[{"month":"06","publication_identifier":{"isbn":["978-1-6654-4501-6"],"eissn":["1861-2288"],"eisbn":["978-3-9031-7639-3"]},"conference":{"start_date":"2021-06-21","location":"Espoo and Helsinki, Finland","end_date":"2021-06-24","name":"2021 IFIP Networking Conference (IFIP Networking)"},"doi":"10.23919/IFIPNetworking52078.2021.9472205","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/2104.04293","open_access":"1"}],"oa":1,"external_id":{"isi":["000853016800008"],"arxiv":["2104.04293"]},"quality_controlled":"1","isi":1,"project":[{"grant_number":"682815","_id":"258AA5B2-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Teaching Old Crypto New Tricks"}],"ec_funded":1,"author":[{"last_name":"Pietrzak","first_name":"Krzysztof Z","orcid":"0000-0002-9139-1654","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","full_name":"Pietrzak, Krzysztof Z"},{"full_name":"Salem, Iosif","first_name":"Iosif","last_name":"Salem"},{"full_name":"Schmid, Stefan","last_name":"Schmid","first_name":"Stefan"},{"full_name":"Yeo, Michelle X","first_name":"Michelle X","last_name":"Yeo","id":"2D82B818-F248-11E8-B48F-1D18A9856A87"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"14506"}]},"date_updated":"2023-11-30T10:54:50Z","date_created":"2021-08-29T22:01:16Z","year":"2021","publication_status":"published","department":[{"_id":"KrPi"}],"publisher":"IEEE","day":"21","article_processing_charge":"No","scopus_import":"1","date_published":"2021-06-21T00:00:00Z","citation":{"short":"K.Z. Pietrzak, I. Salem, S. Schmid, M.X. Yeo, in:, IEEE, 2021.","mla":"Pietrzak, Krzysztof Z., et al. LightPIR: Privacy-Preserving Route Discovery for Payment Channel Networks. IEEE, 2021, doi:10.23919/IFIPNetworking52078.2021.9472205.","chicago":"Pietrzak, Krzysztof Z, Iosif Salem, Stefan Schmid, and Michelle X Yeo. “LightPIR: Privacy-Preserving Route Discovery for Payment Channel Networks.” IEEE, 2021. https://doi.org/10.23919/IFIPNetworking52078.2021.9472205.","ama":"Pietrzak KZ, Salem I, Schmid S, Yeo MX. LightPIR: Privacy-preserving route discovery for payment channel networks. In: IEEE; 2021. doi:10.23919/IFIPNetworking52078.2021.9472205","ieee":"K. Z. Pietrzak, I. Salem, S. Schmid, and M. X. Yeo, “LightPIR: Privacy-preserving route discovery for payment channel networks,” presented at the 2021 IFIP Networking Conference (IFIP Networking), Espoo and Helsinki, Finland, 2021.","apa":"Pietrzak, K. Z., Salem, I., Schmid, S., & Yeo, M. X. (2021). LightPIR: Privacy-preserving route discovery for payment channel networks. Presented at the 2021 IFIP Networking Conference (IFIP Networking), Espoo and Helsinki, Finland: IEEE. https://doi.org/10.23919/IFIPNetworking52078.2021.9472205","ista":"Pietrzak KZ, Salem I, Schmid S, Yeo MX. 2021. LightPIR: Privacy-preserving route discovery for payment channel networks. 2021 IFIP Networking Conference (IFIP Networking)."},"abstract":[{"text":"Payment channel networks are a promising approach to improve the scalability of cryptocurrencies: they allow to perform transactions in a peer-to-peer fashion, along multihop routes in the network, without requiring consensus on the blockchain. However, during the discovery of cost-efficient routes for the transaction, critical information may be revealed about the transacting entities. This paper initiates the study of privacy-preserving route discovery mechanisms for payment channel networks. In particular, we present LightPIR, an approach which allows a client to learn the shortest (or cheapest in terms of fees) path between two nodes without revealing any information about the endpoints of the transaction to the servers. The two main observations which allow for an efficient solution in LightPIR are that: (1) surprisingly, hub labelling algorithms – which were developed to preprocess “street network like” graphs so one can later efficiently compute shortest paths – also perform well for the graphs underlying payment channel networks, and that (2) hub labelling algorithms can be conveniently combined with private information retrieval. LightPIR relies on a simple hub labeling heuristic on top of existing hub labeling algorithms which leverages the specific topological features of cryptocurrency