[{"alternative_title":["LNCS"],"main_file_link":[{"url":"https://eprint.iacr.org/2023/1123","open_access":"1"}],"title":"On the cost of post-compromise security in concurrent Continuous Group-Key Agreement","doi":"10.1007/978-3-031-48621-0_10","year":"2023","publication_identifier":{"eissn":["1611-3349"],"isbn":["9783031486203"],"issn":["0302-9743"]},"_id":"14691","quality_controlled":"1","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","volume":14371,"date_updated":"2023-12-18T08:36:51Z","oa":1,"abstract":[{"lang":"eng","text":"Continuous Group-Key Agreement (CGKA) allows a group of users to maintain a shared key. It is the fundamental cryptographic primitive underlying group messaging schemes and related protocols, most notably TreeKEM, the underlying key agreement protocol of the Messaging Layer Security (MLS) protocol, a standard for group messaging by the IETF. CKGA works in an asynchronous setting where parties only occasionally must come online, and their messages are relayed by an untrusted server. The most expensive operation provided by CKGA is that which allows for a user to refresh their key material in order to achieve forward secrecy (old messages are secure when a user is compromised) and post-compromise security (users can heal from compromise). One caveat of early CGKA protocols is that these update operations had to be performed sequentially, with any user wanting to update their key material having had to receive and process all previous updates. Late versions of TreeKEM do allow for concurrent updates at the cost of a communication overhead per update message that is linear in the number of updating parties. This was shown to be indeed necessary when achieving PCS in just two rounds of communication by [Bienstock et al. TCC’20].\r\nThe recently proposed protocol CoCoA [Alwen et al. Eurocrypt’22], however, shows that this overhead can be reduced if PCS requirements are relaxed, and only a logarithmic number of rounds is required. The natural question, thus, is whether CoCoA is optimal in this setting.\r\nIn this work we answer this question, providing a lower bound on the cost (concretely, the amount of data to be uploaded to the server) for CGKA protocols that heal in an arbitrary k number of rounds, that shows that CoCoA is very close to optimal. Additionally, we extend CoCoA to heal in an arbitrary number of rounds, and propose a modification of it, with a reduced communication cost for certain k.\r\nWe prove our bound in a combinatorial setting where the state of the protocol progresses in rounds, and the state of the protocol in each round is captured by a set system, each set specifying a set of users who share a secret key. We show this combinatorial model is equivalent to a symbolic model capturing building blocks including PRFs and public-key encryption, related to the one used by Bienstock et al.\r\nOur lower bound is of order k•n1+1/(k-1)/log(k), where 2≤k≤log(n) is the number of updates per user the protocol requires to heal. This generalizes the n2 bound for k=2 from Bienstock et al.. This bound almost matches the k⋅n1+2/(k-1) or k2⋅n1+1/(k-1) efficiency we get for the variants of the CoCoA protocol also introduced in this paper."}],"author":[{"id":"D33D2B18-E445-11E9-ABB7-15F4E5697425","first_name":"Benedikt","orcid":"0000-0002-7553-6606","last_name":"Auerbach","full_name":"Auerbach, Benedikt"},{"id":"ffc563a3-f6e0-11ea-865d-e3cce03d17cc","first_name":"Miguel","full_name":"Cueto Noval, Miguel","last_name":"Cueto Noval"},{"id":"2D7ABD02-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8630-415X","last_name":"Pascual Perez","full_name":"Pascual Perez, Guillermo","first_name":"Guillermo"},{"full_name":"Pietrzak, Krzysztof Z","last_name":"Pietrzak","orcid":"0000-0002-9139-1654","first_name":"Krzysztof Z","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87"}],"citation":{"ista":"Auerbach B, Cueto Noval M, Pascual Perez G, Pietrzak KZ. 2023. On the cost of post-compromise security in concurrent Continuous Group-Key Agreement. 