peer
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Derive=ALICE_zero_secp521r1
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PeerKey=BOB_zero_secp521r1_PUB
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SharedSecret=003fc3028f61db94b20c7cd177923b6e73f12f0ab067c9ce8866755e3c82abb39c9863cde74fa80b32520bd7dd0eb156c30c08911503b67b2661f1264d09bb231423
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PrivateKey=ALICE_zero_wap-wsg-idm-ecid-wtls7
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-----BEGIN PRIVATE KEY-----
|
||||
MDMCAQAwEAYHKoZIzj0CAQYFZysBBAcEHDAaAgEBBBUAoGng7WzYr4P9vtdc3BS/UiNWmc0=
|
||||
-----END PRIVATE KEY-----
|
||||
|
||||
PublicKey=BOB_zero_wap-wsg-idm-ecid-wtls7_PUB
|
||||
-----BEGIN PUBLIC KEY-----
|
||||
MD4wEAYHKoZIzj0CAQYFZysBBAcDKgAEAAAAAAAAAAAAAAAAAAAAAAAAAAAZtSBSZqfmXp47v5z2
|
||||
ZZZl2JFxDg==
|
||||
-----END PUBLIC KEY-----
|
||||
|
||||
# ECDH Alice with Bob peer
|
||||
Derive=ALICE_zero_wap-wsg-idm-ecid-wtls7
|
||||
PeerKey=BOB_zero_wap-wsg-idm-ecid-wtls7_PUB
|
||||
SharedSecret=6582fc03bbb340fcf24a5fe8fcdf722655efa8b9
|
||||
|
||||
# tests: 14
|
||||
|
|
|
|||
Loading…
Reference in a new issue