From a457d827937593818871e8c6b267f8129c06f46b Mon Sep 17 00:00:00 2001 From: Kevin Lewi Date: Fri, 19 Feb 2021 12:02:44 -0800 Subject: [PATCH] Updating transcript computation for 3DH (#143) --- Cargo.lock | 2 +- Cargo.toml | 2 +- src/group.rs | 2 +- src/key_exchange/tripledh.rs | 97 +++++----- src/opaque.rs | 13 +- src/tests/full_test.rs | 52 +++--- src/tests/opaque_test_vectors.rs | 300 +++++++++++++++---------------- 7 files changed, 237 insertions(+), 231 deletions(-) diff --git a/Cargo.lock b/Cargo.lock index 795ca48..7d3e52e 100644 --- a/Cargo.lock +++ b/Cargo.lock @@ -573,7 +573,7 @@ checksum = "624a8340c38c1b80fd549087862da4ba43e08858af025b236e509b6649fc13d5" [[package]] name = "opaque-ke" -version = "0.3.1" +version = "0.4.0-pre.1" dependencies = [ "anyhow", "base64", diff --git a/Cargo.toml b/Cargo.toml index 8c36cd9..3688efe 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -1,6 +1,6 @@ [package] name = "opaque-ke" -version = "0.3.1" +version = "0.4.0-pre.1" repository = "https://github.com/novifinancial/opaque-ke" keywords = ["cryptography", "crypto", "opaque", "passwords", "authentication"] description = "An implementation of the OPAQUE password-authenticated key exchange protocol" diff --git a/src/group.rs b/src/group.rs index 3f077d1..34f8e2c 100644 --- a/src/group.rs +++ b/src/group.rs @@ -25,7 +25,7 @@ use zeroize::Zeroize; /// A prime-order subgroup of a base field (EC, prime-order field ...). This /// subgroup is noted additively — as in the draft RFC — in this trait. -pub trait Group: Sized + for<'a> Mul<&'a ::Scalar, Output = Self> { +pub trait Group: Copy + Sized + for<'a> Mul<&'a ::Scalar, Output = Self> { /// The type of base field scalars type Scalar: Zeroize + Clone; /// The byte length necessary to represent scalars diff --git a/src/key_exchange/tripledh.rs b/src/key_exchange/tripledh.rs index 30a7b32..d12d1eb 100644 --- a/src/key_exchange/tripledh.rs +++ b/src/key_exchange/tripledh.rs @@ -30,7 +30,7 @@ use std::convert::TryFrom; const KEY_LEN: usize = 32; pub(crate) type NonceLen = U32; -static STR_3DH: &[u8] = b"3DH keys"; +static STR_3DH: &[u8] = b"3DH"; static STR_CLIENT_MAC: &[u8] = b"client mac"; static STR_HANDSHAKE_SECRET: &[u8] = b"handshake secret"; static STR_SERVER_MAC: &[u8] = b"server mac"; @@ -95,6 +95,22 @@ impl KeyExchange for TripleDH { GenericArray::clone_from_slice(&server_nonce_bytes) }; + let server_transcript = [ + &l2_bytes[..], + &server_nonce[..], + &server_e_kp.public().to_arr(), + ] + .concat(); + + let derivation_transcript = [ + STR_3DH, + &serialize(&id_u, 2), + &serialized_credential_request[..], + &serialize(&id_s, 2), + &server_transcript[..], + ] + .concat(); + let (session_key, km2, ke2, km3) = derive_3dh_keys::( TripleDHComponents { pk1: ke1_message.client_e_pk.clone(), @@ -104,10 +120,7 @@ impl KeyExchange for TripleDH { pk3: client_s_pk, sk3: server_e_kp.private().clone(), }, - &ke1_message.client_nonce, - &server_nonce, - &id_u, - &id_s, + &derivation_transcript, )?; // Compute encryption of e_info @@ -121,14 +134,8 @@ impl KeyExchange for TripleDH { .map(|(&x1, &x2)| x1 ^ x2) .collect(); - let transcript2: Vec = [ - &serialized_credential_request[..], - &l2_bytes[..], - &server_nonce[..], - &server_e_kp.public().to_arr(), - &serialize(&ciphertext, 2), - ] - .concat(); + let transcript2: Vec = + [&derivation_transcript[..], &serialize(&ciphertext, 2)].concat(); let mut hasher = D::new(); hasher.update(&transcript2); @@ -170,6 +177,21 @@ impl KeyExchange for TripleDH { id_u: Vec, id_s: Vec, ) -> Result<(Vec, Vec, Self::KE3Message), ProtocolError> { + let server_transcript = [ + &l2_component[..], + &ke2_message.to_bytes_without_info_or_mac(), + ] + .concat(); + + let derivation_transcript = [ + STR_3DH, + &serialize(&id_u, 2), + &serialized_credential_request, + &serialize(&id_s, 2), + &server_transcript[..], + ] + .concat(); + let (session_key, km2, ke2, km3) = derive_3dh_keys::( TripleDHComponents { pk1: ke2_message.server_e_pk.clone(), @@ -179,16 +201,12 @@ impl KeyExchange for TripleDH { pk3: ke2_message.server_e_pk.clone(), sk3: client_s_sk, }, - &ke1_state.client_nonce, - &ke2_message.server_nonce, - &id_u, - &id_s, + &derivation_transcript, )?; let transcript: Vec = [ - &serialized_credential_request, - &l2_component[..], - &ke2_message.to_bytes_without_mac(), + &derivation_transcript[..], + &serialize(&ke2_message.e_info[..], 2), ] .concat(); @@ -370,18 +388,18 @@ impl> TryFrom<&[u8]> for Ke2State { impl> ToBytes for Ke2Message { fn to_bytes(&self) -> Vec { - [&self.to_bytes_without_mac(), &self.mac[..]].concat() + [ + &self.to_bytes_without_info_or_mac(), + &serialize(&self.e_info, 2), + &self.mac[..], + ] + .concat() } } impl> Ke2Message { - fn to_bytes_without_mac(&self) -> Vec { - [ - &self.server_nonce[..], - &self.server_e_pk.to_arr(), - &serialize(&self.e_info, 2), - ] - .concat() + fn to_bytes_without_info_or_mac(&self) -> Vec { + [&self.server_nonce[..], &self.server_e_pk.to_arr()].concat() } } @@ -457,10 +475,7 @@ impl> TryFrom<&[u8]> for Ke3Message { // with some auxiliary metadata, to produce the session key and two MAC keys fn derive_3dh_keys( dh: TripleDHComponents, - client_nonce: &GenericArray, - server_nonce: &GenericArray, - id_u: &[u8], - id_s: &[u8], + derivation_transcript: &[u8], ) -> Result, ProtocolError> { let ikm: Vec = [ &KeyPair::::diffie_hellman(dh.pk1, dh.sk1)?