21st International Conference on Theory of Cryptography. TCC: Theory of Cryptography, LNCS, vol. 14371, 271–300.","short":"B. Auerbach, M. Cueto Noval, G. Pascual Perez, K.Z. Pietrzak, in:, 21st International Conference on Theory of Cryptography, Springer Nature, 2023, pp. 271–300.","mla":"Auerbach, Benedikt, et al. “On the Cost of Post-Compromise Security in Concurrent Continuous Group-Key Agreement.” <i>21st International Conference on Theory of Cryptography</i>, vol. 14371, Springer Nature, 2023, pp. 271–300, doi:<a href=\"https://doi.org/10.1007/978-3-031-48621-0_10\">10.1007/978-3-031-48621-0_10</a>.","ama":"Auerbach B, Cueto Noval M, Pascual Perez G, Pietrzak KZ. On the cost of post-compromise security in concurrent Continuous Group-Key Agreement. In: <i>21st International Conference on Theory of Cryptography</i>. Vol 14371. Springer Nature; 2023:271-300. doi:<a href=\"https://doi.org/10.1007/978-3-031-48621-0_10\">10.1007/978-3-031-48621-0_10</a>","chicago":"Auerbach, Benedikt, Miguel Cueto Noval, Guillermo Pascual Perez, and Krzysztof Z Pietrzak. “On the Cost of Post-Compromise Security in Concurrent Continuous Group-Key Agreement.” In <i>21st International Conference on Theory of Cryptography</i>, 14371:271–300. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/978-3-031-48621-0_10\">https://doi.org/10.1007/978-3-031-48621-0_10</a>.","apa":"Auerbach, B., Cueto Noval, M., Pascual Perez, G., &#38; Pietrzak, K. Z. (2023). On the cost of post-compromise security in concurrent Continuous Group-Key Agreement. In <i>21st International Conference on Theory of Cryptography</i> (Vol. 14371, pp. 271–300). Taipei, Taiwan: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-48621-0_10\">https://doi.org/10.1007/978-3-031-48621-0_10</a>","ieee":"B. Auerbach, M. Cueto Noval, G. Pascual Perez, and K. Z. Pietrzak, “On the cost of post-compromise security in concurrent Continuous Group-Key Agreement,” in <i>21st International Conference on Theory of Cryptography</i>, Taipei, Taiwan, 2023, vol. 14371, pp. 271–300."},"publication_status":"published","conference":{"start_date":"2023-11-29","location":"Taipei, Taiwan","end_date":"2023-12-02","name":"TCC: Theory of Cryptography"},"date_created":"2023-12-17T23:00:53Z","department":[{"_id":"KrPi"}],"scopus_import":"1","publisher":"Springer Nature","language":[{"iso":"eng"}],"month":"11","date_published":"2023-11-27T00:00:00Z","publication":"21st International Conference on Theory of Cryptography","page":"271-300","intvolume":"     14371","status":"public","day":"27","type":"conference"},{"isi":1,"main_file_link":[{"open_access":"1","url":"https://eprint.iacr.org/2022/251"}],"alternative_title":["LNCS"],"ec_funded":1,"doi":"10.1007/978-3-031-07085-3_28","year":"2022","place":"Cham","title":"CoCoA: Concurrent continuous group key agreement","external_id":{"isi":["000832305300028"]},"volume":13276,"oa":1,"date_updated":"2023-08-03T07:25:02Z","article_processing_charge":"No","acknowledgement":"We thank Marta Mularczyk and Yiannis Tselekounis for their very helpful feedback on an earlier draft of this paper.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"name":"Teaching Old Crypto New Tricks","_id":"258AA5B2-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"682815"},{"grant_number":"665385","call_identifier":"H2020","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","oa_version":"Preprint","_id":"11476","publication_identifier":{"eisbn":["9783031070853"],"issn":["0302-9743"],"isbn":["9783031070846"],"eissn":["1611-3349"]},"publication_status":"published","citation":{"short":"J. Alwen, B. Auerbach, M. Cueto Noval, K. Klein, G. Pascual Perez, K.Z. Pietrzak, M. Walter, in:, Advances in Cryptology – EUROCRYPT 2022, Springer Nature, Cham, 2022, pp. 815–844.","ista":"Alwen J, Auerbach B, Cueto Noval M, Klein K, Pascual Perez G, Pietrzak KZ, Walter M. 2022. CoCoA: Concurrent continuous group key agreement. Advances in Cryptology – EUROCRYPT 2022. EUROCRYPT: Annual