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A number of works have appeared in the literature proposing different definitional frameworks and schemes secure under a wide range of assumptions. In the previous work [1, 2], the authors proposed a meaningful relaxation of the watermarking model and gave constructions that allow direct watermarking of popular cryptographic schemes (e.g. ElGamal Encryption). A definitional framework for watermarking public\u2010key cryptographic functionalities and implementations which covers both deterministic (e.g. decryption) and probabilistic (e.g. signing) secret\u2010key algorithms is provided. The authors\u2019 work unifies the previous results of [1, 2] where deterministic and probabilistic circuits to be watermarked as separate cases are considered. The constructions of [1, 2] were previously presented as extended abstracts missing rigorous security proofs. The authors prove those constructions secure under their new, unified framework. In the authors\u2019 schemes secret detection of the watermark is provided, and security under minimal hardness assumptions assuming only the existence of one\u2010way functions, is proved.<\/jats:p>","DOI":"10.1049\/ise2.12013","type":"journal-article","created":{"date-parts":[[2021,4,10]],"date-time":"2021-04-10T12:32:13Z","timestamp":1618057933000},"page":"205-222","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Watermarking public\u2010key cryptographic functionalities and implementations: The case of encryption and signatures"],"prefix":"10.1049","volume":"15","author":[{"given":"Foteini","family":"Baldimtsi","sequence":"first","affiliation":[{"name":"Computer Science Department George Mason University  Fairfax USA"}]},{"given":"Aggelos","family":"Kiayias","sequence":"additional","affiliation":[{"name":"University of Edinburgh and IOHK  Edinburgh UK"}]},{"given":"Katerina","family":"Samari","sequence":"additional","affiliation":[{"name":"Department of Informatics and Telecommunications National and Kapodistrian University of Athens  Greece"}]}],"member":"265","published-online":{"date-parts":[[2021,4,10]]},"reference":[{"key":"e_1_2_9_2_1","first-page":"173","article-title":"Watermarking public\u2010key cryptographic functionalities and implementations","author":"Baldimtsi F.","year":"2017","journal-title":"ISC 2017"},{"key":"e_1_2_9_3_1","article-title":"Watermarking probabilistic circuits: the case of digital signatures","author":"Baldimtsi F.","year":"2018","journal-title":"Proceedings of BalkanCryptSec"},{"doi-asserted-by":"publisher","key":"e_1_2_9_4_1","DOI":"10.1145\/947380.947395"},{"volume-title":"Digital Watermarking","year":"2002","author":"Cox I.J.","key":"e_1_2_9_5_1"},{"doi-asserted-by":"publisher","key":"e_1_2_9_6_1","DOI":"10.1109\/79.939835"},{"key":"e_1_2_9_7_1","first-page":"709","article-title":"A survey of digital image watermarking techniques","author":"Potdar V.M.","year":"2005","journal-title":"INDIN 2005"},{"key":"e_1_2_9_8_1","first-page":"362","article-title":"From weak to strong watermarking","author":"Hopper N.","year":"2007","journal-title":"TCC 2007"},{"key":"e_1_2_9_9_1","first-page":"1","article-title":"On the (im)possibility of obfuscating programs","author":"Barak B.","year":"2001","journal-title":"CRYPTO 2001"},{"doi-asserted-by":"publisher","key":"e_1_2_9_10_1","DOI":"10.1145\/2160158.2160159"},{"key":"e_1_2_9_11_1","first-page":"40","article-title":"Candidate indistinguishability obfuscation and functional encryption for all circuits","author":"Garg S.","year":"2013","journal-title":"FOCS 2013"},{"key":"e_1_2_9_12_1","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/978-3-642-38348-9_7","volume-title":"EUROCRYPT 2013","author":"Nishimaki R.","year":"2013"},{"unstructured":"Nishimaki R.: \u2018How to watermark cryptographic functions\u2019 (2014). 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