[..], @@ -469,18 +484,14 @@ fn derive_3dh_keys( ] .concat(); - let info: Vec = [ - STR_3DH, - &serialize(&client_nonce, 2), - &serialize(&server_nonce, 2), - &serialize(id_u, 2), - &serialize(id_s, 2), - ] - .concat(); - let extracted_ikm = Hkdf::::new(None, &ikm); - let handshake_secret = derive_secrets::(&extracted_ikm, &STR_HANDSHAKE_SECRET, &info)?; - let session_key = derive_secrets::(&extracted_ikm, &STR_SESSION_KEY, &info)?; + let handshake_secret = derive_secrets::( + &extracted_ikm, + &STR_HANDSHAKE_SECRET, + &derivation_transcript, + )?; + let session_key = + derive_secrets::(&extracted_ikm, &STR_SESSION_KEY, &derivation_transcript)?; let km2 = hkdf_expand_label::( &handshake_secret, diff --git a/src/opaque.rs b/src/opaque.rs index 05077e2..ba9c6fc 100644 --- a/src/opaque.rs +++ b/src/opaque.rs @@ -584,7 +584,6 @@ impl ClientLogin { ClientLoginFinishParameters::WithIdentifiers(id_u, id_s) => Some((id_u, id_s)), }; - let l2_beta_bytes = &l2.beta.to_arr()[..]; let server_s_pk_bytes = l2.server_s_pk.to_arr().to_vec(); let password_derived_key = @@ -604,20 +603,16 @@ impl ClientLogin { KeyPair::::public_from_private(&client_s_sk) .to_arr() .to_vec(), - server_s_pk_bytes.clone(), + server_s_pk_bytes, ), Some((id_u, id_s)) => (id_u, id_s), }; - let l2_bytes: Vec = [ - l2_beta_bytes, - &serialize(&server_s_pk_bytes, 2), - &l2.envelope.to_bytes(), - ] - .concat(); + let credential_response_component = + CredentialResponse::::serialize_without_ke(&l2.beta, &l2.server_s_pk, &l2.envelope); let (confidential_info, session_key, ke3_message) = CS::KeyExchange::generate_ke3( - l2_bytes, + credential_response_component, l2.ke2_message, &self.ke1_state, &self.serialized_credential_request, diff --git a/src/tests/full_test.rs b/src/tests/full_test.rs index 1c448f7..2b2be31 100644 --- a/src/tests/full_test.rs +++ b/src/tests/full_test.rs @@ -68,37 +68,37 @@ pub struct TestVectorParameters { static TEST_VECTOR: &str = r#" { - "client_s_pk": "2c3247e1d7fcf2bef09a0c6e771c44fe922f36deb5726998c89f7816323bc373", - "client_s_sk": "d7dd5397912dc1dce64a26b8d24bee59b7929b15a6b9769ad6357913a13e7f09", - "client_e_pk": "3431e8f57ce0c1ae9da2b4f37a2f877a64b244a86bc1384ba70a9c39985b3729", - "client_e_sk": "8410c0520fd2a37775e54000d9abb5a84825d37649827d8f2721dd655cd64c0c", - "server_s_pk": "6a55f77ffb17741d5dfd404ef7079ef276cb2114a76f507c0ae7172847da647a", - "server_s_sk": "f4433f94dea3f4bf877ab760566efa36340e34d516dc4462b2ad5b9600157a06", - "server_e_pk": "32d56c7e3b882b9ac1a4e38d60456c4942ec6b6aceed91d069ead967a825df74", - "server_e_sk": "256f9cdddb2c4bed42866e37d5dff019b4a9584b7486e5683d52b56842d82b0d", + "client_s_pk": "88a330a73dd4b166307c5efc6e7a0a30d9b36ff6cc13cdb7f4e9adb9308a7637", + "client_s_sk": "a3f2becb1604e524d414d75e34d69b1984403715f4fb64dbecdf94ee67c56007", + "client_e_pk": "782e5d1fba5fc5127f56d026a0796320670260a58007b0c7b8e2c4591a6c2441", + "client_e_sk": "117dbea41b3a73f38af6ec5e94f4addcb157fafd01db5640a782cbd205af1c01", + "server_s_pk": "ce16950ab0939c9827479b7f7c94662f2aad8149a47260b4e9a36f3013472924", + "server_s_sk": "7731db9c827d8d2736dcec7900e635d05b8eb024ba03398be7b3e14380983a07