International Conference on the Theory and Applications of Cryptology and Information Security, LNCS, vol. 13276, 815–844.","ama":"Alwen J, Auerbach B, Cueto Noval M, et al. CoCoA: Concurrent continuous group key agreement. In: <i>Advances in Cryptology – EUROCRYPT 2022</i>. Vol 13276. Cham: Springer Nature; 2022:815–844. doi:<a href=\"https://doi.org/10.1007/978-3-031-07085-3_28\">10.1007/978-3-031-07085-3_28</a>","mla":"Alwen, Joël, et al. “CoCoA: Concurrent Continuous Group Key Agreement.” <i>Advances in Cryptology – EUROCRYPT 2022</i>, vol. 13276, Springer Nature, 2022, pp. 815–844, doi:<a href=\"https://doi.org/10.1007/978-3-031-07085-3_28\">10.1007/978-3-031-07085-3_28</a>.","chicago":"Alwen, Joël, Benedikt Auerbach, Miguel Cueto Noval, Karen Klein, Guillermo Pascual Perez, Krzysztof Z Pietrzak, and Michael Walter. “CoCoA: Concurrent Continuous Group Key Agreement.” In <i>Advances in Cryptology – EUROCRYPT 2022</i>, 13276:815–844. Cham: Springer Nature, 2022. <a href=\"https://doi.org/10.1007/978-3-031-07085-3_28\">https://doi.org/10.1007/978-3-031-07085-3_28</a>.","ieee":"J. Alwen <i>et al.</i>, “CoCoA: Concurrent continuous group key agreement,” in <i>Advances in Cryptology – EUROCRYPT 2022</i>, Trondheim, Norway, 2022, vol. 13276, pp. 815–844.","apa":"Alwen, J., Auerbach, B., Cueto Noval, M., Klein, K., Pascual Perez, G., Pietrzak, K. Z., &#38; Walter, M. (2022). CoCoA: Concurrent continuous group key agreement. In <i>Advances in Cryptology – EUROCRYPT 2022</i> (Vol. 13276, pp. 815–844). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-07085-3_28\">https://doi.org/10.1007/978-3-031-07085-3_28</a>"},"author":[{"first_name":"Joël","full_name":"Alwen, Joël","last_name":"Alwen"},{"id":"D33D2B18-E445-11E9-ABB7-15F4E5697425","first_name":"Benedikt","orcid":"0000-0002-7553-6606","full_name":"Auerbach, Benedikt","last_name":"Auerbach"},{"full_name":"Cueto Noval, Miguel","last_name":"Cueto Noval","first_name":"Miguel","id":"ffc563a3-f6e0-11ea-865d-e3cce03d17cc"},{"id":"3E83A2F8-F248-11E8-B48F-1D18A9856A87","first_name":"Karen","full_name":"Klein, Karen","last_name":"Klein"},{"full_name":"Pascual Perez, Guillermo","last_name":"Pascual Perez","first_name":"Guillermo","id":"2D7ABD02-F248-11E8-B48F-1D18A9856A87"},{"id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","first_name":"Krzysztof Z","full_name":"Pietrzak, Krzysztof Z","last_name":"Pietrzak","orcid":"0000-0002-9139-1654"},{"full_name":"Walter, Michael","last_name":"Walter","first_name":"Michael"}],"abstract":[{"text":"Messaging platforms like Signal are widely deployed and provide strong security in an asynchronous setting. It is a challenging problem to construct a protocol with similar security guarantees that can efficiently scale to large groups. A major bottleneck are the frequent key rotations users need to perform to achieve post compromise forward security.\r\n\r\nIn current proposals – most notably in TreeKEM (which is part of the IETF’s Messaging Layer Security (MLS) protocol draft) – for users in a group of size n to rotate their keys, they must each craft a message of size log(n) to be broadcast to the group using an (untrusted) delivery server.\r\n\r\nIn larger groups, having users sequentially rotate their keys requires too much bandwidth (or takes too long), so variants allowing any T≤n users to simultaneously rotate their keys in just 2 communication rounds have been suggested (e.g. “Propose and Commit” by MLS). Unfortunately, 2-round concurrent updates are either damaging or expensive (or both); i.e. they either result in future operations being more costly (e.g. via “blanking” or “tainting”) or are costly themselves requiring Ω(T) communication for each user [Bienstock et al., TCC’20].\r\n\r\nIn this paper we propose CoCoA; a new scheme that allows for T concurrent updates that are neither damaging nor costly. That is, they add no cost to future operations yet they only require Ω(log2(n)) communication per user. To circumvent the [Bienstock et al.] lower bound, CoCoA increases the number of rounds needed to complete all updates from 2 up to (at most) log(n); though typically fewer rounds are needed.