networks to further minimize storage and bandwidth overheads. In a case study considering the Lightning network, we show that our approach is an order of magnitude more efficient compared to a privacy-preserving baseline based on using private information retrieval on a database that stores all pairs shortest paths.","lang":"eng"}],"type":"conference","oa_version":"Submitted Version","_id":"9969","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","title":"LightPIR: Privacy-preserving route discovery for payment channel networks"},{"abstract":[{"text":"Reverse firewalls were introduced at Eurocrypt 2015 by Miro-nov and Stephens-Davidowitz, as a method for protecting cryptographic protocols against attacks on the devices of the honest parties. In a nutshell: a reverse firewall is placed outside of a device and its goal is to “sanitize” the messages sent by it, in such a way that a malicious device cannot leak its secrets to the outside world. It is typically assumed that the cryptographic devices are attacked in a “functionality-preserving way” (i.e. informally speaking, the functionality of the protocol remains unchanged under this attacks). In their paper, Mironov and Stephens-Davidowitz construct a protocol for passively-secure two-party computations with firewalls, leaving extension of this result to stronger models as an open question.\r\nIn this paper, we address this problem by constructing a protocol for secure computation with firewalls that has two main advantages over the original protocol from Eurocrypt 2015. Firstly, it is a multiparty computation protocol (i.e. it works for an arbitrary number n of the parties, and not just for 2). Secondly, it is secure in much stronger corruption settings, namely in the active corruption model. More precisely: we consider an adversary that can fully corrupt up to 𝑛−1 parties, while the remaining parties are corrupt in a functionality-preserving way.\r\nOur core techniques are: malleable commitments and malleable non-interactive zero-knowledge, which in particular allow us to create a novel protocol for multiparty augmented coin-tossing into the well with reverse firewalls (that is based on a protocol of Lindell from Crypto 2001).","lang":"eng"}],"type":"conference","alternative_title":["LNCS"],"oa_version":"Preprint","_id":"8322","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Reverse firewalls for actively secure MPCs","status":"public","intvolume":" 12171","day":"10","article_processing_charge":"No","scopus_import":"1","date_published":"2020-08-10T00:00:00Z","publication":"Advances in Cryptology – CRYPTO 2020","citation":{"apa":"Chakraborty, S., Dziembowski, S., & Nielsen, J. B. (2020). Reverse firewalls for actively secure MPCs. In Advances in Cryptology – CRYPTO 2020 (Vol. 12171, pp. 732–762). Santa Barbara, CA, United States: Springer Nature. https://doi.org/10.1007/978-3-030-56880-1_26","ieee":"S. Chakraborty, S. Dziembowski, and J. B. Nielsen, “Reverse firewalls for actively secure MPCs,” in Advances in Cryptology – CRYPTO 2020, Santa Barbara, CA, United States, 2020, vol. 12171, pp. 732–762.","ista":"Chakraborty S, Dziembowski S, Nielsen JB. 2020. Reverse firewalls for actively secure MPCs. Advances in Cryptology – CRYPTO 2020. CRYPTO: Annual International Cryptology Conference, LNCS, vol. 12171, 732–762.","ama":"Chakraborty S, Dziembowski S, Nielsen JB. Reverse firewalls for actively secure MPCs. In: Advances in Cryptology – CRYPTO 2020. Vol 12171. Springer Nature; 2020:732-762. doi:10.1007/978-3-030-56880-1_26","chicago":"Chakraborty, Suvradip, Stefan Dziembowski, and Jesper Buus Nielsen. “Reverse Firewalls for Actively Secure MPCs.” In Advances in Cryptology – CRYPTO 2020, 12171:732–62. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-56880-1_26.","short":"S. Chakraborty, S. Dziembowski, J.B. Nielsen, in:, Advances in Cryptology – CRYPTO 2020, Springer Nature, 2020, pp. 732–762.","mla":"Chakraborty, Suvradip, et al. “Reverse Firewalls for Actively Secure MPCs.” Advances in Cryptology – CRYPTO 2020, vol. 12171, Springer Nature, 2020, pp. 732–62, doi:10.1007/978-3-030-56880-1_26."