", + "server_e_pk": "f8f1a6de4b3708baec68ea94f47b9577f3d36458e82e36f431ba8ce77e2d2e11", + "server_e_sk": "f7b415289b0e0f043465d9bf5d6f93393b042aa6f45eb74c1ed29e63484dd705", "id_u": "696455", "id_s": "696453", "password": "70617373776f7264", - "blinding_factor": "c0937fddc5b7a8cbb76301cbe588268d52a9efe6a205af21a0a12b1fadf3a008", - "oprf_key": "f386e8710c12c870a0ec74f09364811142050a5266ca53d36c11e369343a5e09", - "envelope_nonce": "2338be69855ad2a280ab5ed67fb04cd96691841241dbb4873ca776adc60d1c93", - "client_nonce": "09f2721189a82d90e891d346aa9be462e003cc6b6824a55352da7df685eca5bf", - "server_nonce": "5c11e9abe0d5d677dd1a66cd1c8e9baa1f1a44c7554ffe61978b100e657f79f4", + "blinding_factor": "7691a5530384fae7ce5d118b770900b38d523d0ea62f7328410718cdc26a5707", + "oprf_key": "c66dc3992fbcbb969647fe94390db974c4a5c6c46457373f28385c8898e9fb07", + "envelope_nonce": "a2c8292a03df900668a81badb1003c80bacbb9a4776228997a264d58e7b2a2c6", + "client_nonce": "d54b0fb476f66a3c5ac93647c462590431594e63f8b21aeb371cb0f835841a40", + "server_nonce": "458b1ca0d48d3d04e6a21127db53ae4208cd5c6ae0aa6b0e2db3146022725c45", "info1": "696e666f31", "einfo2": "65696e666f32", - "registration_request": "58e629f68bd59f1d5fcee531a5afeedb4e07d2c6aed98d15cab686d063f2f46e", - "registration_response": "a2227384ed34860b7d879d617f7daa802b6a878eaa5eab33669400f30ad0431d00206a55f77ffb17741d5dfd404ef7079ef276cb2114a76f507c0ae7172847da647a", - "registration_upload": "00202c3247e1d7fcf2bef09a0c6e771c44fe922f36deb5726998c89f7816323bc373022338be69855ad2a280ab5ed67fb04cd96691841241dbb4873ca776adc60d1c930022576b449b09abeb68d5f6c56082b0c2f560c636bff4f0af3b44b6377045201b545598d319af3122041f06e3ab86371bff6c0727557c77d20efeb9a0b9f24573e3646735eeebed45e741d11d0120741af27b04c2716eb6bdfe950daff937cfcae8569e", - "credential_request": "58e629f68bd59f1d5fcee531a5afeedb4e07d2c6aed98d15cab686d063f2f46e09f2721189a82d90e891d346aa9be462e003cc6b6824a55352da7df685eca5bf0005696e666f313431e8f57ce0c1ae9da2b4f37a2f877a64b244a86bc1384ba70a9c39985b3729", - "credential_response": "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", - "credential_finalization": "b1fad859f343f1a15df14bd7782db9ab6ee4493225a470152e53b3b7601dc954bc80d7b7dadfe70f743b1ab1552a054e7a9d192399ea42073a1d1c5839aabfc2", - "client_registration_state": "c0937fddc5b7a8cbb76301cbe588268d52a9efe6a205af21a0a12b1fadf3a00870617373776f7264", - "client_login_state": "c0937fddc5b7a8cbb76301cbe588268d52a9efe6a205af21a0a12b1fadf3a008006758e629f68bd59f1d5fcee531a5afeedb4e07d2c6aed98d15cab686d063f2f46e09f2721189a82d90e891d346aa9be462e003cc6b6824a55352da7df685eca5bf0005696e666f313431e8f57ce0c1ae9da2b4f37a2f877a64b244a86bc1384ba70a9c39985b372900408410c0520fd2a37775e54000d9abb5a84825d37649827d8f2721dd655cd64c0c09f2721189a82d90e891d346aa9be462e003cc6b6824a55352da7df685eca5bf70617373776f7264", - "server_registration