\r\n\r\nThe key insight of our protocol is the following: in the (non-concurrent version of) TreeKEM, a delivery server which gets T concurrent update requests will approve one and reject the remaining T−1. In contrast, our server attempts to apply all of them. If more than one user requests to rotate the same key during a round, the server arbitrarily picks a winner. Surprisingly, we prove that regardless of how the server chooses the winners, all previously compromised users will recover after at most log(n) such update rounds.\r\n\r\nTo keep the communication complexity low, CoCoA is a server-aided CGKA. That is, the delivery server no longer blindly forwards packets, but instead actively computes individualized packets tailored to each user. As the server is untrusted, this change requires us to develop new mechanisms ensuring robustness of the protocol.","lang":"eng"}],"department":[{"_id":"GradSch"},{"_id":"KrPi"}],"date_created":"2022-06-30T16:48:00Z","conference":{"end_date":"2022-06-03","name":"EUROCRYPT: Annual International Conference on the Theory and Applications of Cryptology and Information Security","location":"Trondheim, Norway","start_date":"2022-05-30"},"date_published":"2022-05-25T00:00:00Z","month":"05","language":[{"iso":"eng"}],"publisher":"Springer Nature","scopus_import":"1","page":"815–844","publication":"Advances in Cryptology – EUROCRYPT 2022","type":"conference","day":"25","status":"public","intvolume":"     13276"},{"alternative_title":["LNCS"],"isi":1,"main_file_link":[{"open_access":"1","url":"https://eprint.iacr.org/2022/093"}],"external_id":{"isi":["000921318200020"]},"title":"Public-Key Encryption from Homogeneous CLWE","doi":"10.1007/978-3-031-22365-5_20","year":"2022","publication_identifier":{"eissn":["1611-3349"],"isbn":["9783031223648"],"issn":["0302-9743"]},"_id":"12516","quality_controlled":"1","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"We are grateful to Devika Sharma and Luca Trevisan for their insight and advice and to an anonymous reviewer for helpful comments.\r\n\r\nThis work was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 101019547). The first author was additionally supported by RGC GRF CUHK14209920 and the fourth author was additionally supported by ISF grant No. 1399/17, project PROMETHEUS (Grant 780701), and Cariplo CRYPTONOMEX grant.","article_processing_charge":"No","oa":1,"date_updated":"2023-08-04T10:39:30Z","volume":13748,"abstract":[{"text":"The homogeneous continuous LWE (hCLWE) problem is to distinguish samples of a specific high-dimensional Gaussian mixture from standard normal samples. It was shown to be at least as hard as Learning with Errors, but no reduction in the other direction is currently known.\r\nWe present four new public-key encryption schemes based on the hardness of hCLWE, with varying tradeoffs between decryption and security errors, and different discretization techniques. Our schemes yield a polynomial-time algorithm for solving hCLWE using a Statistical Zero-Knowledge oracle.","lang":"eng"}],"author":[{"last_name":"Bogdanov","full_name":"Bogdanov, Andrej","first_name":"Andrej"},{"id":"ffc563a3-f6e0-11ea-865d-e3cce03d17cc","first_name":"Miguel","full_name":"Cueto Noval, Miguel","last_name":"Cueto Noval"},{"first_name":"Charlotte","last_name":"Hoffmann","full_name":"Hoffmann, Charlotte","id":"0f78d746-dc7d-11ea-9b2f-83f92091afe7"},{"full_name":"Rosen, Alon","last_name":"Rosen","first_name":"Alon"}],"citation":{"ieee":"A. Bogdanov, M. Cueto Noval, C. Hoffmann, and A. Rosen, “Public-Key Encryption from Homogeneous CLWE,” in <i>Theory of Cryptography</i>, Chicago, IL, United States, 2022, vol. 13748, pp. 565–592.","apa":"Bogdanov, A., Cueto Noval, M., Hoffmann, C., &#38; Rosen, A. (2022). Public-Key Encryption from Homogeneous CLWE. In <i>Theory of Cryptography</i> (Vol. 13748, pp. 565–592). Chicago, IL, United States: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-22365-5_20\">https://doi.org/10.1007/978-3-031-22365-5_20</a>","chicago":"Bogdanov, Andrej, Miguel Cueto Noval, Charlotte Hoffmann, and Alon Rosen. “Public-Key Encryption from Homogeneous CLWE.” In <i>Theory of Cryptography</i>, 13748:565–92. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/978-3-031-22365-5_20\">https://doi.org/10.1007/978-3-031-22365-5_20</a>.","ama":"Bogdanov A, Cueto Noval M, Hoffmann C, Rosen A. Public-Key Encryption from Homogeneous CLWE. In: <i>Theory of Cryptography</i>. Vol 13748. Springer Nature; 2022:565-592. doi:<a href=\"https://doi.org/10.1007/978-3-031-22365-5_20\">10.1007/978-3-031-22365-5_20</a>","mla":"Bogdanov, Andrej, et al. “Public-Key Encryption from Homogeneous CLWE.” <i>Theory of Cryptography</i>, vol. 13748, Springer Nature, 2022, pp. 565–92, doi:<a href=\"https://doi.org/10.1007/978-3-031-22365-5_20\">10.1007/978-3-031-22365-5_20</a>.","ista":"Bogdanov A, Cueto Noval M, Hoffmann C, Rosen A. 2022. Public-Key Encryption from Homogeneous CLWE. Theory of Cryptography. TCC: Theory of Cryptography, LNCS, vol. 13748, 565–592.","short":"A. Bogdanov, M. Cueto Noval, C. Hoffmann, A. Rosen, in:, Theory of Cryptography, Springer Nature, 2022, pp. 565–592."},"publication_status":"published","conference":{"start_date":"2022-11-07","end_date":"2022-11-10","location":"Chicago, IL, United States","name":"TCC: Theory of Cryptography"},"date_created":"2023-02-05T23:01:00Z","department":[{"_id":"KrPi"}],"scopus_import":"1","publisher":"Springer Nature","language":[{"iso":"eng"}],"month":"12","date_published":"2022-12-21T00:00:00Z","publication":"Theory of Cryptography","page":"565-592","intvolume":"     13748","status":"public","day":"21","type":"conference"},{"status":"public","type":"conference","day":"26","page":"268-284","publication":"2021 IEEE Symposium on Security and Privacy ","language":[{"iso":"eng"}],"publisher":"IEEE","date_published":"2021-08-26T00:00:00Z","month":"08","date_created":"2021-09-27T13:46:27Z","conference":{"end_date":"2021-05-27","location":"San Francisco, CA, United States","name":"SP: Symposium on Security and Privacy","start_date":"2021-05-24"},"department":[{"_id":"KrPi"},{"_id":"DaAl"}],"author":[{"full_name":"Klein, Karen","last_name":"Klein","first_name":"Karen","id":"3E83A2F8-F248-11E8-B48F-1D18A9856A87"},{"id":"2D7ABD02-F248-11E8-B48F-1D18A9856A87","first_name":"Guillermo","orcid":"0000-0001-8630-415X","last_name":"Pascual Perez","full_name":"Pascual Perez, Guillermo"},{"id":"488F98B0-F248-11E8-B48F-1D18A9856A87","first_name":"Michael","orcid":"0000-0003-3186-2482","last_name":"Walter","full_name":"Walter, Michael"},{"id":"4BD3F30E-F248-11E8-B48F-1D18A9856A87","first_name":"Chethan","full_name":"Kamath Hosdurg, Chethan","last_name":"Kamath Hosdurg"},{"full_name":"Capretto, Margarita","last_name":"Capretto","first_name":"Margarita"},{"id":"ffc563a3-f6e0-11ea-865d-e3cce03d17cc","first_name":"Miguel","last_name":"Cueto Noval","full_name":"Cueto Noval, Miguel"},{"first_name":"Ilia","last_name":"Markov","full_name":"Markov, Ilia","id":"D0CF4148-C985-11E9-8066-0BDEE5697425"},{"id":"2D82B818-F248-11E8-B48F-1D18A9856A87","first_name":"Michelle X","full_name":"Yeo, Michelle X","last_name":"Yeo"},{"last_name":"Alwen","full_name":"Alwen, Joel F","first_name":"Joel F","id":"2A8DFA8C-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Krzysztof Z","orcid":"0000-0002-9139-1654","last_name":"Pietrzak","full_name":"Pietrzak, Krzysztof Z","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87"}],"abstract":[{"text":"While messaging systems with strong security guarantees are widely used in practice, designing a protocol that scales efficiently to large groups and enjoys similar security guarantees remains largely open. The two existing proposals to date are ART (Cohn-Gordon et al., CCS18) and TreeKEM (IETF, The Messaging Layer Security Protocol, draft). TreeKEM is the currently considered candidate by the IETF MLS