},"page":"732-762","ec_funded":1,"author":[{"full_name":"Chakraborty, Suvradip","last_name":"Chakraborty","first_name":"Suvradip","id":"B9CD0494-D033-11E9-B219-A439E6697425"},{"full_name":"Dziembowski, Stefan","last_name":"Dziembowski","first_name":"Stefan"},{"full_name":"Nielsen, Jesper Buus","first_name":"Jesper Buus","last_name":"Nielsen"}],"date_updated":"2021-01-12T08:18:08Z","date_created":"2020-08-30T22:01:12Z","volume":12171,"year":"2020","acknowledgement":"We would like to thank the anonymous reviewers for their helpful comments and suggestions. The work was initiated while the first author was in IIT Madras, India. Part of this work was done while the author was visiting the University of Warsaw. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (682815 - TOCNeT) and from the Foundation for Polish Science under grant TEAM/2016-1/4 founded within the UE 2014–2020 Smart Growth Operational Program. The last author was supported by the Independent Research Fund Denmark project BETHE and the Concordium Blockchain Research Center, Aarhus University, Denmark.","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"KrPi"}],"month":"08","publication_identifier":{"issn":["03029743"],"eissn":["16113349"],"isbn":["9783030568795"]},"conference":{"name":"CRYPTO: Annual International Cryptology Conference","end_date":"2020-08-21","location":"Santa Barbara, CA, United States","start_date":"2020-08-17"},"doi":"10.1007/978-3-030-56880-1_26","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://eprint.iacr.org/2019/1317"}],"oa":1,"quality_controlled":"1","project":[{"name":"Teaching Old Crypto New Tricks","call_identifier":"H2020","grant_number":"682815","_id":"258AA5B2-B435-11E9-9278-68D0E5697425"}]},{"abstract":[{"text":"Discrete Gaussian distributions over lattices are central to lattice-based cryptography, and to the computational and mathematical aspects of lattices more broadly. The literature contains a wealth of useful theorems about the behavior of discrete Gaussians under convolutions and related operations. Yet despite their structural similarities, most of these theorems are formally incomparable, and their proofs tend to be monolithic and written nearly “from scratch,” making them unnecessarily hard to verify, understand, and extend.\r\nIn this work we present a modular framework for analyzing linear operations on discrete Gaussian distributions. The framework abstracts away the particulars of Gaussians, and usually reduces proofs to the choice of appropriate linear transformations and elementary linear algebra. To showcase the approach, we establish several general properties of discrete Gaussians, and show how to obtain all prior convolution theorems (along with some new ones) as straightforward corollaries. As another application, we describe a self-reduction for Learning With Errors (LWE) that uses a fixed number of samples to generate an unlimited number of additional ones (having somewhat larger error). The distinguishing features of our reduction are its simple analysis in our framework, and its exclusive use of discrete Gaussians without any loss in parameters relative to a prior mixed discrete-and-continuous approach.\r\nAs a contribution of independent interest, for subgaussian random matrices we prove a singular value concentration bound with explicitly stated constants, and we give tighter heuristics for specific distributions that are commonly used for generating lattice trapdoors. These bounds yield improvements in the concrete bit-security estimates for trapdoor lattice cryptosystems.","lang":"eng"}],"type":"conference","alternative_title":["LNCS"],"oa_version":"Preprint","_id":"8339","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Improved discrete Gaussian and subgaussian analysis for lattice cryptography","status":"public","intvolume":" 12110","day":"15","article_processing_charge":"No","scopus_import":"1","date_published":"2020-05-15T00:00:00Z","publication":"23rd IACR International Conference on the Practice and Theory of Public-Key Cryptography","citation":{"ama":"Genise N, Micciancio D, Peikert C, Walter M. Improved discrete Gaussian and subgaussian analysis for lattice cryptography. In: 23rd IACR International Conference on the Practice and Theory of Public-Key Cryptography. Vol 12110. Springer Nature; 2020:623-651. doi:10.1007/978-3-030-45374-9_21","ista":"Genise N, Micciancio D, Peikert C, Walter M. 2020. Improved discrete Gaussian and subgaussian analysis for lattice cryptography. 