_state": "f386e8710c12c870a0ec74f09364811142050a5266ca53d36c11e369343a5e09", - "server_login_state": "761333eea593c396021c3930fb36cf97aad7c7ea00f1ff983e4df9ca002885017161427303fddb4508c9136a67612e01b673ed88b1de49ed6628d0a77e43c590595f53bf0b0766c165b876173c509efc982868d3860df5dad3f0753477ec9bdd103b71dab9540537f2b10964da82032a6339da6d663a409f4e8e5dea03e3653bb6202f265ed814df39f446486197e1c6091ec6b74200f18df5eef59813ff7f245d69b34e8843be496630921601ab784b1f3ccbfe2ff014ea132199c5c76deda7", - "password_file": "f386e8710c12c870a0ec74f09364811142050a5266ca53d36c11e369343a5e092c3247e1d7fcf2bef09a0c6e771c44fe922f36deb5726998c89f7816323bc373022338be69855ad2a280ab5ed67fb04cd96691841241dbb4873ca776adc60d1c930022576b449b09abeb68d5f6c56082b0c2f560c636bff4f0af3b44b6377045201b545598d319af3122041f06e3ab86371bff6c0727557c77d20efeb9a0b9f24573e3646735eeebed45e741d11d0120741af27b04c2716eb6bdfe950daff937cfcae8569e", - "export_key": "96b95891f06c7f02ab9c508f30e1a82ddea25e2f4fc4ffdafeb199ee65e24e418b2648a201e889eaf84301a1a8d0c3b7fea0ec8d4611686e6daee12430f60c05", - "session_key": "b6202f265ed814df39f446486197e1c6091ec6b74200f18df5eef59813ff7f245d69b34e8843be496630921601ab784b1f3ccbfe2ff014ea132199c5c76deda7" + "registration_request": "86115e7b95618fbd5015765d2f212494d5d68e770b96da153d0bb9a00bc5f54d", + "registration_response": "42538263dcf753f1255c85eb66b558c32bd593f3787d284eb126787393d586330020ce16950ab0939c9827479b7f7c94662f2aad8149a47260b4e9a36f3013472924", + "registration_upload": "002088a330a73dd4b166307c5efc6e7a0a30d9b36ff6cc13cdb7f4e9adb9308a763702a2c8292a03df900668a81badb1003c80bacbb9a4776228997a264d58e7b2a2c60022fe0b9953fd5e784a3f47ed9b1ea1a33a39231dff88e930edebd1d437b850972a2a1c51bcf77483a4315eeb5db1cb61e7dbd874194f893daaf32006de7502a0e33860cadcfec6e038662e8484e9f488efa1f336bf10a125409d20bce6a6cb22a70d8e", + "credential_request": "86115e7b95618fbd5015765d2f212494d5d68e770b96da153d0bb9a00bc5f54dd54b0fb476f66a3c5ac93647c462590431594e63f8b21aeb371cb0f835841a400005696e666f31782e5d1fba5fc5127f56d026a0796320670260a58007b0c7b8e2c4591a6c2441", + "credential_response": "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", + "credential_finalization": "afa7239945acc304e0c40a6a9e594d7978aaff24565a44fcb5bc62b577211e854be9cb3f55261f1e34a8ebac192f98625ec59d54ce5c64346e1f9afa18facda3", + "client_registration_state": "7691a5530384fae7ce5d118b770900b38d523d0ea62f7328410718cdc26a570770617373776f7264", + "client_login_state": "7691a5530384fae7ce5d118b770900b38d523d0ea62f7328410718cdc26a5707006786115e7b95618fbd5015765d2f212494d5d68e770b96da153d0bb9a00bc5f54dd54b0fb476f66a3c5ac93647c462590431594e63f8b21aeb371cb0f835841a400005696e666f31782e5d1fba5fc5127f56d026a0796320670260a58007b0c7b8e2c4591a6c24410040117dbea41b3a73f38af6ec5e94f4addcb157fafd01db5640a782cbd205af1c01d54b0fb476f66a3c5ac93647c462590431594e63f8b21aeb