{"id":168204,"date":"2014-12-01T00:00:00","date_gmt":"2014-12-01T00:00:00","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/msr-research-item\/balancing-output-length-and-query-bound-in-hardness-preserving-constructions-of-pseudorandom-functions\/"},"modified":"2018-10-16T20:09:59","modified_gmt":"2018-10-17T03:09:59","slug":"balancing-output-length-and-query-bound-in-hardness-preserving-constructions-of-pseudorandom-functions","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/balancing-output-length-and-query-bound-in-hardness-preserving-constructions-of-pseudorandom-functions\/","title":{"rendered":"Balancing Output Length and Query Bound in Hardness Preserving Constructions of Pseudorandom Functions"},"content":{"rendered":"

We revisit hardness-preserving constructions of a pseudo-random function (PRF) from any length doubling pseudo-random generator (PRG) when there is a non-trivial upper bound q<\/mi><\/math>\">q<\/span><\/span><\/span><\/span><\/span><\/span> on the number of queries that the adversary can make to the PRF. Very recently, Jain, Pietrzak, and Tentes (TCC 2012) gave a hardness-preserving construction of a PRF that makes only O<\/mi>(<\/mo>log<\/mi>⁡<\/mo>q<\/mi>)<\/mo><\/math>\">O<\/span>(<\/span>log<\/span><\/span>q<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span> calls to the underlying PRG when q<\/mi>=<\/mo>2<\/mn>n<\/mi>ϵ<\/mi><\/msup><\/mrow><\/msup><\/math>\">q<\/span>=<\/span>2<\/span>n<\/span>\u03f5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> and ϵ<\/mi>≥<\/mo>1<\/mn>2<\/mn><\/mfrac><\/math>\">\u03f5<\/span>\u2265<\/span>1<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>. This dramatically improves upon the efficiency of the construction of Goldreich, Goldwasser, and Micali (FOCS 1984). However, they explicitly left open the question of whether such constructions exist when ϵ<\/mi><<\/mo>1<\/mn>2<\/mn><\/mfrac><\/math>\">\u03f5<\/span><<\/span>1<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>. In this work, we give constructions of PRFs that make only O<\/mi>(<\/mo>log<\/mi>⁡<\/mo>q<\/mi>)<\/mo><\/math>\">O<\/span>(<\/span>log<\/span><\/span>q<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span> calls to the underlying PRG when q<\/mi>=<\/mo>2<\/mn>n<\/mi>ϵ<\/mi><\/msup><\/mrow><\/msup><\/math>\">q<\/span>=<\/span>2<\/span>n<\/span>\u03f5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, for 0<\/mn><<\/mo>ϵ<\/mi><<\/mo>1<\/mn><\/math>\">0<\/span><<\/span>\u03f5<\/span><<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span>; our PRF outputs O<\/mi>(<\/mo>n<\/mi>2<\/mn>ϵ<\/mi><\/mrow><\/msup>)<\/mo><\/math>\">O<\/span>(<\/span>n<\/span>2<\/span>\u03f5<\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span> bits (on every input), as opposed to the construction of Jain et al.<\/em> that outputs n<\/mi><\/math>\">n<\/span><\/span><\/span><\/span><\/span><\/span> bits. That is, our PRF is not length preserving; however it outputs more bits than the PRF of Jain et al.<\/em> when ϵ<\/mi>><\/mo>1<\/mn>2<\/mn><\/mfrac><\/math>\">\u03f5<\/span>><\/span>1<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>. We obtain our construction through the use of information-theoretic tools such as almost<\/em>α<\/mi><\/math>\">\u03b1<\/span><\/span><\/span><\/span><\/span><\/span>-wise independent hash functions coupled with a novel proof strategy.<\/p>\n","protected":false},"excerpt":{"rendered":"

We revisit hardness-preserving constructions of a pseudo-random function (PRF) from any length doubling pseudo-random generator (PRG) when there is a non-trivial upper bound q on the number of queries that the adversary can make to the PRF. Very recently, Jain, Pietrzak, and Tentes (TCC 2012) gave a hardness-preserving construction of a PRF that makes only […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Springer","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"Progress in Cryptology - INDOCRYPT 2014 - 15th International Conference on Cryptology in India, New Delhi, India, December 14-17, 2014, Proceedings","msr_editors":"","msr_how_published":"","msr_isbn":"978-3-319-13038-5","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"89\u2013103","msr_page_range_start":"89","msr_page_range_end":"103","msr_series":"Lecture Notes in Computer Science","msr_volume":"8885","msr_copyright":"","msr_conference_name":"Progress in Cryptology - INDOCRYPT 2014 - 15th International Conference on Cryptology in India, New Delhi, India, December 14-17, 2014, Proceedings","msr_doi":"10.1007\/978-3-319-13039-2_6","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Sanjam Garg","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","msr_host":"","msr_version":"","msr_duration":"","msr_original_fields_of_study":"","msr_release_tracker_id":"","msr_s2_match_type":"","msr_citation_count_updated":"","msr_published_date":"2014-12-14","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"http:\/\/dx.doi.org\/10.1007\/978-3-319-13039-2_6","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_s2_pdf_url":"","msr_year":2014,"msr_citation_count":0,"msr_influential_citations":0,"msr_reference_count":0,"msr_s2_match_confidence":0,"msr_microsoftintellectualproperty":true,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":0,"footnotes":""},"msr-research-highlight":[],"research-area":[13561],"msr-publication-type":[193716],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-168204","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-locale-en_us"],"msr_publishername":"Springer","msr_edition":"Progress in Cryptology - 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