23rd IACR International Conference on the Practice and Theory of Public-Key Cryptography. PKC: Public-Key Cryptography, LNCS, vol. 12110, 623–651.","ieee":"N. Genise, D. Micciancio, C. Peikert, and M. Walter, “Improved discrete Gaussian and subgaussian analysis for lattice cryptography,” in 23rd IACR International Conference on the Practice and Theory of Public-Key Cryptography, Edinburgh, United Kingdom, 2020, vol. 12110, pp. 623–651.","apa":"Genise, N., Micciancio, D., Peikert, C., & Walter, M. (2020). Improved discrete Gaussian and subgaussian analysis for lattice cryptography. In 23rd IACR International Conference on the Practice and Theory of Public-Key Cryptography (Vol. 12110, pp. 623–651). Edinburgh, United Kingdom: Springer Nature. https://doi.org/10.1007/978-3-030-45374-9_21","mla":"Genise, Nicholas, et al. “Improved Discrete Gaussian and Subgaussian Analysis for Lattice Cryptography.” 23rd IACR International Conference on the Practice and Theory of Public-Key Cryptography, vol. 12110, Springer Nature, 2020, pp. 623–51, doi:10.1007/978-3-030-45374-9_21.","short":"N. Genise, D. Micciancio, C. Peikert, M. Walter, in:, 23rd IACR International Conference on the Practice and Theory of Public-Key Cryptography, Springer Nature, 2020, pp. 623–651.","chicago":"Genise, Nicholas, Daniele Micciancio, Chris Peikert, and Michael Walter. “Improved Discrete Gaussian and Subgaussian Analysis for Lattice Cryptography.” In 23rd IACR International Conference on the Practice and Theory of Public-Key Cryptography, 12110:623–51. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-45374-9_21."},"page":"623-651","ec_funded":1,"author":[{"full_name":"Genise, Nicholas","last_name":"Genise","first_name":"Nicholas"},{"full_name":"Micciancio, Daniele","first_name":"Daniele","last_name":"Micciancio"},{"full_name":"Peikert, Chris","first_name":"Chris","last_name":"Peikert"},{"full_name":"Walter, Michael","orcid":"0000-0003-3186-2482","id":"488F98B0-F248-11E8-B48F-1D18A9856A87","last_name":"Walter","first_name":"Michael"}],"date_created":"2020-09-06T22:01:13Z","date_updated":"2023-02-23T13:31:06Z","volume":12110,"year":"2020","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"KrPi"}],"month":"05","publication_identifier":{"eissn":["16113349"],"isbn":["9783030453732"],"issn":["03029743"]},"conference":{"location":"Edinburgh, United Kingdom","start_date":"2020-05-04","end_date":"2020-05-07","name":"PKC: Public-Key Cryptography"},"doi":"10.1007/978-3-030-45374-9_21","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://eprint.iacr.org/2020/337","open_access":"1"}],"oa":1,"quality_controlled":"1","project":[{"call_identifier":"H2020","name":"Teaching Old Crypto New Tricks","_id":"258AA5B2-B435-11E9-9278-68D0E5697425","grant_number":"682815"}]},{"date_published":"2020-12-08T00:00:00Z","publication":"Progress in Cryptology","citation":{"short":"K.Z. Pietrzak, in:, Progress in Cryptology, Springer Nature, 2020, pp. 3–15.","mla":"Pietrzak, Krzysztof Z. “Delayed Authentication: Preventing Replay and Relay Attacks in Private Contact Tracing.” Progress in Cryptology, vol. 12578, Springer Nature, 2020, pp. 3–15, doi:10.1007/978-3-030-65277-7_1.","chicago":"Pietrzak, Krzysztof Z. “Delayed Authentication: Preventing Replay and Relay Attacks in Private Contact Tracing.” In Progress in Cryptology, 12578:3–15. LNCS. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-65277-7_1.","ama":"Pietrzak KZ. Delayed authentication: Preventing replay and relay attacks in private contact tracing. In: Progress in Cryptology. Vol 12578. LNCS. Springer Nature; 2020:3-15. doi:10.1007/978-3-030-65277-7_1","ieee":"K. Z. Pietrzak, “Delayed authentication: Preventing replay and relay attacks in private contact tracing,” in Progress in Cryptology, Bangalore, India, 2020, vol. 12578, pp. 3–15.","apa":"Pietrzak, K. Z. (2020). Delayed authentication: Preventing replay and relay attacks in private contact tracing. In Progress in Cryptology (Vol. 12578, pp. 3–15). Bangalore, India: Springer Nature. https://doi.org/10.1007/978-3-030-65277-7_1","ista":"Pietrzak KZ. 2020. Delayed authentication: Preventing replay and relay attacks in private contact tracing. Progress in Cryptology. INDOCRYPT: International Conference on Cryptology in IndiaLNCS vol. 12578, 3–15."