371cb0f835841a4070617373776f7264", + "server_registration_state": "c66dc3992fbcbb969647fe94390db974c4a5c6c46457373f28385c8898e9fb07", + "server_login_state": "e05749068700eec7d07c4e2e6e5e63336e41cc1f3c0ddf3c635b46c6d53deffed876378fc1eb32dcfd1d7e35a63c52e638c0b8da7977269143be95f88024ab0735fac1d0b2dce50a5c19e6500c73aa055fabff9f548720dd1cacaa21566b7afde7a9b97fbc4da0482aaf2063c627926bbeeab98356b151881973460c4fad531f13721b6f004e8f73c8d2010df34700717c74350c9275fb29991f6296c85f7d1dd931f784f47ccd6bc2866423cc200fb3872a1cb29a47088b6f6750432e3f6c72", + "password_file": "c66dc3992fbcbb969647fe94390db974c4a5c6c46457373f28385c8898e9fb0788a330a73dd4b166307c5efc6e7a0a30d9b36ff6cc13cdb7f4e9adb9308a763702a2c8292a03df900668a81badb1003c80bacbb9a4776228997a264d58e7b2a2c60022fe0b9953fd5e784a3f47ed9b1ea1a33a39231dff88e930edebd1d437b850972a2a1c51bcf77483a4315eeb5db1cb61e7dbd874194f893daaf32006de7502a0e33860cadcfec6e038662e8484e9f488efa1f336bf10a125409d20bce6a6cb22a70d8e", + "export_key": "aa2cdeaa4281a834bda57d4fff88702cba1a22d556790e812bdfd408162ba3b6a17305c576ea9549523592470ef3047aa8ace4be71f92d71f0b5cc6465dfc9e4", + "session_key": "13721b6f004e8f73c8d2010df34700717c74350c9275fb29991f6296c85f7d1dd931f784f47ccd6bc2866423cc200fb3872a1cb29a47088b6f6750432e3f6c72" } "#; diff --git a/src/tests/opaque_test_vectors.rs b/src/tests/opaque_test_vectors.rs index 7c1f741..eb2c9e6 100644 --- a/src/tests/opaque_test_vectors.rs +++ b/src/tests/opaque_test_vectors.rs @@ -67,93 +67,93 @@ EnvelopeMode: 01 OPRF: 0001 SlowHash: Identity Hash: SHA512 -server_nonce: a4997137a8fa0d4baf7052a499bf877057f9404e03c889d641a0d7c -807b6a518 +server_nonce: 0ef5dc5c619b5a58eecb1c8fba63ae5e723e059552bb067bc460efd +910ff58af oprf_key: 5ed895206bfc53316d307b23e46ecc6623afb3086da74189a416012be03 7e50b password: 436f7272656374486f72736542617474657279537461706c65 blind_login: ed8366feb6b1d05d1f46acb727061e43aadfafe9c10e5a64e7518d63 e3263503 -server_private_keyshare: 31587dff30b8001d9d43584decc22e358fa7f9d6e606 -29fb1223081c3bae7103 -client_nonce: 75a1ad27ab77578bc08b44c4318f09b31d53145c9ba3b42abf0ea08 -a781277a6 +server_private_keyshare: ac56b748ee205ea817e823697857b4b40ad758328074 +6897e9eb9192636db704 +client_nonce: d0298cebb277efb5af53932af6bb10180b2ac35e5f69b55ad4c4191 +4d579add6 server_info: 6772656574696e677320616c696365 client_info: 68656c6c6f20626f62 -client_private_keyshare: fbbf4ad24119f08a35bf999f8ae0c779ed7b3e266bf3 -3f793f6bf9ebf4578005 -envelope_nonce: 6c6bb9021b9833c788dd25994d3ce7f3811338744fd6dc556e037 -585783444c0 -server_keyshare: 82be40ef93bf7c6edd43d4ed9f52fa19827649b819de39c52a22 -43e985b75d62 +client_private_keyshare: 46244633cd475d25f3db6a6eb8304e2fe02e2a006805 +3efee984e49b7f4ff60e +envelope_nonce: 9a87511fa84547961a5467f96caba559fb15f3a203146e4041bb4 +b2179e83594 +server_keyshare: a83ddbb1abf9e8e8c73fe39d3c18da434dd3f6fd52f01279028f +086126893d7f blind_registration: c604c785ada70d77a5256ae21767de8c3304115237d262134 f5e46e512cf8e03 -client_public_key: b2d1b10f3741a8efef3139f4d2889f2b11f776b79b9aa2c3ef -caba4f1c4ae861 -client_private_key: f0f56cfb488649fe28691dd9aa5dc9ff4c0e6028075baa3c5 -615398a2cb12304 -client_keyshare: 484e47e31b3132f4ee512e41805a1690891111a7b885bc526198 -22c14cabf360 -server_public_key: 5442a6f57333a332b4c6f07308f6fa846bde3ed27425820cdc -eeeb935924a903 -server_private_key: d63d709e3a739a128929a9f289ff263fdcbc457f2f47f7c43 -ccafbbfee72290c -auth_key: 22198da4ad73b1d35cd8bb875e64ce1a9fc2edeb073d760e114d1d7a2f8 -6d47411caf1787907e2ff96cd3190b14d101101d74cff234259d9f19a18f2cfe29d0b 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-30cdba66ccb379e57200205442a6f57333a332b4c6f07308f6fa846bde3ed27425820 -cdceeeb935924a903 -export_key: 6ca2c344763e5bc9e3d2bbfe3d982b826b709da597e28e85f9594ec54 -2a20c697d55de277ccce1d1af7c48ab7fea1467ac1e3a99c71dcf6326a909d280bd2f -6f -registration_upload: 0020b2d1b10f3741a8efef3139f4d2889f2b11f776b79b9a -a2c3efcaba4f1c4ae861016c6bb9021b9833c788dd25994d3ce7f3811338744fd6dc5 -56e037585783444c00022e9b28440a1dc99cca7513e8eb754d427caf8515642b45a92 -c73838c043fc316deeb83deface81589bc8e5c2c767b5ab79218834fbf4fa4f87cf23 -775aa54633ed75665cd88f451e044cac1b282d890269476d1ac18ff9a4c0cb832e114 -3ffa7d447a +30cdba66ccb379e57200203881fefba6d687143ecaaec0d8658eb7fa247555f05fedb +0757866d49ea9883e +export_key: 93c48fa650a6c2b9fddc27c9697be2f259b0083515b650a7b1520af92 +e631c85946fb811b22d636d137ef97380bf9322606b5d97452ca262e9136284d23467 +76 +registration_upload: 0020dec9d1223019c1aaaaac7397355016f8ea099b949fb5 +bcf5de3b9b0b1b298301019a87511fa84547961a5467f96caba559fb15f3a203146e4 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-00205442a6f57333a332b4c6f07308f6fa846bde3ed27425820cdceeeb935924a9030 -16c6bb9021b9833c788dd25994d3ce7f3811338744fd6dc556e037585783444c00022 -e9b28440a1dc99cca7513e8eb754d427caf8515642b45a92c73838c043fc316deeb83 -deface81589bc8e5c2c767b5ab79218834fbf4fa4f87cf23775aa54633ed75665cd88 -f451e044cac1b282d890269476d1ac18ff9a4c0cb832e1143ffa7d447aa4997137a8f -a0d4baf7052a499bf877057f9404e03c889d641a0d7c807b6a51882be40ef93bf7c6e -dd43d4ed9f52fa19827649b819de39c52a2243e985b75d62000f13aed85ae30aee2f8 -9ac5e1c5dd53609b890267ef2d765bb56000bc704c2ba4e4256107befee6655cdb084 -64e6c75d8b251642e0d721b3fce38f245568b50e7f6c98825d54cc1a26d6eafadcc1d -344 +00203881fefba6d687143ecaaec0d8658eb7fa247555f05fedb0757866d49ea9883e0 +19a87511fa84547961a5467f96caba559fb15f3a203146e4041bb4b2179e835940022 +62a8d608d300886f5a2bd8b9abe76da19af847755fda0541a1729bfd57e94fbd79be8 +c03267be7f578b1a017eaff6f23a667f378ac41c516591d04681db955609ac4a200b3 +98d0ea88faaa4a74f0291f462119a5cd51491c0935171d75a6421c4b620ef5dc5c619 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