working group, but dynamic group operations (i.e. adding and removing users) can cause efficiency issues. In this paper we formalize and analyze a variant of TreeKEM which we term Tainted TreeKEM (TTKEM for short). The basic idea underlying TTKEM was suggested by Millican (MLS mailing list, February 2018). This version is more efficient than TreeKEM for some natural distributions of group operations, we quantify this through simulations.Our second contribution is two security proofs for TTKEM which establish post compromise and forward secrecy even against adaptive attackers. The security loss (to the underlying PKE) in the Random Oracle Model is a polynomial factor, and a quasipolynomial one in the Standard Model. Our proofs can be adapted to TreeKEM as well. Before our work no security proof for any TreeKEM-like protocol establishing tight security against an adversary who can adaptively choose the sequence of operations was known. We also are the first to prove (or even formalize) active security where the server can arbitrarily deviate from the protocol specification. Proving fully active security – where also the users can arbitrarily deviate – remains open.","lang":"eng"}],"publication_status":"published","citation":{"ieee":"K. Klein <i>et al.</i>, “Keep the dirt: tainted TreeKEM, adaptively and actively secure continuous group key agreement,” in <i>2021 IEEE Symposium on Security and Privacy </i>, San Francisco, CA, United States, 2021, pp. 268–284.","apa":"Klein, K., Pascual Perez, G., Walter, M., Kamath Hosdurg, C., Capretto, M., Cueto Noval, M., … Pietrzak, K. Z. (2021). Keep the dirt: tainted TreeKEM, adaptively and actively secure continuous group key agreement. In <i>2021 IEEE Symposium on Security and Privacy </i> (pp. 268–284). San Francisco, CA, United States: IEEE. <a href=\"https://doi.org/10.1109/sp40001.2021.00035\">https://doi.org/10.1109/sp40001.2021.00035</a>","chicago":"Klein, Karen, Guillermo Pascual Perez, Michael Walter, Chethan Kamath Hosdurg, Margarita Capretto, Miguel Cueto Noval, Ilia Markov, Michelle X Yeo, Joel F Alwen, and Krzysztof Z Pietrzak. “Keep the Dirt: Tainted TreeKEM, Adaptively and Actively Secure Continuous Group Key Agreement.” In <i>2021 IEEE Symposium on Security and Privacy </i>, 268–84. IEEE, 2021. <a href=\"https://doi.org/10.1109/sp40001.2021.00035\">https://doi.org/10.1109/sp40001.2021.00035</a>.","mla":"Klein, Karen, et al. “Keep the Dirt: Tainted TreeKEM, Adaptively and Actively Secure Continuous Group Key Agreement.” <i>2021 IEEE Symposium on Security and Privacy </i>, IEEE, 2021, pp. 268–84, doi:<a href=\"https://doi.org/10.1109/sp40001.2021.00035\">10.1109/sp40001.2021.00035</a>.","ama":"Klein K, Pascual Perez G, Walter M, et al. Keep the dirt: tainted TreeKEM, adaptively and actively secure continuous group key agreement. In: <i>2021 IEEE Symposium on Security and Privacy </i>. IEEE; 2021:268-284. doi:<a href=\"https://doi.org/10.1109/sp40001.2021.00035\">10.1109/sp40001.2021.00035</a>","short":"K. Klein, G. Pascual Perez, M. Walter, C. Kamath Hosdurg, M. Capretto, M. Cueto Noval, I. Markov, M.X. Yeo, J.F. Alwen, K.Z. Pietrzak, in:, 2021 IEEE Symposium on Security and Privacy , IEEE, 2021, pp. 268–284.","ista":"Klein K, Pascual Perez G, Walter M, Kamath Hosdurg C, Capretto M, Cueto Noval M, Markov I, Yeo MX, Alwen JF, Pietrzak KZ. 2021. Keep the dirt: tainted TreeKEM, adaptively and actively secure continuous group key agreement. 2021 IEEE Symposium on Security and Privacy . SP: Symposium on Security and Privacy, 268–284."