},"page":"3-15","day":"08","article_processing_charge":"No","scopus_import":"1","series_title":"LNCS","oa_version":"Preprint","_id":"8987","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Delayed authentication: Preventing replay and relay attacks in private contact tracing","status":"public","intvolume":" 12578","abstract":[{"lang":"eng","text":"Currently several projects aim at designing and implementing protocols for privacy preserving automated contact tracing to help fight the current pandemic. Those proposal are quite similar, and in their most basic form basically propose an app for mobile phones which broadcasts frequently changing pseudorandom identifiers via (low energy) Bluetooth, and at the same time, the app stores IDs broadcast by phones in its proximity. Only if a user is tested positive, they upload either the beacons they did broadcast (which is the case in decentralized proposals as DP-3T, east and west coast PACT or Covid watch) or received (as in Popp-PT or ROBERT) during the last two weeks or so.\r\n\r\nVaudenay [eprint 2020/399] observes that this basic scheme (he considers the DP-3T proposal) succumbs to relay and even replay attacks, and proposes more complex interactive schemes which prevent those attacks without giving up too many privacy aspects. Unfortunately interaction is problematic for this application for efficiency and security reasons. The countermeasures that have been suggested so far are either not practical or give up on key privacy aspects. We propose a simple non-interactive variant of the basic protocol that\r\n(security) Provably prevents replay and (if location data is available) relay attacks.\r\n(privacy) The data of all parties (even jointly) reveals no information on the location or time where encounters happened.\r\n(efficiency) The broadcasted message can fit into 128 bits and uses only basic crypto (commitments and secret key authentication).\r\n\r\nTowards this end we introduce the concept of “delayed authentication”, which basically is a message authentication code where verification can be done in two steps, where the first doesn’t require the key, and the second doesn’t require the message."}],"type":"conference","conference":{"end_date":"2020-12-16","start_date":"2020-12-13","location":"Bangalore, India","name":"INDOCRYPT: International Conference on Cryptology in India"},"doi":"10.1007/978-3-030-65277-7_1","language":[{"iso":"eng"}],"oa":1,"external_id":{"isi":["000927592800001"]},"main_file_link":[{"url":"https://eprint.iacr.org/2020/418","open_access":"1"}],"isi":1,"quality_controlled":"1","project":[{"name":"Teaching Old Crypto New Tricks","call_identifier":"H2020","grant_number":"682815","_id":"258AA5B2-B435-11E9-9278-68D0E5697425"}],"month":"12","publication_identifier":{"isbn":["9783030652760"],"eissn":["16113349"],"issn":["03029743"]},"author":[{"id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9139-1654","first_name":"Krzysztof Z","last_name":"Pietrzak","full_name":"Pietrzak, Krzysztof Z"}],"date_updated":"2023-08-24T11:08:58Z","date_created":"2021-01-03T23:01:23Z","volume":12578,"year":"2020","publication_status":"published","department":[{"_id":"KrPi"}],"publisher":"Springer Nature","ec_funded":1},{"publication_identifier":{"eissn":["1611-3349"],"isbn":["9783030457266","9783030457273"],"issn":["0302-9743"]},"month":"05","doi":"10.1007/978-3-030-45727-3_16","conference":{"name":"EUROCRYPT: Theory and Applications of Cryptographic Techniques","start_date":"2020-05-11","end_date":"2020-05-15"},"language":[{"iso":"eng"}],"external_id":{"isi":["000828688000016"]},"oa":1,"main_file_link":[{"url":"https://eprint.iacr.org/2019/364","open_access":"1"}],"project":[{"call_identifier":"H2020","name":"Teaching Old Crypto New