},"acknowledgement":"The first three authors contributed equally to this work. Funded by the European Research Council (ERC) under the European Union’s Horizon2020 research and innovation programme (682815-TOCNeT). Funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No.665385.","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","project":[{"grant_number":"665385","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program"},{"grant_number":"682815","_id":"258AA5B2-B435-11E9-9278-68D0E5697425","name":"Teaching Old Crypto New Tricks","call_identifier":"H2020"}],"oa_version":"Preprint","quality_controlled":"1","_id":"10049","oa":1,"date_updated":"2023-09-07T13:32:11Z","article_processing_charge":"No","title":"Keep the dirt: tainted TreeKEM, adaptively and actively secure continuous group key agreement","ec_funded":1,"doi":"10.1109/sp40001.2021.00035","year":"2021","related_material":{"record":[{"status":"public","id":"10035","relation":"dissertation_contains"}]},"main_file_link":[{"url":"https://eprint.iacr.org/2019/1489","open_access":"1"}]},{"date_published":"2021-11-04T00:00:00Z","month":"11","language":[{"iso":"eng"}],"publisher":"Springer Nature","scopus_import":"1","department":[{"_id":"KrPi"}],"date_created":"2021-12-05T23:01:42Z","conference":{"start_date":"2021-11-08","location":"Raleigh, NC, United States","end_date":"2021-11-11","name":"TCC: Theory of Cryptography"},"type":"conference","day":"04","status":"public","intvolume":"     13044","page":"222-253","publication":"19th International Conference","ec_funded":1,"year":"2021","doi":"10.1007/978-3-030-90456-2_8","external_id":{"isi":["000728363700008"]},"title":"Grafting key trees: Efficient key management for overlapping groups","main_file_link":[{"url":"https://eprint.iacr.org/2021/1158","open_access":"1"}],"isi":1,"alternative_title":["LNCS"],"publication_status":"published","citation":{"apa":"Alwen, J. F., Auerbach, B., Baig, M. A., Cueto Noval, M., Klein, K., Pascual Perez, G., … Walter, M. (2021). Grafting key trees: Efficient key management for overlapping groups. In <i>19th International Conference</i> (Vol. 13044, pp. 222–253). Raleigh, NC, United States: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-90456-2_8\">https://doi.org/10.1007/978-3-030-90456-2_8</a>","ieee":"J. F. Alwen <i>et al.</i>, “Grafting key trees: Efficient key management for overlapping groups,” in <i>19th International Conference</i>, Raleigh, NC, United States, 2021, vol. 13044, pp. 222–253.","chicago":"Alwen, Joel F, Benedikt Auerbach, Mirza Ahad Baig, Miguel Cueto Noval, Karen Klein, Guillermo Pascual Perez, Krzysztof Z Pietrzak, and Michael Walter. “Grafting Key Trees: Efficient Key Management for Overlapping Groups.” In <i>19th International Conference</i>, 13044:222–53. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/978-3-030-90456-2_8\">https://doi.org/10.1007/978-3-030-90456-2_8</a>.","ama":"Alwen JF, Auerbach B, Baig MA, et al. Grafting key trees: Efficient key management for overlapping groups. In: <i>19th International Conference</i>. Vol 13044. Springer Nature; 2021:222-253. doi:<a href=\"https://doi.org/10.1007/978-3-030-90456-2_8\">10.1007/978-3-030-90456-2_8</a>","mla":"Alwen, Joel F., et al. “Grafting Key Trees: Efficient Key Management for Overlapping Groups.” <i>19th International Conference</i>, vol. 13044, Springer Nature, 2021, pp. 222–53, doi:<a href=\"https://doi.org/10.1007/978-3-030-90456-2_8\">10.1007/978-3-030-90456-2_8</a>.","ista":"Alwen JF, Auerbach B, Baig MA, Cueto Noval M, Klein K, Pascual Perez G, Pietrzak KZ, Walter M. 2021. Grafting key trees: Efficient key management for overlapping groups. 19th International Conference. TCC: Theory of Cryptography, LNCS, vol. 13044, 222–253.","short":"J.F. Alwen, B. Auerbach, M.A. Baig, M. Cueto Noval, K. Klein, G. Pascual Perez, K.Z. Pietrzak, M. Walter, in:, 19th International Conference, Springer Nature, 2021, pp. 222–253."},"author":[{"last_name":"Alwen","full_name":"Alwen, Joel F","first_name":"Joel F","id":"2A8DFA8C-F248-11E8-B48F-1D18A9856A87"},{"id":"D33D2B18-E445-11E9-ABB7-15F4E5697425","first_name":"Benedikt","full_name":"Auerbach, Benedikt","last_name":"Auerbach","orcid":"0000-0002-7553-6606"},{"id":"3EDE6DE4-AA5A-11E9-986D-341CE6697425","first_name":"Mirza Ahad","last_name":"Baig","full_name":"Baig, Mirza Ahad"},{"id":"ffc563a3-f6e0-11ea-865d-e3cce03d17cc","last_name":"Cueto Noval","full_name":"Cueto Noval, Miguel","first_name":"Miguel"},{"first_name":"Karen","last_name":"Klein","full_name":"Klein, Karen","id":"3E83A2F8-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Guillermo","last_name":"Pascual Perez","full_name":"Pascual Perez, Guillermo","orcid":"0000-0001-8630-415X","id":"2D7ABD02-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Pietrzak","full_name":"Pietrzak, Krzysztof Z","orcid":"0000-0002-9139-1654","first_name":"Krzysztof Z","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87"},{"id":"488F98B0-F248-11E8-B48F-1D18A9856A87","first_name":"Michael","full_name":"Walter, Michael","last_name":"Walter","orcid":"0000-0003-3186-2482"}],"abstract":[{"lang":"eng","text":"Key trees are often the best solution in terms of transmission cost and storage requirements for managing keys in a setting where a group needs to share a secret key, while being able to efficiently rotate the key material of users (in order to recover from a potential compromise, or to add or remove users). Applications include multicast encryption protocols like LKH (Logical Key Hierarchies) or group messaging like the current IETF proposal TreeKEM. A key tree is a (typically balanced) binary tree, where each node is identified with a key: leaf nodes hold users’ secret keys while the root is the shared group key. For a group of size N, each user just holds   log(N)  keys (the keys on the path from its leaf to the root) and its entire key material can be rotated by broadcasting   2log(N)  ciphertexts (encrypting each fresh key on the path under the keys of its parents). In this work we consider the natural setting where we have many groups with partially overlapping sets of users, and ask if we can find solutions where the cost of rotating a key is better than in the trivial one where we have a separate key tree for each group. We show that in an asymptotic setting (where the number m of groups is fixed while the number N of users grows) there exist more general key graphs whose cost converges to the cost of a single group, thus saving a factor linear in the number of groups over the trivial solution. As our asymptotic “solution” converges very slowly and performs poorly on concrete examples, we propose an algorithm that uses a natural heuristic to compute a key graph for any given group structure. Our algorithm combines two greedy algorithms, and is thus very efficient: it first converts the group structure into a “lattice graph”, which is then turned into a key graph by repeatedly applying the algorithm for constructing a Huffman code. To better understand how far our proposal is from an optimal solution, we prove lower bounds on the update cost of continuous group-key agreement and multicast encryption in a symbolic model admitting (asymmetric) encryption, pseudorandom generators, and secret sharing as building blocks."}],"date_updated":"2023-08-14T13:19:39Z","volume":13044,"oa":1,"article_processing_charge":"No","acknowledgement":"B. Auerbach, M.A. Baig and K. Pietrzak—received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (682815 - TOCNeT); Karen Klein was supported in part by ERC CoG grant 724307 and conducted part of this work at IST Austria, funded by the ERC under the European Union’s Horizon 2020 research and innovation programme (682815 - TOCNeT); Guillermo Pascual-Perez was funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385; Michael Walter conducted part of this work at IST Austria, funded by the ERC under the European Union’s Horizon 2020 research and innovation programme (682815 - TOCNeT).","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","quality_controlled":"1","oa_version":"Preprint","project":[{"grant_number":"682815","_id":"258AA5B2-B435-11E9-9278-68D0E5697425","name":"Teaching Old Crypto New Tricks","call_identifier":"H2020"},{"grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program","call_identifier":"H2020"}],"_id":"10408","publication_identifier":{"eissn":["1611-3349"],"isbn":["9-783-0309-0455-5"],"eisbn":["978-3-030-90456-2"],"issn":["0302-9743"]}}]