Tricks","_id":"258AA5B2-B435-11E9-9278-68D0E5697425","grant_number":"682815"}],"isi":1,"quality_controlled":"1","ec_funded":1,"author":[{"orcid":"0000-0002-7553-6606","id":"D33D2B18-E445-11E9-ABB7-15F4E5697425","last_name":"Auerbach","first_name":"Benedikt","full_name":"Auerbach, Benedikt"},{"full_name":"Giacon, Federico","first_name":"Federico","last_name":"Giacon"},{"full_name":"Kiltz, Eike","last_name":"Kiltz","first_name":"Eike"}],"volume":12107,"date_created":"2020-06-15T07:13:37Z","date_updated":"2023-09-05T15:06:40Z","year":"2020","publisher":"Springer Nature","department":[{"_id":"KrPi"}],"publication_status":"published","article_processing_charge":"No","day":"01","date_published":"2020-05-01T00:00:00Z","citation":{"ista":"Auerbach B, Giacon F, Kiltz E. 2020. Everybody’s a target: Scalability in public-key encryption. Advances in Cryptology – EUROCRYPT 2020. EUROCRYPT: Theory and Applications of Cryptographic Techniques, LNCS, vol. 12107, 475–506.","apa":"Auerbach, B., Giacon, F., & Kiltz, E. (2020). Everybody’s a target: Scalability in public-key encryption. In Advances in Cryptology – EUROCRYPT 2020 (Vol. 12107, pp. 475–506). Springer Nature. https://doi.org/10.1007/978-3-030-45727-3_16","ieee":"B. Auerbach, F. Giacon, and E. Kiltz, “Everybody’s a target: Scalability in public-key encryption,” in Advances in Cryptology – EUROCRYPT 2020, 2020, vol. 12107, pp. 475–506.","ama":"Auerbach B, Giacon F, Kiltz E. Everybody’s a target: Scalability in public-key encryption. In: Advances in Cryptology – EUROCRYPT 2020. Vol 12107. Springer Nature; 2020:475-506. doi:10.1007/978-3-030-45727-3_16","chicago":"Auerbach, Benedikt, Federico Giacon, and Eike Kiltz. “Everybody’s a Target: Scalability in Public-Key Encryption.” In Advances in Cryptology – EUROCRYPT 2020, 12107:475–506. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-45727-3_16.","mla":"Auerbach, Benedikt, et al. “Everybody’s a Target: Scalability in Public-Key Encryption.” Advances in Cryptology – EUROCRYPT 2020, vol. 12107, Springer Nature, 2020, pp. 475–506, doi:10.1007/978-3-030-45727-3_16.","short":"B. Auerbach, F. Giacon, E. Kiltz, in:, Advances in Cryptology – EUROCRYPT 2020, Springer Nature, 2020, pp. 475–506."},"publication":"Advances in Cryptology – EUROCRYPT 2020","page":"475-506","abstract":[{"text":"For 1≤m≤n, we consider a natural m-out-of-n multi-instance scenario for a public-key encryption (PKE) scheme. An adversary, given n independent instances of PKE, wins if he breaks at least m out of the n instances. In this work, we are interested in the scaling factor of PKE schemes, SF, which measures how well the difficulty of breaking m out of the n instances scales in m. That is, a scaling factor SF=ℓ indicates that breaking m out of n instances is at least ℓ times more difficult than breaking one single instance. A PKE scheme with small scaling factor hence provides an ideal target for mass surveillance. In fact, the Logjam attack (CCS 2015) implicitly exploited, among other things, an almost constant scaling factor of ElGamal over finite fields (with shared group parameters).\r\n\r\nFor Hashed ElGamal over elliptic curves, we use the generic group model to argue that the scaling factor depends on the scheme's granularity. In low granularity, meaning each public key contains its independent group parameter, the scheme has optimal scaling factor SF=m; In medium and high granularity, meaning all public keys share the same group parameter, the scheme still has a reasonable scaling factor SF=√m. Our findings underline that instantiating ElGamal over elliptic curves should be preferred to finite fields in a multi-instance scenario.\r\n\r\nAs our main technical contribution, we derive new generic-group lower bounds of Ω(√(mp)) on the difficulty of solving both the m-out-of-n Gap Discrete Logarithm and the m-out-of-n Gap Computational Diffie-Hellman problem over groups of prime order p, extending a recent result by Yun (EUROCRYPT 2015). We establish the lower bound by studying the hardness of a related computational problem which we call the search-by-hypersurface problem.","lang":"eng"}],"type":"conference","alternative_title":["LNCS"],"oa_version":"Submitted Version","_id":"7966","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","intvolume":" 12107","title":"Everybody’s a target: Scalability in public-key encryption","status":"public"}]